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Optical properties of low-dimensional cuprates
Optical Materials 90 (2019) 244–251
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Optical properties of low-dimensional cuprates A.S. Moskvin a b
T
a,b,∗
Ural Federal University, Ekaterinburg, Russia Institute of Metal Physics, Ekaterinburg, Russia
ARTICLE INFO
ABSTRACT
Keywords: Cuprates Low dimension Charge transfer transitions Optical response EELS
I present a short overview of the optical properties of different low-dimensional cuprates with different arrangement of the CuO4plaquettes being main elements of their crystalline and electronic structure. The focus of the paper is on intra- and inter-center charge transfer transitions.
1. Introduction Despite a giant number of experimental and theoretical works on cuprates published after the discovery of high-Tc superconductivity [1] we deal actually with a lack of detailed studies of electron-hole (EH) excitations both in parent and high-Tc cuprates. The nature of the lowenergy EH excitations as well as those with higher energy and high intensity is still unclear. Here in the paper we address optical properties with a focus on the charge transfer (CT) excitations in a large variety of nominally insulating cuprates with CuO4 plaquettes to be a main building block of their crystal and electronic structure. These incorporate monooxide CuO, parent quasi-2D cuprates such as La2CuO4, Sr2CuO2Cl2, YBa2Cu3O6 with a 2D arrangement of the corner-shared CuO4 plaquettes, their 1D counterparts such as Sr2CuO3 with a chain 1D arrangement of the corner-shared CuO4 plaquettes, Li2CuO2, LiCu2O2, CuGeO3 with a chain 1D arrangement of the edge-shared CuO4 plaquettes, and rather exotic 0D systems with the well isolated CuO4 plaquettes, such as CuB2O4. 2. Electronic structure of the copper-oxygen CuO4 cluster As an efficient approach to describe excitonic states, especially with small effective electron-hole separation we propose here the embedded molecular cluster method. In the present context we use one or two neighboring CuO4 clusters embedded into the insulating cuprate. This method provides both a clear physical picture of the electronic structure and energy spectrum, as well as the possibility of quantitative modeling. Eskes et al. [2], as well as Ghijsen et al. [3] have shown that, in a
∗
certain sense, cluster calculations can provide a better description of the electronic structure of insulating cuprates than the band-structure calculations, since they allow for a better account of the correlation effects (see also Ref. [4]). Starting with the five Cu 3d and the twelve O 2p atomic orbitals for CuO4 cluster with the D4h symmetry, it is easy to form the seventeen symmetrized even-parity a1g , a2g , b1g , b2g , eg and odd-parity a2u , b2u , eu ( ), eu ( ) orbitals. The even-parity Cu 3d a1g (3d z 2 ) , b1g (3d x 2 y2 ) , b2g (3d xy ) , eg (3d xz , 3d yz ) orbitals hybridize, due to a strong Cu 3d -O 2p covalency, with the even-parity O 2p -orbitals of the same symmetry, thus forming appropriate bonding b and antibonding a states. Among the odd-parity orbitals only eu ( ) and eu ( ) hybridize due to the nearest-neighbor pp overlap and transfer thus forming appropriate bonding eub and antibonding eua purely oxygen states. The purely oxygen a2g , a2u , b2u orbitals are the nonbonding ones. All ”planar” O 2p orbitals in accordance with the orientation of lobes could be classified as σ (a1g , b1g , eu ( ) ) or π (a2g , b2g , eu ( ) ) orbitals, respectively. Among purely oxygen nonbonding orbitals only eu ( ) and eu ( ) hybridize with each other (equally for both types ( x , y ) of such orbitals): |eub = cos
e
|eu ( ) + sin
e
|eu ( ) ; |eua = sin
e
|eu ( )
cos
e
|eu ( ) ,
(1) where
tan2 and
e
=
t epp u
2t epp u peu ( )
=
, peu ( )
(2)
(tpp + tpp ) is an effective transfer integral with tpp < 0 ,
Ural Federal University, Ekaterinburg, Russia. E-mail address: [email protected].
https://doi.org/10.1016/j.optmat.2019.02.033 Received 30 October 2018; Received in revised form 21 February 2019; Accepted 22 February 2019 0925-3467/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Model single-hole energy spectrum for a CuO4 plaquette with parameters relevant for Sr2CuO2Cl2 and a number of other insulating cuprates with the cornershared CuO4 plaquettes.
tpp > 0 being the two types of the p p transfer integrals, for the σ and 1 π bonding, respectively (|tpp | 2 |tpp |), peu ( , ) are energies of the molecular orbitals. Hereafter, we keep the notation eu ( ), eu ( ) for predominantly σ or π orbitals, respectively. Interestingly, that the eu ( ), eu ( ) orbitals could form the two types of circular current p±1-like states: eu ± 1 ( ), eu ± 1 ( ) , respectively, with the Ising-like orbital moment eu ± 1 ( )|lz |eu ± 1 ( ) =
eu ± 1 ( )|lz |eu ± 1 ( ) = ± sin 2 ,
3. Charge transfer transitions in cuprates
d CT transitions
3.1. Conventional intra-center p
For a typical cuprate with the CuO4 plaquettes we predict the three eua, b from the types of dipole-allowed intra-center CT transitions: b1bg b ground state b1g to the purely oxygen doublet O 2p -O 2p hybrid states eua, b , which are allowed in ”in-plane” polarization E C4 , and the b1bg b2u transition to purely oxygen O 2pz -like state, which is allowed in the ”out-of-plane” polarization E C4 . The two CT transitions b1bg eub and b1bg eua differ by the oxygen hole density distribution in final state: for the former this has a predominantly O 2p character, while for the latter it has the O 2p one. In the framework of a local approximation their relative intensity is determined by the strength of the p - p mixing as follows:
(3)
or the two types of the currentless px , y -like eux, y ( ), eux , y ( ) states with a quenched orbital moment. Fig. 1 presents a single-hole energy spectrum for a CuO4 plaquette embedded into an insulating cuprate such as Sr2CuO2Cl2 [5] calculated with the parameters based on the results of numerous theoretical and experimental studies [6–10]. For illustration we show a step-by-step formation of the cluster energy levels from the bare Cu 3d and O 2p levels with the successive inclusion of the crystal field (CF) effects, O 2p-O 2p, and Cu 3d-O 2p covalency. It is worth noting that the b1bg character of the ground hole state in CuO64 cluster seems to be one of a few indisputable points in cuprate physics. Recent resonant inelastic X-ray scattering (RIXS) spectroscopy measurements for different insulating cuprates (see Ref. [11] and references therein) with the incident photon energy tuned to the Cu K edge (hard X-rays) have revealed the low- (1.5–2.0 eV) and high-energy (5–7 eV) bands of the d d excitations attributed to the intra-center b1bg a1bg , b2bg , egb and b1bg a1ag , b1ag , b2ag , ega transitions from the b ground b1g state to the low-energy bonding and high-energy antibonding Cu 3d-O 2p hybridized orbitals, respectively. Hence, the b1bg b1ag separation could be estimated to be 6.0 eV.
f I = = |tan |2 = I f
tpp + tpp peu ( )
2
,
peu ( )
This ratio, given the typical values of parameters, does not exceed 0.1. The low-energy (near 2 eV) part of the absorption spectrum for a single CuO4 plaquette is believed to be formed by an interplay of the b2bg , a1bg , egb ), dipole-forbidden crystal field d d transitions (b1bg b b b1g a2g and allowed b1g eu ( ) CT transitions, respectively, which are all close in energy. The a2g hole has the minimal energy among all the purely oxygen states: a2g = eu ( ) 2tpp . In accordance with the model energy spectrum (see Fig. 1) its energy should be of the order of 1. 5 ÷ 1. 8 eV, or in other words appears to be markedly lower than the main optical gap. 3.2. Inter-center d
d and d
p CT transitions
The local inter-atomic O 2p - Cu 3d charge transfer generates not only intra-center excitations within one CuO4 plaquette but also the inter-plaquette (inter-center) transitions. These inter-center transitions between two CuO4 plaquettes may be considered as quanta of the 245
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disproportionation reaction
CuO64
+
CuO64
CuO74
+
CuGeO3, that is nominally 1D systems with the edge-sharing CuO4 plaquettes. However, since the CueOeCu bond angle along the chain is almost 90 , the main σ-σ transfer from one plaquette to its nearest neighbors is strongly suppressed. Thus, the in-plane charge excitations are localized within a single plaquette, hence with respect to the electronic properties the CuO4 centers in these compounds can be addressed to be approximately isolated [17]. This standpoint is fairly well confirmed in optical and EELS data for Li2CuO2 [15,17]. In terms of perpendicular out-of-plane O 2pz orbitals, these systems should be considered as typical 1D chain systems with O 2pπ bonding. The absorption spectra of CuGeO3 from 1 to 4.2 eV, for the two polarizations E c ( chain direction) and E b ( chain direction) [13,14], are shown in Fig. 2. A relatively weak absorption structure, observed in the lower-energy range, is followed by a region of a relative transparency and, above 3 eV, by a sharp and anisotropic increase of the absorption coefficient with a small temperature dependent feature visible at 3.1–3.2 eV for E c [18] and an order of magnitude more intensive feature visible at 4.1 eV for E b [14] (see Fig. 2). Ellipsometric measurements of CuGeO3 [14] reveal two intensive CT bands with maxima of the imaginary part of the pseudodielectric function at 3.6 and 4.5 eV, which may be ascribed to CT transitions allowed in E c and E c polarization, respectively. The low-energy 2 eV band, both in position and absorption coefficient, is a structureless analogue of the respective band in CuB2O4. The effective oscillator strength has a specific ¯ ph temperature trend: f (T ) coth 2kT , where ¯ ph 240 cm−1 is an average phonon energy, that in conjunction with the small absolute values of f (T ) , seems appropriate to phonon-assisted transitions, normally forbidden by parity considerations [13]. The polarization dependence of the absorption coefficient agrees with the in-plane character of the CT excitations, if to account for a complete (E c ) or partial (E b ) in-plane light polarization. Similar weak feature is distinctly observed in experimental EELS spectra for CuGeO3 [16] at small momenta near 1.7 eV. The loss function spectra in CuGeO3 for q c are dominated by two features: an intense broad peak with the triangularlike shape at 6.2 eV and a feature with much lower intensity at 3.5 eV. Atzkern et al. [16] attributed the high-energy feature to a superposition of strong dipole allowed intra-center b1bg eu ( ) CT transition peaked b1ag and b1bg eu near 6.0 eV and the high-energy inter-center b1bg transitions, while the low-energy feature was attributed to the lowb1bg Zhang-Rice (ZR)-like transition. The loss energy inter-center b1bg function spectra for the q b polarization are assigned to a superposition eu ( ) CT transition peaked near 6.5 eV and the two of intra-center b1bg transitions peaked at 5.5 and 7.3 eV which can be assigned to intrab2u and O 2p - Ge 4s (p) CT transitions, respectively [16]. center b1bg However, a more reasonable interpretation can be proposed that implies a rather strong eu ( ) -eu ( ) separation with formation of the two quasi-doublets eu ( ) and eu ( ) , near 4 eV and 6 eV, respectively, each split by 0.5–1.0 eV due to the p p transfer. It seems more reasonable to relate the inter-center b1bg b1bg ZR-like transition with a weak spectral feature observed by Pagliara et al. [18] at 3.2 eV for E c , rather than with a two orders of magnitude more intense band at 3.6 eV. A distinctly seen shoulder in absorption spectra for E b (Fig. 3) may be b2u p d CT transition peaked near ascribed to the intra-center b1bg
CuO54
with the creation of electron CuO74 and hole CuO54 centers. The former correspond to completely filled Cu 3d and O 2p shells, or the vacuum state for holes, while the latter may be found in different two-hole states. The hole CT transitions from the ground b1bg state for the CuO4 plaquette to the predominantly Cu 3d g state on the neighboring plaquette will generate the d d CT transitions, while the transitions to predominantly O 2p u, g states will generate the d p inter-center CT transitions. However, the b1bg u, g designation seems more appropriate anyway. For the corner-shared CuO4 plaquettes we point to the three CT channels governed by the strongest σ bond: b12g (Zhang-Rice channel [5]), b1g a1g , b1g eu ( ) , respectively, in accordance with the symmetry of the final two-hole state. Interestingly that the strongest σ-σ CueOeCu bonding does not at work for the edge-shared 90 CueOeCu geometry of the CuO4 plaquettes in many 1D CuO2 chains. 4. CT transitions in 0D, 1D, and 2D insulating cuprates probed by electron energy loss spectroscopy (EELS) and optical spectroscopy Comparative analysis of the optical and EELS spectra in cuprates with different dimensionality and bonding of the CuO4 network is extremely interesting and informative in many respects. In particular, considerable general interest in comparing the various physical properties of 0D, 1D and 2D cuprates is caused by such challenging problems as the low-dimensional aspect of electronic structure and high-Tc superconductivity. It is worth noting that the 0D cuprates with isolated CuO4 plaquettes such as CuB2O4 or Bi2CuO4, the corner-shared and edge-shared 1D chain cuprates such as Sr2CuO3 and Li2CuO2, respectively, as well as the 2D systems such as Sr2CuO2Cl2 should reveal similar signatures of the intra-center excitations. 4.1. 0D and 1D cuprates with well isolated or weakly coupled CuO4 plaquettes The optical and EELS spectra for 0D cuprates are governed only by the intra-center transitions. In Fig. 2 we reproduce the low-energy absorption spectrum for 0D cuprate CuB2O4 [12] which is most likely formed by dipole-forbidden b1bg b2bg , a1bg , egb ) (crystal-field d d ) and b b1g a2g , eu ( ) ( p d ) transitions. Unlike most 1D and 2D cuprates where the low-energy absorption bands are broad and featureless, the absorption spectra for a true 0D cuprate CuB2O4 provide a remarkable opportunity to observe a ”fine structure” of low-energy forbidden transitions. The experimental spectrum shows up a number of narrow zero-phonon peaks with up to the seventy well-resolved phonon sidebands [12] imposed on a rather broad band near 2 eV. It is worth noting that the absorption coefficient for 2 eV band is very small and corresponds to the dielectric function 2 of the order of 0.01. It might be surprising that among the best candidates for the ”optically” 0D cuprates are such systems as Li2CuO2, LiCu2O2, LiVCuO4, or
Fig. 2. Low-energy absorption spectra for 0D cuprates: Left panel:CuB2O4 (k z, E z ) [12]; CuGeO3 [13]. Right panel: absorption coefficient for CuGeO3 at higher energy [14]. 246
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Fig. 3. Left panel: Optical conductivity of Li2CuO2 [15](E chain ). Right panel: low-energy part of the EELS spectrum of CuGeO3 [16]. Inset shows an imaginary part of the pseudodielectric function of CuGeO3 [14].
4.1 eV, which is dipole-allowed in the out-of-plane polarization. Experimental data available for another edge-shared system, Li2CuO2 [15,17] is not enough to arrive at any decisive conclusion. Most likely the optical [15] (see Fig. 3) and EELS [17] data evidence a rather small ( 0.5 eV) eu ( ) -eu ( ) separation as compared with CuGeO3 and a net redshift of the eu ( ) -eu ( ) quartet to 3–4 eV. Both low-energy intracenter and numerous nn as well as the nnn inter-center CT transitions with the spectral onset at 1.5 eV appear to be hidden in the tails of the nonvanishing spectral weight of the main CT bands. A more dramatic situation has been uncovered in a mixed valent Cu1+-Cu2+ 1D cuprate LiCu2O2, where all the spectral range 1–6 eV is dominated by anomalously strong dipole allowed intra-atomic 3d – 4p transition in Cu1+ ions [19] peaked at 3.26 eV (see Fig. 4). It is worth noting that in Ref. [20] this huge peak was ambiguously ascribed to a conventional intra-center p d CT transition. However, comparing the corresponding values of the optical response for Li2CuO2 and CuGeO3 with that of LiCu2O2 we do unambiguously reject such assignement. Peak values of imaginary part of the dielectric function
Fig. 5. EELS spectra in Sr2CuO3 for longitudinal q a (left panel) and transversal q b (right panel) response with an illustration of intra- and inter-center excitons.
and optical conductivity in LiCu2O2 are an order of magnitude greater than the corresponding values determined by the edge-shared CuO4 plaquettes in cuprates with a single type (Cu2+) of copper ions. 4.1.1. Polarization dependent EELS spectroscopy of 1D copper oxide Sr2CuO3 and separation of the intra- and inter-center CT excitons In contrast to optics, the angle-resolved EELS spectroscopy provides unique opportunities to reveal the exciton dispersion and separate the intra- and inter-center CT excitons. The one-dimensional cuprate compounds are good candidates for such a study since the scattering of electrons with a transferred momentum q perpendicular to the chain direction excites only the EH pairs sitting on a single CuO4 plaquette. On the other hand, for q parallel to the chain direction, the both types of excitons (intra- and inter-center) can be observed. The EELS spectra for Sr2CuO3 in ”longitudinal” response with the transferred momentum oriented along the chain direction were measured earlier in Ref. [21] and have been interpreted within standard Hubbard models. However, such models can describe properly only the ”longitudinal” response with the transferred momentum oriented along the chain direction. The EELS spectra for Sr2CuO3 in both polarizations are presented in Fig. 5 [22]. Their comparison leads to very important conclusions. We see a drastically strong difference between the two sets of spectra. First, this concerns the well-defined dispersionless EELS peaks at 2.0 and 5.5 eV in transversal polarization (right hand side panel in Fig. 5). The intensity considerations and the absence of noticeable energy dispersion allow us to associate them with dipole-allowed CT transitions having a particularly localized nature. Moreover, when comparing the both spectra we see that despite the strong inequivalence of longitudinal and transversal polarizations in Sr2CuO3 the low-energy transition peaked near 2 eV is equally present in both polarizations. Though for longitudinal polarization this is partly hidden for low momentum values by the intensive band peaked at 2.6 eV and is seen as a shoulder, near the BZ boundary it is a well-separated weak band due to a large blue shift of the intense neighbor. This fact implies that the excitation is
Fig. 4. (Color online) (a) Low temperature (T = 26 K) spectra of the real 1 (open circles) and imaginary 2 (solid circles) parts of the dielectric functions in LiCu2O2 for the light polarized along the x axis and their fit with the set of Lorentz oscillators (lines) [19]; (b) the positions of the main Lorentz oscillators in the 2xx spectra. Inset: Optical conductivity spectra at T = 26 and 300 K (solid and open circles). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 247
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localized on a single CuO4 plaquette being the only common element of longitudinal and transversal geometry in this 1D cuprate with the corner-shared CuO4 plaquettes. Hence, by taking into account the intensity ratio we can unambiguously identify the 2.0 and 5.5 eV peaks in the EELS spectrum of Sr2CuO3 with the intra-center CT excitons eu ( ) and eu ( ) , respectively. So, for the polarization perpendicular to chain direction, the 1D cuprates such as Sr2CuO3 provide the optical and EELS response typical for a 0D system. Contrary to CuBi2O4, the both dipoleeub, a transitions in Sr2CuO3 manifest themselves more allowed b1bg distinctly with well-defined EELS-peaks at 2.0 and 5.4 eV, respectively. The corresponding peaks in optical conductivity are situated at 1.8 and 4.3 eV, respectively. One should note that the EELS data present a straightforward experimental manifestation of the dipole-allowed intracenter b1bg eub, a excitations without the ”parasitic” effect of the intercenter transitions. Large spectral weight and sizeable dispersion of the most intense low-lying CT exciton peaked in EELS at 2.6 eV agree with its inter-center nature. Thus, we have shown that the polarization-dependent angle-resolved EELS study of the 1D cuprate Sr2CuO3 with the corner-shared CuO4 plaquettes provides a unique opportunity to separate both intraand inter-center CT excitons as well as two types of intra-center CT excitons [23]. Furthermore, for the first time, we unequivocally demonstrated the important role of the O 2pπ-holes in determining lowenergy excitations in cuprates. In this regard, we would like to emphasize once more the decisive role of direct EELS measurements in the observation and unambiguous assignment of the intra- and inter-center excitons in Sr2CuO3 as compared with conventional indirect optical data.
Fig. 6. The spectral dependence of the imaginary part of dielectric function ( ) for Sr2CuO2Cl2. Arrows mark the predicted energy position of intra-center, inter-center b12g -channel, and b1g eu -channel CT transitions. Inset: optical conductivity in Sr2CuO2Cl2 [24].
in energy b12g transition with ZR-singlet as a final hole state, while the more intense high-energy b1g eu ; dp transition is blue-shifted by 5.0 eV with regard to the same transition. The most intense CT transition in this quartet with the b1g eu ; pp final state is expected to have the maximal energy ~13 ÷ 14 eV among all the CT transitions governed by the strong σ bond.
4.2. CT transitions in 2D insulating cuprates In 2D systems, we usually deal with spectra representing the superposition of both types of excitons, which makes the problem of separating different transitions rather complicated. Thus, some uncertainty remains regarding the reliable identification of two dipoleallowed intra-center CT excitons and seven main inter-center CT excitons, which may cast doubt on their existence as well-defined states. Unfortunately, this concerns also the structure of the low-energy optical response observed in the spectral range 2 ÷ 3 eV, which is of a special importance since it is associated with the states which are believed to mainly define the unconventional properties of the cuprates. However, making use of the theoretical predictions, justified and supported by numerous experimental data for 0D and 1D cuprates, we can establish an overall picture of optical and EELS spectra (at the -point). These spectra are governed by dipole-allowed intra- and inter-center CT excitations and include:
We verified all these predictions for Sr2CuO2Cl2 to be one of the best realizations of a 2D antiferromagnetic insulating model cuprate. In Fig. 6 we present the spectrum of the imaginary part of dielectric permittivity derived from the Kramers-Kronig transformation of the EELS data [5,25]. Remarkably, all the excitations which were analysed before correspond to visible features in 2 . The weak low-energy feature near 2.2 eV in the EELS spectra (2.0 eV in 2 and optical conductivity) eu ( ) could be ascribed to the lowest in energy intra-center b1bg transition. This feature occupies the tail of a rather intensive band peaked at 2.7 eV in EELS spectra (2.4 eV in 2 and optical conductivity). b1g This band is naturally associated with the lowest in energy b1bg inter-center CT transition with ZR-singlet as a final hole state. Its energy is of a particular importance for the whole set of inter-center transitions. Having positioned the lowest intra- and inter-center excitons, the higher states are fixed by the chosen parameter values (see Fig. 6). Two features in EELS, near 4.2 eV and 7.1 eV could be related to inter-center b1g eu ; dp and b1g eu ; dp transitions, respectively, while the broad band near 6.0 eV in EELS could be naturally assigned to the intra-center b1bg eu ( ) transition, whose energy is slightly higher than that of its two-hole counterpart. The spectrum of the most intense transitions generated by the Cu 3d-O 2p σ transfer ends with very strong features near 9 ÷ 10 and 12 ÷ 13 eV in the EELS spectrum, which can definitely be associated with high-energy inter-center b12g ; pp CT transition with a Zhang-Rice singlet type final hole state of predominantly pp configuration, and the transitions to the b1g eu ; pp and b1g eu ; pp final states, respectively. All this shows that important spectral information is contained in the range above 8 eV. The peak at about 18 eV is likely to be attributed to transitions with O 2s initial state. The interpretation of EELS spectra for nonzero momentum becomes more complicated due to the energy and intensity dispersion of the dipole-allowed modes and the appearance of numerous new modes which are forbidden at the -point. Hereafter, we focus only on angleresolved EELS spectra in the spectral range up to 8.0 8.5 eV for several
eu ( ) trani) the lowest in energy (1. 5 ÷ 2. 0 eV) intra-center b1bg sition with a rather small intensity due to the predominantly O 2p nature of the final state and a strong tendency to self-localization (trapping); ii) the high-energy ( 5.0 eV) and rather intensive intra-center b1bg eu ( ) transition; iii) within the b12g -channel we predict the three inter-center CT transitions: 1) the lowest in energy (2. 0 ÷ 3. 0 eV) and relatively intense transition with the ZR-singlet as a final hole state; 2) the most intense high-energy transition with the ZR-singlet-like final hole state blue-shifted to 7.0 eV; and 3) the less intensive transition blueshifted to 5.0 eV with regard to the first one; iv) within the b1g eu -channel we predict the two doublets of inter-center CT transitions, generated by the CT to eu ( ) and eu ( ) orbitals with smaller and larger weight of O 2pσ orbitals, and shifted by 6.0 eV with regard to each other. The high-energy doublet is relatively more intense. The transitions within each doublet are shifted by 3. 0 ÷ 3. 5 eV with regard to each other. The low-energy b1g eu ; dp transition is blue-shifted by 1. 5 ÷ 2. 0 eV with regard to the lowest 248
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momentum values in [100] and [110] directions, obtained by Wang et al. [26] and by Fink et al. [27,28] The spectra differ somewhat by the maximal momenta values and the considerably better resolution in the latter case. The low-energy part of the EELS spectra in the 2D system Sr2CuO2Cl2 along the [110] direction and the longitudinal spectra in the 1D system Sr2CuO3 have a very similar structure up to some quantitative coincidence. For the both compounds the main spectral feature is associated with an intense band assigned to the inter-center b12g exciton, or so-called Zhang-Ng (ZN)-exciton, with a clear dispersion extending from 2.6 eV near the -point to 3.0 eV near the BZ boundary [26,29]. In both systems this band has the low-energy shoulder near 2.0 eV which is distinctly seen in the -point or near the BZ boundary. This two-peak structure of the CT band in Sr2CuO2Cl2 and isostructural Ca2CuO2Cl2 is corroborated by conventional optical measurements [24,30–32]. The EELS spectra along the [100] direction manifest an expected overall drop in intensity with relatively small energy dispersion. In contrast to the [100] direction, the main peak for the [110] direction of Sr2CuO2Cl2 exhibits clear signatures of strong dispersion, particularly for momentum values in the range (0. 5 ÷ 0. 7) kmax . Namely this effect was a starting point for the model theory of the CT excitons by Zhang and Ng [26,29]. However, in our opinion, here we deal with an unconventional behavior of the intensity dispersion for different excitons with the peculiarities especially in the momentum range (0. 5 ÷ 1. 0) kmax rather than with the strong energy dispersion of the ZN-exciton. Indeed, as it was emphasized above, the intensity of the main peak in the low-energy part of the EELS spectrum for Sr2CuO2Cl2, assigned to the dipole-allowed exciton associated with the b1bg b1g inter-center CT transition with the ZR-singlet as a final hole state, sharply decreases with the increase of momentum along [110] direction with a probable compensation point near the BZ boundary. This circumstance allows to clearly observe a sharp rise of the spectral weight in a rather broad range with the well-defined peak in EELS near 3.8 eV. This spectral feature may be unambiguously associated with the dipole-forbidden Ag counterpart of the inter-center b1g eu ; dp exciton, which is allowed and rather intensive at the ( , ) point. Interestingly that the result of this specific behavior of the EELS intensity for different excitons might be mistaken for manifestation of the energy dispersion of the main peak associated with the g u dipole-allowed inter-center b12g exciton, as it was made by Wang et al. [26]. Obviously, this error led to the conclusion that there is a very large ( 1.5 eV) energy dispersion for this exciton. The real energy dispersion for different CT excitons in our opinion may not exceed the reasonable values of the order of 0.5 eV. Thus, the overall analysis of the experimental EELS spectra in the model 2D insulating cuprate Sr2CuO2Cl2 allows us to certainly assign a set of distinctly observed features in a rather wide spectral range 2. 0 ÷ 14. 0 eV to the predicted intra- and inter-center CT excitons, and confirm the validity of the theoretical concept based on the embedded CuO4 cluster model. A close examination of other materials shows that the two-component structure of the CT gap appears to be a common place for all parent cuprates with the corner-shared CuO4 plaquettes (see e.g., Refs. eub excitation within the [32–36]). The dipole-allowed localized b1g CuO4 plaquette related essentially to the eu ( ) state is distinctly seen in optical and EELS spectra for different insulating cuprates as a separate weak feature or a low-energy shoulder of the more intensive band near 2.5 eV assigned to the inter-center CT transition associated with the ZRsinglet-like excitation b12g ; pd . Both components are characterized by a different coupling to the magnetic and phonon subsystems thus providing additional ways to separate them. Generally speaking, the CT exciton creation is usually accompanied by an excitation of lattice modes. Indeed, the hole transfer from Cu 3d to O 2p state, or from an ionic to a covalent configuration is accompanied by a significant shortening of the equilibrium CueO bond length. The exciton-phonon interaction strongly influences the line shape of absorption and results in a phonon Raman scattering. The
measurement of the Raman intensity as a function of excitation light energy is a very informative probe of the origin of electronic transitions [37]. In particular, this method has allowed [38] to resolve a fine structure of the low-energy (LE) excitonic feature in La2CuO4 with a sharp peak at 2.14 eV as narrow as 50 meV and a broader structure at 1.9 eV. In our opinion, such an unusual behavior of the LE exciton could eu transition be associated with its Jahn-Teller nature. Indeed, the b1g to the orbital doublet eu represents a textbook example of a so-called A E transition [39]. The excited, orbitally degenerate eu state is unstable with regard to vibronic coupling with the local distortion modes A1g , B1g , B2g , Eu and the formation of a polaron-like (soliton-like) vibronic center with a complex two- or four-well adiabatic potential and a rather strong renormalization of vibration frequencies. In other words, the doublet eu state tends to a spontaneous local symmetry breaking, including removal of the inversion center due to interaction with the close in energy even states and pseudo-Jahn-Teller effect. Namely the eu exlatter would result in a strong resonance coupling of the b1g citon with odd Eu lattice modes. Naturally, the structure of such a center would strongly depend on differences in the bare lattice and elastic parameters and differ in 214 and 123 systems. One should emphasize that the formation of the heavy polaron-like, or localized small exciton would result in a strong enhancement of its effective mass. For small intra-center excitons we have a rather conventional s = 1/2 s = 1/2 transition with spin-density fluctuation localized inside the CuO4 plaquette. Such a transition is not accompanied by strong two-magnon (2 M) Raman processes, that could be used to identify this type of excitons. The redistribution of spin density from the eu transition switches on copper atom to the oxygen ones for the b1g the strong ferromagnetic Heisenberg O 2p-Cu 3d exchange with the nearest-neighbor CuO4 plaquettes. Interestingly, the different sign of exchange coupling for eu and b1g holes with the same neighborhood, ferromagnetic for the former, and antiferromagnetic for the latter, leads to a number of temperature anomalies near the 2D-3D antiferromagnetic phase transition. There is, firstly, the blue-shift effect for eu by lowering the the energy of the small intra-center exciton b1g TN , the average moletemperature near and below TN . Indeed, at T cular field for the CuO4 center turns to zero. The 3D antiferromagnetic ordering is accompanied by a rise of exchange molecular fields and respective spin splittings. Due to the different signs of molecular fields for eu and b1g states this is accompanied by an increase of the transition (|Hb1g | + |Heu |) . This energy with maximal value of the blue shift quantity could be as large as several tenths of eV. Additionally, one has to expect a strong (of the same order of magnitude) broadening of the excitonic line with increase of the temperature due to strong fluctuations of molecular fields. All these expectations are experimentally found for the 2.0 eV line in Sr2CuO2Cl2 [24] confirming its intra-center excitonic nature. A similar situation is observed in La2CuO4 [34] although the authors have explained the data by assuming a polaronic nature of electrons and holes with a short-range interaction in between. 4.3. CT transitions in copper monoxide CuO Copper oxide CuO has been actively studied both experimentally and theoretically as a prototype model system for the semiconducting phase of the copper-oxygen high-temperature superconducting (HTSC) systems. This monoclinic (C2h6 ) [40] cuprate has a very narrow phase homogeneity range and is robust with regard to different chemical doping used to reach the insulator-to-metal transition in parent cuprates such as La2CuO4, YBa2Cu3O6. Despite this the CuO single crystals exhibit many features typical for a wide family of nominally pure or slightly doped parent cuprates. Below TN1 231 K CuO has antiferromagnetic ordering: the noncollinear one in range 213 ÷ 231 K and the collinear one below TN2 213 K with spins, ordered parallel to baxis. First detailed studies of optical absorption of nominally pure 249
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Fig. 7. Left panel: Absorption spectra of single-crystalline CuO samples before and after irradiation by high-energy electrons and He+ ions [43,44], insets show a typical MIR spectrum and temperature dependence of the absorption coefficient variation K (T ) = K (T ) K (T = 80 K) at 3.13 eV for a single-crystalline CuO sample, respectively. Right panel: Typical absorption spectrum of nanocrystalline CuO samples [46], inset shows a remarkable temperature-dependent ”peak-diphump” feature near 1. 3 ÷ 1. 6 eV for a sample with 60 nm grains.
stoichiometric single crystalline CuO samples, as well the samples, exposed to the fluence of the neutrons, electrons, He+-particles, and high density polydisperse CuO nanoceramics were performed by Russian group [41–46]. Several results are summarized in Fig. 7. The behavior of intra- and inter-center excitons in monoxide CuO [41,42] has some specific features due to the low (monoclinic) crystal symmetry which makes difficult their unambiguous assignement. A fine structure near 1.7 eV was assigned to a weakly dipole allowed intra-center p d (b1g eu ( ) ) CT exciton. The final eu ( ) -hole state is split into two components with markedly differing inter-chain eu ( ) b1g exchange, and the respective CT bands show markedly different temperature behavior [42]. To the best of our knowledge, it was the first indication of an optical manifestation of low-lying nonbonding O 2pπ states. Band peaked near 3.13 eV was assigned to a weakly dipole allowed intracenter p d (b1g b2u ( ) ) CT exciton, however, a remarkable temperature dependence of its absorption coefficient near magnetic phase transitions (see inset in Fig. 7, left panel) agrees also with its intercenter d d CT origin, if account for a specific temperature dependence of the spin correlation factor for the incommensurate spin phase. The low-energy absorption spectra of the single crystalline CuO samples reveal a well developed mid-infrared (MIR) band which has the structure typical for other insulating cuprates. Such a band is believed to represent something like a superposition of the magnetic excitations within the antiferromagnetic background and a contribution of the selftrapped CT excitons and the EH droplet phase. As in the case of non-isovalent chemical substitution in other cuprates, the accumulation of the defects under the irradiation in a nanocrystalline state leads to the red shift of the spectral weight with a characteristic evolution of the MIR band evidencing the rise in the EH droplet volume fraction. Two bands, rather narrow one with a peak near 0.1 eV and the second broader one with a peak near 0.2–0.3 eV are the most common features of the MIR band. These may be assigned to the low- and high-energy dipole allowed CT transitions within a selftrapped inter-center two-particle d d CT exciton. In addition, all the CuO samples with well developed MIR bands exhibit a remarkable 1.3 eV peak which may be attributed to the inter-center one-particle d d CT transition with the EH-recombination in the EH-droplets. Note that this peak was earlier on assigned to the surface plasmon (Mie) resonances due to a small volume fraction of metallic-like nanoscale EH droplets with Drude optical response embedded in the bare insulating medium [41,46]. Ellipsometric measurements of single-crystalline CuO samples in the region 2–4 eV [14] have revealed the strongest CT band peaked near 3.5 eV that can be assigned to a dipole-allowed b1bg eu ( ) p d CT transition. As for other cuprates the CuO RIXS spectroscopy [11] reveals a wide band peaked near 5 eV attributed to bonding-antibonding b1bg b1ag , b2ag , a1ag , ega CT transitions.
5. Conclusion Starting with the predictions of a simple cluster model theory we were able to give a semi-quantitative description of the experimental optical and EELS spectra for a large variety of nominally insulating cuprates with the CuO4 plaquettes to be a main building block of their crystal and electronic structure. These include monooxide CuO, parent quasi-2D cuprates La2CuO4, Sr2CuO2Cl2, YBa2Cu3O6 with a 2D arrangement of the corner-shared CuO4 plaquettes, their 1D counterpart Sr2CuO3 with a chain 1D arrangement of the corner-shared CuO4 plaquettes, Li2CuO2, LiCu2O2, CuGeO3 with a chain 1D arrangement of the edge-shared CuO4 plaquettes, and exotic 0D system CuB2O4 with the well isolated CuO4 plaquettes. Both different experimental data and theoretical analysis show that the nature of the CT gap in insulating 1D and 2D parent cuprates is determined by the nearly degenerate in energy intra-center p d and inter-center d d CT excitons. The former is associated with the hole eu ( ) from the Cu 3d-O 2p hybrid b1g d x 2 y2 state CT transition b1g to purely oxygen O 2 p state localized on the CuO4 plaquette, while the b1g CT transition between neighboring plaquettes latter does with b1g with the ZR singlet to be the final two-hole state. The structure of the optical gap with the two well-defined CT excitons seems to be typical for a wide group of parent cuprates that implies a revisit of some generally accepted views on the electronic structure both of the 1D and 2D cuprates including the nature of the superconducting state in these systems. Rather simple quantum-chemical CuO4 cluster model represents a physically clear albeit rather simplified approach to consider EH excitations in cuprates. However, it seems such an approach allows to catch the essential physics of the CT transitions, and should be a necessary step both in qualitative and semi-quantitative description of insulating cuprates. Declaration of interests The author declare that he have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement I acknowledges the stimulating discussions with R. V. Pisarev, B. B. Krichevtsov, N. N. Loshkareva, Yu. P. Sukhorukov, S.-L. Drechsler, and R. Hayn. Special thanks to Prof. G. J. Babonas for sending unpublished experimental data. Supported by Act 211 Government of the Russian Federation, agreement 02.A03.21.0006 and by the Ministry of Education and Science, projects 2277 and 5719. 250
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Optical Materials journal homepage: www.elsevier.com/locate/optmat
Optical properties of low-dimensional cuprates A.S. Moskvin a b
T
a,b,∗
Ural Federal University, Ekaterinburg, Russia Institute of Metal Physics, Ekaterinburg, Russia
ARTICLE INFO
ABSTRACT
Keywords: Cuprates Low dimension Charge transfer transitions Optical response EELS
I present a short overview of the optical properties of different low-dimensional cuprates with different arrangement of the CuO4plaquettes being main elements of their crystalline and electronic structure. The focus of the paper is on intra- and inter-center charge transfer transitions.
1. Introduction Despite a giant number of experimental and theoretical works on cuprates published after the discovery of high-Tc superconductivity [1] we deal actually with a lack of detailed studies of electron-hole (EH) excitations both in parent and high-Tc cuprates. The nature of the lowenergy EH excitations as well as those with higher energy and high intensity is still unclear. Here in the paper we address optical properties with a focus on the charge transfer (CT) excitations in a large variety of nominally insulating cuprates with CuO4 plaquettes to be a main building block of their crystal and electronic structure. These incorporate monooxide CuO, parent quasi-2D cuprates such as La2CuO4, Sr2CuO2Cl2, YBa2Cu3O6 with a 2D arrangement of the corner-shared CuO4 plaquettes, their 1D counterparts such as Sr2CuO3 with a chain 1D arrangement of the corner-shared CuO4 plaquettes, Li2CuO2, LiCu2O2, CuGeO3 with a chain 1D arrangement of the edge-shared CuO4 plaquettes, and rather exotic 0D systems with the well isolated CuO4 plaquettes, such as CuB2O4. 2. Electronic structure of the copper-oxygen CuO4 cluster As an efficient approach to describe excitonic states, especially with small effective electron-hole separation we propose here the embedded molecular cluster method. In the present context we use one or two neighboring CuO4 clusters embedded into the insulating cuprate. This method provides both a clear physical picture of the electronic structure and energy spectrum, as well as the possibility of quantitative modeling. Eskes et al. [2], as well as Ghijsen et al. [3] have shown that, in a
∗
certain sense, cluster calculations can provide a better description of the electronic structure of insulating cuprates than the band-structure calculations, since they allow for a better account of the correlation effects (see also Ref. [4]). Starting with the five Cu 3d and the twelve O 2p atomic orbitals for CuO4 cluster with the D4h symmetry, it is easy to form the seventeen symmetrized even-parity a1g , a2g , b1g , b2g , eg and odd-parity a2u , b2u , eu ( ), eu ( ) orbitals. The even-parity Cu 3d a1g (3d z 2 ) , b1g (3d x 2 y2 ) , b2g (3d xy ) , eg (3d xz , 3d yz ) orbitals hybridize, due to a strong Cu 3d -O 2p covalency, with the even-parity O 2p -orbitals of the same symmetry, thus forming appropriate bonding b and antibonding a states. Among the odd-parity orbitals only eu ( ) and eu ( ) hybridize due to the nearest-neighbor pp overlap and transfer thus forming appropriate bonding eub and antibonding eua purely oxygen states. The purely oxygen a2g , a2u , b2u orbitals are the nonbonding ones. All ”planar” O 2p orbitals in accordance with the orientation of lobes could be classified as σ (a1g , b1g , eu ( ) ) or π (a2g , b2g , eu ( ) ) orbitals, respectively. Among purely oxygen nonbonding orbitals only eu ( ) and eu ( ) hybridize with each other (equally for both types ( x , y ) of such orbitals): |eub = cos
e
|eu ( ) + sin
e
|eu ( ) ; |eua = sin
e
|eu ( )
cos
e
|eu ( ) ,
(1) where
tan2 and
e
=
t epp u
2t epp u peu ( )
=
, peu ( )
(2)
(tpp + tpp ) is an effective transfer integral with tpp < 0 ,
Ural Federal University, Ekaterinburg, Russia. E-mail address: [email protected].
https://doi.org/10.1016/j.optmat.2019.02.033 Received 30 October 2018; Received in revised form 21 February 2019; Accepted 22 February 2019 0925-3467/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Model single-hole energy spectrum for a CuO4 plaquette with parameters relevant for Sr2CuO2Cl2 and a number of other insulating cuprates with the cornershared CuO4 plaquettes.
tpp > 0 being the two types of the p p transfer integrals, for the σ and 1 π bonding, respectively (|tpp | 2 |tpp |), peu ( , ) are energies of the molecular orbitals. Hereafter, we keep the notation eu ( ), eu ( ) for predominantly σ or π orbitals, respectively. Interestingly, that the eu ( ), eu ( ) orbitals could form the two types of circular current p±1-like states: eu ± 1 ( ), eu ± 1 ( ) , respectively, with the Ising-like orbital moment eu ± 1 ( )|lz |eu ± 1 ( ) =
eu ± 1 ( )|lz |eu ± 1 ( ) = ± sin 2 ,
3. Charge transfer transitions in cuprates
d CT transitions
3.1. Conventional intra-center p
For a typical cuprate with the CuO4 plaquettes we predict the three eua, b from the types of dipole-allowed intra-center CT transitions: b1bg b ground state b1g to the purely oxygen doublet O 2p -O 2p hybrid states eua, b , which are allowed in ”in-plane” polarization E C4 , and the b1bg b2u transition to purely oxygen O 2pz -like state, which is allowed in the ”out-of-plane” polarization E C4 . The two CT transitions b1bg eub and b1bg eua differ by the oxygen hole density distribution in final state: for the former this has a predominantly O 2p character, while for the latter it has the O 2p one. In the framework of a local approximation their relative intensity is determined by the strength of the p - p mixing as follows:
(3)
or the two types of the currentless px , y -like eux, y ( ), eux , y ( ) states with a quenched orbital moment. Fig. 1 presents a single-hole energy spectrum for a CuO4 plaquette embedded into an insulating cuprate such as Sr2CuO2Cl2 [5] calculated with the parameters based on the results of numerous theoretical and experimental studies [6–10]. For illustration we show a step-by-step formation of the cluster energy levels from the bare Cu 3d and O 2p levels with the successive inclusion of the crystal field (CF) effects, O 2p-O 2p, and Cu 3d-O 2p covalency. It is worth noting that the b1bg character of the ground hole state in CuO64 cluster seems to be one of a few indisputable points in cuprate physics. Recent resonant inelastic X-ray scattering (RIXS) spectroscopy measurements for different insulating cuprates (see Ref. [11] and references therein) with the incident photon energy tuned to the Cu K edge (hard X-rays) have revealed the low- (1.5–2.0 eV) and high-energy (5–7 eV) bands of the d d excitations attributed to the intra-center b1bg a1bg , b2bg , egb and b1bg a1ag , b1ag , b2ag , ega transitions from the b ground b1g state to the low-energy bonding and high-energy antibonding Cu 3d-O 2p hybridized orbitals, respectively. Hence, the b1bg b1ag separation could be estimated to be 6.0 eV.
f I = = |tan |2 = I f
tpp + tpp peu ( )
2
,
peu ( )
This ratio, given the typical values of parameters, does not exceed 0.1. The low-energy (near 2 eV) part of the absorption spectrum for a single CuO4 plaquette is believed to be formed by an interplay of the b2bg , a1bg , egb ), dipole-forbidden crystal field d d transitions (b1bg b b b1g a2g and allowed b1g eu ( ) CT transitions, respectively, which are all close in energy. The a2g hole has the minimal energy among all the purely oxygen states: a2g = eu ( ) 2tpp . In accordance with the model energy spectrum (see Fig. 1) its energy should be of the order of 1. 5 ÷ 1. 8 eV, or in other words appears to be markedly lower than the main optical gap. 3.2. Inter-center d
d and d
p CT transitions
The local inter-atomic O 2p - Cu 3d charge transfer generates not only intra-center excitations within one CuO4 plaquette but also the inter-plaquette (inter-center) transitions. These inter-center transitions between two CuO4 plaquettes may be considered as quanta of the 245
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disproportionation reaction
CuO64
+
CuO64
CuO74
+
CuGeO3, that is nominally 1D systems with the edge-sharing CuO4 plaquettes. However, since the CueOeCu bond angle along the chain is almost 90 , the main σ-σ transfer from one plaquette to its nearest neighbors is strongly suppressed. Thus, the in-plane charge excitations are localized within a single plaquette, hence with respect to the electronic properties the CuO4 centers in these compounds can be addressed to be approximately isolated [17]. This standpoint is fairly well confirmed in optical and EELS data for Li2CuO2 [15,17]. In terms of perpendicular out-of-plane O 2pz orbitals, these systems should be considered as typical 1D chain systems with O 2pπ bonding. The absorption spectra of CuGeO3 from 1 to 4.2 eV, for the two polarizations E c ( chain direction) and E b ( chain direction) [13,14], are shown in Fig. 2. A relatively weak absorption structure, observed in the lower-energy range, is followed by a region of a relative transparency and, above 3 eV, by a sharp and anisotropic increase of the absorption coefficient with a small temperature dependent feature visible at 3.1–3.2 eV for E c [18] and an order of magnitude more intensive feature visible at 4.1 eV for E b [14] (see Fig. 2). Ellipsometric measurements of CuGeO3 [14] reveal two intensive CT bands with maxima of the imaginary part of the pseudodielectric function at 3.6 and 4.5 eV, which may be ascribed to CT transitions allowed in E c and E c polarization, respectively. The low-energy 2 eV band, both in position and absorption coefficient, is a structureless analogue of the respective band in CuB2O4. The effective oscillator strength has a specific ¯ ph temperature trend: f (T ) coth 2kT , where ¯ ph 240 cm−1 is an average phonon energy, that in conjunction with the small absolute values of f (T ) , seems appropriate to phonon-assisted transitions, normally forbidden by parity considerations [13]. The polarization dependence of the absorption coefficient agrees with the in-plane character of the CT excitations, if to account for a complete (E c ) or partial (E b ) in-plane light polarization. Similar weak feature is distinctly observed in experimental EELS spectra for CuGeO3 [16] at small momenta near 1.7 eV. The loss function spectra in CuGeO3 for q c are dominated by two features: an intense broad peak with the triangularlike shape at 6.2 eV and a feature with much lower intensity at 3.5 eV. Atzkern et al. [16] attributed the high-energy feature to a superposition of strong dipole allowed intra-center b1bg eu ( ) CT transition peaked b1ag and b1bg eu near 6.0 eV and the high-energy inter-center b1bg transitions, while the low-energy feature was attributed to the lowb1bg Zhang-Rice (ZR)-like transition. The loss energy inter-center b1bg function spectra for the q b polarization are assigned to a superposition eu ( ) CT transition peaked near 6.5 eV and the two of intra-center b1bg transitions peaked at 5.5 and 7.3 eV which can be assigned to intrab2u and O 2p - Ge 4s (p) CT transitions, respectively [16]. center b1bg However, a more reasonable interpretation can be proposed that implies a rather strong eu ( ) -eu ( ) separation with formation of the two quasi-doublets eu ( ) and eu ( ) , near 4 eV and 6 eV, respectively, each split by 0.5–1.0 eV due to the p p transfer. It seems more reasonable to relate the inter-center b1bg b1bg ZR-like transition with a weak spectral feature observed by Pagliara et al. [18] at 3.2 eV for E c , rather than with a two orders of magnitude more intense band at 3.6 eV. A distinctly seen shoulder in absorption spectra for E b (Fig. 3) may be b2u p d CT transition peaked near ascribed to the intra-center b1bg
CuO54
with the creation of electron CuO74 and hole CuO54 centers. The former correspond to completely filled Cu 3d and O 2p shells, or the vacuum state for holes, while the latter may be found in different two-hole states. The hole CT transitions from the ground b1bg state for the CuO4 plaquette to the predominantly Cu 3d g state on the neighboring plaquette will generate the d d CT transitions, while the transitions to predominantly O 2p u, g states will generate the d p inter-center CT transitions. However, the b1bg u, g designation seems more appropriate anyway. For the corner-shared CuO4 plaquettes we point to the three CT channels governed by the strongest σ bond: b12g (Zhang-Rice channel [5]), b1g a1g , b1g eu ( ) , respectively, in accordance with the symmetry of the final two-hole state. Interestingly that the strongest σ-σ CueOeCu bonding does not at work for the edge-shared 90 CueOeCu geometry of the CuO4 plaquettes in many 1D CuO2 chains. 4. CT transitions in 0D, 1D, and 2D insulating cuprates probed by electron energy loss spectroscopy (EELS) and optical spectroscopy Comparative analysis of the optical and EELS spectra in cuprates with different dimensionality and bonding of the CuO4 network is extremely interesting and informative in many respects. In particular, considerable general interest in comparing the various physical properties of 0D, 1D and 2D cuprates is caused by such challenging problems as the low-dimensional aspect of electronic structure and high-Tc superconductivity. It is worth noting that the 0D cuprates with isolated CuO4 plaquettes such as CuB2O4 or Bi2CuO4, the corner-shared and edge-shared 1D chain cuprates such as Sr2CuO3 and Li2CuO2, respectively, as well as the 2D systems such as Sr2CuO2Cl2 should reveal similar signatures of the intra-center excitations. 4.1. 0D and 1D cuprates with well isolated or weakly coupled CuO4 plaquettes The optical and EELS spectra for 0D cuprates are governed only by the intra-center transitions. In Fig. 2 we reproduce the low-energy absorption spectrum for 0D cuprate CuB2O4 [12] which is most likely formed by dipole-forbidden b1bg b2bg , a1bg , egb ) (crystal-field d d ) and b b1g a2g , eu ( ) ( p d ) transitions. Unlike most 1D and 2D cuprates where the low-energy absorption bands are broad and featureless, the absorption spectra for a true 0D cuprate CuB2O4 provide a remarkable opportunity to observe a ”fine structure” of low-energy forbidden transitions. The experimental spectrum shows up a number of narrow zero-phonon peaks with up to the seventy well-resolved phonon sidebands [12] imposed on a rather broad band near 2 eV. It is worth noting that the absorption coefficient for 2 eV band is very small and corresponds to the dielectric function 2 of the order of 0.01. It might be surprising that among the best candidates for the ”optically” 0D cuprates are such systems as Li2CuO2, LiCu2O2, LiVCuO4, or
Fig. 2. Low-energy absorption spectra for 0D cuprates: Left panel:CuB2O4 (k z, E z ) [12]; CuGeO3 [13]. Right panel: absorption coefficient for CuGeO3 at higher energy [14]. 246
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Fig. 3. Left panel: Optical conductivity of Li2CuO2 [15](E chain ). Right panel: low-energy part of the EELS spectrum of CuGeO3 [16]. Inset shows an imaginary part of the pseudodielectric function of CuGeO3 [14].
4.1 eV, which is dipole-allowed in the out-of-plane polarization. Experimental data available for another edge-shared system, Li2CuO2 [15,17] is not enough to arrive at any decisive conclusion. Most likely the optical [15] (see Fig. 3) and EELS [17] data evidence a rather small ( 0.5 eV) eu ( ) -eu ( ) separation as compared with CuGeO3 and a net redshift of the eu ( ) -eu ( ) quartet to 3–4 eV. Both low-energy intracenter and numerous nn as well as the nnn inter-center CT transitions with the spectral onset at 1.5 eV appear to be hidden in the tails of the nonvanishing spectral weight of the main CT bands. A more dramatic situation has been uncovered in a mixed valent Cu1+-Cu2+ 1D cuprate LiCu2O2, where all the spectral range 1–6 eV is dominated by anomalously strong dipole allowed intra-atomic 3d – 4p transition in Cu1+ ions [19] peaked at 3.26 eV (see Fig. 4). It is worth noting that in Ref. [20] this huge peak was ambiguously ascribed to a conventional intra-center p d CT transition. However, comparing the corresponding values of the optical response for Li2CuO2 and CuGeO3 with that of LiCu2O2 we do unambiguously reject such assignement. Peak values of imaginary part of the dielectric function
Fig. 5. EELS spectra in Sr2CuO3 for longitudinal q a (left panel) and transversal q b (right panel) response with an illustration of intra- and inter-center excitons.
and optical conductivity in LiCu2O2 are an order of magnitude greater than the corresponding values determined by the edge-shared CuO4 plaquettes in cuprates with a single type (Cu2+) of copper ions. 4.1.1. Polarization dependent EELS spectroscopy of 1D copper oxide Sr2CuO3 and separation of the intra- and inter-center CT excitons In contrast to optics, the angle-resolved EELS spectroscopy provides unique opportunities to reveal the exciton dispersion and separate the intra- and inter-center CT excitons. The one-dimensional cuprate compounds are good candidates for such a study since the scattering of electrons with a transferred momentum q perpendicular to the chain direction excites only the EH pairs sitting on a single CuO4 plaquette. On the other hand, for q parallel to the chain direction, the both types of excitons (intra- and inter-center) can be observed. The EELS spectra for Sr2CuO3 in ”longitudinal” response with the transferred momentum oriented along the chain direction were measured earlier in Ref. [21] and have been interpreted within standard Hubbard models. However, such models can describe properly only the ”longitudinal” response with the transferred momentum oriented along the chain direction. The EELS spectra for Sr2CuO3 in both polarizations are presented in Fig. 5 [22]. Their comparison leads to very important conclusions. We see a drastically strong difference between the two sets of spectra. First, this concerns the well-defined dispersionless EELS peaks at 2.0 and 5.5 eV in transversal polarization (right hand side panel in Fig. 5). The intensity considerations and the absence of noticeable energy dispersion allow us to associate them with dipole-allowed CT transitions having a particularly localized nature. Moreover, when comparing the both spectra we see that despite the strong inequivalence of longitudinal and transversal polarizations in Sr2CuO3 the low-energy transition peaked near 2 eV is equally present in both polarizations. Though for longitudinal polarization this is partly hidden for low momentum values by the intensive band peaked at 2.6 eV and is seen as a shoulder, near the BZ boundary it is a well-separated weak band due to a large blue shift of the intense neighbor. This fact implies that the excitation is
Fig. 4. (Color online) (a) Low temperature (T = 26 K) spectra of the real 1 (open circles) and imaginary 2 (solid circles) parts of the dielectric functions in LiCu2O2 for the light polarized along the x axis and their fit with the set of Lorentz oscillators (lines) [19]; (b) the positions of the main Lorentz oscillators in the 2xx spectra. Inset: Optical conductivity spectra at T = 26 and 300 K (solid and open circles). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 247
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localized on a single CuO4 plaquette being the only common element of longitudinal and transversal geometry in this 1D cuprate with the corner-shared CuO4 plaquettes. Hence, by taking into account the intensity ratio we can unambiguously identify the 2.0 and 5.5 eV peaks in the EELS spectrum of Sr2CuO3 with the intra-center CT excitons eu ( ) and eu ( ) , respectively. So, for the polarization perpendicular to chain direction, the 1D cuprates such as Sr2CuO3 provide the optical and EELS response typical for a 0D system. Contrary to CuBi2O4, the both dipoleeub, a transitions in Sr2CuO3 manifest themselves more allowed b1bg distinctly with well-defined EELS-peaks at 2.0 and 5.4 eV, respectively. The corresponding peaks in optical conductivity are situated at 1.8 and 4.3 eV, respectively. One should note that the EELS data present a straightforward experimental manifestation of the dipole-allowed intracenter b1bg eub, a excitations without the ”parasitic” effect of the intercenter transitions. Large spectral weight and sizeable dispersion of the most intense low-lying CT exciton peaked in EELS at 2.6 eV agree with its inter-center nature. Thus, we have shown that the polarization-dependent angle-resolved EELS study of the 1D cuprate Sr2CuO3 with the corner-shared CuO4 plaquettes provides a unique opportunity to separate both intraand inter-center CT excitons as well as two types of intra-center CT excitons [23]. Furthermore, for the first time, we unequivocally demonstrated the important role of the O 2pπ-holes in determining lowenergy excitations in cuprates. In this regard, we would like to emphasize once more the decisive role of direct EELS measurements in the observation and unambiguous assignment of the intra- and inter-center excitons in Sr2CuO3 as compared with conventional indirect optical data.
Fig. 6. The spectral dependence of the imaginary part of dielectric function ( ) for Sr2CuO2Cl2. Arrows mark the predicted energy position of intra-center, inter-center b12g -channel, and b1g eu -channel CT transitions. Inset: optical conductivity in Sr2CuO2Cl2 [24].
in energy b12g transition with ZR-singlet as a final hole state, while the more intense high-energy b1g eu ; dp transition is blue-shifted by 5.0 eV with regard to the same transition. The most intense CT transition in this quartet with the b1g eu ; pp final state is expected to have the maximal energy ~13 ÷ 14 eV among all the CT transitions governed by the strong σ bond.
4.2. CT transitions in 2D insulating cuprates In 2D systems, we usually deal with spectra representing the superposition of both types of excitons, which makes the problem of separating different transitions rather complicated. Thus, some uncertainty remains regarding the reliable identification of two dipoleallowed intra-center CT excitons and seven main inter-center CT excitons, which may cast doubt on their existence as well-defined states. Unfortunately, this concerns also the structure of the low-energy optical response observed in the spectral range 2 ÷ 3 eV, which is of a special importance since it is associated with the states which are believed to mainly define the unconventional properties of the cuprates. However, making use of the theoretical predictions, justified and supported by numerous experimental data for 0D and 1D cuprates, we can establish an overall picture of optical and EELS spectra (at the -point). These spectra are governed by dipole-allowed intra- and inter-center CT excitations and include:
We verified all these predictions for Sr2CuO2Cl2 to be one of the best realizations of a 2D antiferromagnetic insulating model cuprate. In Fig. 6 we present the spectrum of the imaginary part of dielectric permittivity derived from the Kramers-Kronig transformation of the EELS data [5,25]. Remarkably, all the excitations which were analysed before correspond to visible features in 2 . The weak low-energy feature near 2.2 eV in the EELS spectra (2.0 eV in 2 and optical conductivity) eu ( ) could be ascribed to the lowest in energy intra-center b1bg transition. This feature occupies the tail of a rather intensive band peaked at 2.7 eV in EELS spectra (2.4 eV in 2 and optical conductivity). b1g This band is naturally associated with the lowest in energy b1bg inter-center CT transition with ZR-singlet as a final hole state. Its energy is of a particular importance for the whole set of inter-center transitions. Having positioned the lowest intra- and inter-center excitons, the higher states are fixed by the chosen parameter values (see Fig. 6). Two features in EELS, near 4.2 eV and 7.1 eV could be related to inter-center b1g eu ; dp and b1g eu ; dp transitions, respectively, while the broad band near 6.0 eV in EELS could be naturally assigned to the intra-center b1bg eu ( ) transition, whose energy is slightly higher than that of its two-hole counterpart. The spectrum of the most intense transitions generated by the Cu 3d-O 2p σ transfer ends with very strong features near 9 ÷ 10 and 12 ÷ 13 eV in the EELS spectrum, which can definitely be associated with high-energy inter-center b12g ; pp CT transition with a Zhang-Rice singlet type final hole state of predominantly pp configuration, and the transitions to the b1g eu ; pp and b1g eu ; pp final states, respectively. All this shows that important spectral information is contained in the range above 8 eV. The peak at about 18 eV is likely to be attributed to transitions with O 2s initial state. The interpretation of EELS spectra for nonzero momentum becomes more complicated due to the energy and intensity dispersion of the dipole-allowed modes and the appearance of numerous new modes which are forbidden at the -point. Hereafter, we focus only on angleresolved EELS spectra in the spectral range up to 8.0 8.5 eV for several
eu ( ) trani) the lowest in energy (1. 5 ÷ 2. 0 eV) intra-center b1bg sition with a rather small intensity due to the predominantly O 2p nature of the final state and a strong tendency to self-localization (trapping); ii) the high-energy ( 5.0 eV) and rather intensive intra-center b1bg eu ( ) transition; iii) within the b12g -channel we predict the three inter-center CT transitions: 1) the lowest in energy (2. 0 ÷ 3. 0 eV) and relatively intense transition with the ZR-singlet as a final hole state; 2) the most intense high-energy transition with the ZR-singlet-like final hole state blue-shifted to 7.0 eV; and 3) the less intensive transition blueshifted to 5.0 eV with regard to the first one; iv) within the b1g eu -channel we predict the two doublets of inter-center CT transitions, generated by the CT to eu ( ) and eu ( ) orbitals with smaller and larger weight of O 2pσ orbitals, and shifted by 6.0 eV with regard to each other. The high-energy doublet is relatively more intense. The transitions within each doublet are shifted by 3. 0 ÷ 3. 5 eV with regard to each other. The low-energy b1g eu ; dp transition is blue-shifted by 1. 5 ÷ 2. 0 eV with regard to the lowest 248
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momentum values in [100] and [110] directions, obtained by Wang et al. [26] and by Fink et al. [27,28] The spectra differ somewhat by the maximal momenta values and the considerably better resolution in the latter case. The low-energy part of the EELS spectra in the 2D system Sr2CuO2Cl2 along the [110] direction and the longitudinal spectra in the 1D system Sr2CuO3 have a very similar structure up to some quantitative coincidence. For the both compounds the main spectral feature is associated with an intense band assigned to the inter-center b12g exciton, or so-called Zhang-Ng (ZN)-exciton, with a clear dispersion extending from 2.6 eV near the -point to 3.0 eV near the BZ boundary [26,29]. In both systems this band has the low-energy shoulder near 2.0 eV which is distinctly seen in the -point or near the BZ boundary. This two-peak structure of the CT band in Sr2CuO2Cl2 and isostructural Ca2CuO2Cl2 is corroborated by conventional optical measurements [24,30–32]. The EELS spectra along the [100] direction manifest an expected overall drop in intensity with relatively small energy dispersion. In contrast to the [100] direction, the main peak for the [110] direction of Sr2CuO2Cl2 exhibits clear signatures of strong dispersion, particularly for momentum values in the range (0. 5 ÷ 0. 7) kmax . Namely this effect was a starting point for the model theory of the CT excitons by Zhang and Ng [26,29]. However, in our opinion, here we deal with an unconventional behavior of the intensity dispersion for different excitons with the peculiarities especially in the momentum range (0. 5 ÷ 1. 0) kmax rather than with the strong energy dispersion of the ZN-exciton. Indeed, as it was emphasized above, the intensity of the main peak in the low-energy part of the EELS spectrum for Sr2CuO2Cl2, assigned to the dipole-allowed exciton associated with the b1bg b1g inter-center CT transition with the ZR-singlet as a final hole state, sharply decreases with the increase of momentum along [110] direction with a probable compensation point near the BZ boundary. This circumstance allows to clearly observe a sharp rise of the spectral weight in a rather broad range with the well-defined peak in EELS near 3.8 eV. This spectral feature may be unambiguously associated with the dipole-forbidden Ag counterpart of the inter-center b1g eu ; dp exciton, which is allowed and rather intensive at the ( , ) point. Interestingly that the result of this specific behavior of the EELS intensity for different excitons might be mistaken for manifestation of the energy dispersion of the main peak associated with the g u dipole-allowed inter-center b12g exciton, as it was made by Wang et al. [26]. Obviously, this error led to the conclusion that there is a very large ( 1.5 eV) energy dispersion for this exciton. The real energy dispersion for different CT excitons in our opinion may not exceed the reasonable values of the order of 0.5 eV. Thus, the overall analysis of the experimental EELS spectra in the model 2D insulating cuprate Sr2CuO2Cl2 allows us to certainly assign a set of distinctly observed features in a rather wide spectral range 2. 0 ÷ 14. 0 eV to the predicted intra- and inter-center CT excitons, and confirm the validity of the theoretical concept based on the embedded CuO4 cluster model. A close examination of other materials shows that the two-component structure of the CT gap appears to be a common place for all parent cuprates with the corner-shared CuO4 plaquettes (see e.g., Refs. eub excitation within the [32–36]). The dipole-allowed localized b1g CuO4 plaquette related essentially to the eu ( ) state is distinctly seen in optical and EELS spectra for different insulating cuprates as a separate weak feature or a low-energy shoulder of the more intensive band near 2.5 eV assigned to the inter-center CT transition associated with the ZRsinglet-like excitation b12g ; pd . Both components are characterized by a different coupling to the magnetic and phonon subsystems thus providing additional ways to separate them. Generally speaking, the CT exciton creation is usually accompanied by an excitation of lattice modes. Indeed, the hole transfer from Cu 3d to O 2p state, or from an ionic to a covalent configuration is accompanied by a significant shortening of the equilibrium CueO bond length. The exciton-phonon interaction strongly influences the line shape of absorption and results in a phonon Raman scattering. The
measurement of the Raman intensity as a function of excitation light energy is a very informative probe of the origin of electronic transitions [37]. In particular, this method has allowed [38] to resolve a fine structure of the low-energy (LE) excitonic feature in La2CuO4 with a sharp peak at 2.14 eV as narrow as 50 meV and a broader structure at 1.9 eV. In our opinion, such an unusual behavior of the LE exciton could eu transition be associated with its Jahn-Teller nature. Indeed, the b1g to the orbital doublet eu represents a textbook example of a so-called A E transition [39]. The excited, orbitally degenerate eu state is unstable with regard to vibronic coupling with the local distortion modes A1g , B1g , B2g , Eu and the formation of a polaron-like (soliton-like) vibronic center with a complex two- or four-well adiabatic potential and a rather strong renormalization of vibration frequencies. In other words, the doublet eu state tends to a spontaneous local symmetry breaking, including removal of the inversion center due to interaction with the close in energy even states and pseudo-Jahn-Teller effect. Namely the eu exlatter would result in a strong resonance coupling of the b1g citon with odd Eu lattice modes. Naturally, the structure of such a center would strongly depend on differences in the bare lattice and elastic parameters and differ in 214 and 123 systems. One should emphasize that the formation of the heavy polaron-like, or localized small exciton would result in a strong enhancement of its effective mass. For small intra-center excitons we have a rather conventional s = 1/2 s = 1/2 transition with spin-density fluctuation localized inside the CuO4 plaquette. Such a transition is not accompanied by strong two-magnon (2 M) Raman processes, that could be used to identify this type of excitons. The redistribution of spin density from the eu transition switches on copper atom to the oxygen ones for the b1g the strong ferromagnetic Heisenberg O 2p-Cu 3d exchange with the nearest-neighbor CuO4 plaquettes. Interestingly, the different sign of exchange coupling for eu and b1g holes with the same neighborhood, ferromagnetic for the former, and antiferromagnetic for the latter, leads to a number of temperature anomalies near the 2D-3D antiferromagnetic phase transition. There is, firstly, the blue-shift effect for eu by lowering the the energy of the small intra-center exciton b1g TN , the average moletemperature near and below TN . Indeed, at T cular field for the CuO4 center turns to zero. The 3D antiferromagnetic ordering is accompanied by a rise of exchange molecular fields and respective spin splittings. Due to the different signs of molecular fields for eu and b1g states this is accompanied by an increase of the transition (|Hb1g | + |Heu |) . This energy with maximal value of the blue shift quantity could be as large as several tenths of eV. Additionally, one has to expect a strong (of the same order of magnitude) broadening of the excitonic line with increase of the temperature due to strong fluctuations of molecular fields. All these expectations are experimentally found for the 2.0 eV line in Sr2CuO2Cl2 [24] confirming its intra-center excitonic nature. A similar situation is observed in La2CuO4 [34] although the authors have explained the data by assuming a polaronic nature of electrons and holes with a short-range interaction in between. 4.3. CT transitions in copper monoxide CuO Copper oxide CuO has been actively studied both experimentally and theoretically as a prototype model system for the semiconducting phase of the copper-oxygen high-temperature superconducting (HTSC) systems. This monoclinic (C2h6 ) [40] cuprate has a very narrow phase homogeneity range and is robust with regard to different chemical doping used to reach the insulator-to-metal transition in parent cuprates such as La2CuO4, YBa2Cu3O6. Despite this the CuO single crystals exhibit many features typical for a wide family of nominally pure or slightly doped parent cuprates. Below TN1 231 K CuO has antiferromagnetic ordering: the noncollinear one in range 213 ÷ 231 K and the collinear one below TN2 213 K with spins, ordered parallel to baxis. First detailed studies of optical absorption of nominally pure 249
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Fig. 7. Left panel: Absorption spectra of single-crystalline CuO samples before and after irradiation by high-energy electrons and He+ ions [43,44], insets show a typical MIR spectrum and temperature dependence of the absorption coefficient variation K (T ) = K (T ) K (T = 80 K) at 3.13 eV for a single-crystalline CuO sample, respectively. Right panel: Typical absorption spectrum of nanocrystalline CuO samples [46], inset shows a remarkable temperature-dependent ”peak-diphump” feature near 1. 3 ÷ 1. 6 eV for a sample with 60 nm grains.
stoichiometric single crystalline CuO samples, as well the samples, exposed to the fluence of the neutrons, electrons, He+-particles, and high density polydisperse CuO nanoceramics were performed by Russian group [41–46]. Several results are summarized in Fig. 7. The behavior of intra- and inter-center excitons in monoxide CuO [41,42] has some specific features due to the low (monoclinic) crystal symmetry which makes difficult their unambiguous assignement. A fine structure near 1.7 eV was assigned to a weakly dipole allowed intra-center p d (b1g eu ( ) ) CT exciton. The final eu ( ) -hole state is split into two components with markedly differing inter-chain eu ( ) b1g exchange, and the respective CT bands show markedly different temperature behavior [42]. To the best of our knowledge, it was the first indication of an optical manifestation of low-lying nonbonding O 2pπ states. Band peaked near 3.13 eV was assigned to a weakly dipole allowed intracenter p d (b1g b2u ( ) ) CT exciton, however, a remarkable temperature dependence of its absorption coefficient near magnetic phase transitions (see inset in Fig. 7, left panel) agrees also with its intercenter d d CT origin, if account for a specific temperature dependence of the spin correlation factor for the incommensurate spin phase. The low-energy absorption spectra of the single crystalline CuO samples reveal a well developed mid-infrared (MIR) band which has the structure typical for other insulating cuprates. Such a band is believed to represent something like a superposition of the magnetic excitations within the antiferromagnetic background and a contribution of the selftrapped CT excitons and the EH droplet phase. As in the case of non-isovalent chemical substitution in other cuprates, the accumulation of the defects under the irradiation in a nanocrystalline state leads to the red shift of the spectral weight with a characteristic evolution of the MIR band evidencing the rise in the EH droplet volume fraction. Two bands, rather narrow one with a peak near 0.1 eV and the second broader one with a peak near 0.2–0.3 eV are the most common features of the MIR band. These may be assigned to the low- and high-energy dipole allowed CT transitions within a selftrapped inter-center two-particle d d CT exciton. In addition, all the CuO samples with well developed MIR bands exhibit a remarkable 1.3 eV peak which may be attributed to the inter-center one-particle d d CT transition with the EH-recombination in the EH-droplets. Note that this peak was earlier on assigned to the surface plasmon (Mie) resonances due to a small volume fraction of metallic-like nanoscale EH droplets with Drude optical response embedded in the bare insulating medium [41,46]. Ellipsometric measurements of single-crystalline CuO samples in the region 2–4 eV [14] have revealed the strongest CT band peaked near 3.5 eV that can be assigned to a dipole-allowed b1bg eu ( ) p d CT transition. As for other cuprates the CuO RIXS spectroscopy [11] reveals a wide band peaked near 5 eV attributed to bonding-antibonding b1bg b1ag , b2ag , a1ag , ega CT transitions.
5. Conclusion Starting with the predictions of a simple cluster model theory we were able to give a semi-quantitative description of the experimental optical and EELS spectra for a large variety of nominally insulating cuprates with the CuO4 plaquettes to be a main building block of their crystal and electronic structure. These include monooxide CuO, parent quasi-2D cuprates La2CuO4, Sr2CuO2Cl2, YBa2Cu3O6 with a 2D arrangement of the corner-shared CuO4 plaquettes, their 1D counterpart Sr2CuO3 with a chain 1D arrangement of the corner-shared CuO4 plaquettes, Li2CuO2, LiCu2O2, CuGeO3 with a chain 1D arrangement of the edge-shared CuO4 plaquettes, and exotic 0D system CuB2O4 with the well isolated CuO4 plaquettes. Both different experimental data and theoretical analysis show that the nature of the CT gap in insulating 1D and 2D parent cuprates is determined by the nearly degenerate in energy intra-center p d and inter-center d d CT excitons. The former is associated with the hole eu ( ) from the Cu 3d-O 2p hybrid b1g d x 2 y2 state CT transition b1g to purely oxygen O 2 p state localized on the CuO4 plaquette, while the b1g CT transition between neighboring plaquettes latter does with b1g with the ZR singlet to be the final two-hole state. The structure of the optical gap with the two well-defined CT excitons seems to be typical for a wide group of parent cuprates that implies a revisit of some generally accepted views on the electronic structure both of the 1D and 2D cuprates including the nature of the superconducting state in these systems. Rather simple quantum-chemical CuO4 cluster model represents a physically clear albeit rather simplified approach to consider EH excitations in cuprates. However, it seems such an approach allows to catch the essential physics of the CT transitions, and should be a necessary step both in qualitative and semi-quantitative description of insulating cuprates. Declaration of interests The author declare that he have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement I acknowledges the stimulating discussions with R. V. Pisarev, B. B. Krichevtsov, N. N. Loshkareva, Yu. P. Sukhorukov, S.-L. Drechsler, and R. Hayn. Special thanks to Prof. G. J. Babonas for sending unpublished experimental data. Supported by Act 211 Government of the Russian Federation, agreement 02.A03.21.0006 and by the Ministry of Education and Science, projects 2277 and 5719. 250
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A.S. Moskvin
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