J. Phys. Chem. Solids Vol. 53, No. II, pp. 1433-1447, 1992 Printed in Great Britain.
W22-3697/92 $S.OO + 0.00 0 1992 Pergamon Press Ltd
ELECTRONIC STRUCTURES OF C,, C,, AND THE FULLERIDES: PHOTOEMISSION AND INVERSE PHOTOEMISSION STUDIES Department
J. H. WEAVER of Materials Science and Chemical Engineering, University of Minnesota, Minneapolis, MN 55455, U.S.A. (Received 16 February 1992)
Abstract-This paper reviews the electronic structures of solid C, and C,Oas measured using optical and electron spectroscopies. It discusses Li, Na, K and Rb doping of C, as well as K doping of C,O. It also discusses alkaline earth doping of C,. Keywords: Fullerenes, fullerides, electronic structure, correlated systems.
1. OVERVIEW In the following paper, we examine the electronic structure of C, and C,, in solid state form and in the form of fullerides produced by mixing with alkali and alkaline earth metals. The emphasis is on insights offered by photoemission and inverse photoemission but optical absorption will also be discussed. Quantitative information about the electronic states is important for isolated fullerenes because the distribution of those states serves as a test of the molecular and solid state structures and the ability of theory to describe these novel carbon-based systems. The state distribution is especially important in understanding the fullerenes in condensed form because of solid state effects, bonding, and band formation of these narrow band molecular solids. Investigations of the electronic states formed by mixing C, with other atoms are critical because they show the way that C, bonds to these atoms in the solid state. For example, experimental and theoretical investigations for K, C, have demonstrated electron transfer to the fullerene, occupation of the LUMOderived band, and ionic compound formation, but relatively little modification of the fullerene orbitals [14]. For the alkaline-earth fullerides, more covalent bonding is observed [7]. For doping with iodine, a possible p-type dopant, there is very little charge transfer [8]. In each case, a detailed investigation of the elctronic states tests our ability to understand cohesion, compressibilities, electron transport, and optical absorption. Knowledge of the distribution of electronic states and their character near EF is crucial for elucidating the mechanisms of superconductivity.
Additional insight into fullerene interactions comes from spectroscopic studies of fullerene bonding to surfaces [9]. Since bonding reflects coupling to electrons of the molecule, the distribution of states and the extent of hybridization can be obtained by electronic structure studies. Such studies are critical for those interested in adsorption, thin film formation and surface-moderated reactions. While space precludes a discussion of such bonding, we refer the reader to the detailed paper by Ohno et al. [9] in which C, bonding to metal and semiconductor surfaces was examined. Here we note that the experimental results for a wide range of substrates demonstrate Fermi level alignment, the formation of an interface dipole, and substrate coupling that reflects a n-resonance. The extent of the dipole depends on the work function of the metal. For Cm growth on n-type GaAs, the dipole represents the transfer of only 0.02 electrons per molecule. The overlayer growth structures will reflect the strength of these interface interactions, but relatively little is known about the details [9, lo]. The techniques of photoemission have been discussed in a number of excellent review articles [1 11. Since photoemission is one of the most frequently used analytical techniques, it is not surprising that some of the earliest studies of fullerenes used photoelectron spectroscopy. Inverse photoemission is less well known but it too is a mature spectroscopy [12]. Most photoemission and inverse photoemission studies of Cso have examined films that were thick enough that substrate contributions were negligible. The exceptions have been studies that emphasized adsorption and bonding [9]. Suitable films have been grown by condensation of Cso sublimed from thermal
1433
J. H. WEAVER
1434
isolated %I (Nfl electrons)
solid
CL30 ground state %I (N f 1 (N electrons) electrons)
Fig. 1. Energy level picture for an isolated C, molecule identifying the ionization potential and electron affinity. Those levels are shown to be screened by solid state effects but the separation between HOMO and LUMO (3.7 eV in the solid) states reflect the (N * 1) electron molecular state. In the N-electron ground state, the HOMO-LUMO separation is substantially less.
surface faceting, defects, and grain boundaries that were sensitive to growth conditions. These structural complexities do not introduce the equivalent of deep levels that pin the Fermi level, as would be the case for conventional semiconductors. This is consistent with the molecular character of the solid and van der Waals bonding. More recent studies have sought to grow larger grains. In photoemission, a photon of energy hv induces electron excitation from an initial state to an empty state. In the independent-particle description of photoemission in a solid, a measurement of the photoelectron energy would yield the energy of the initial state. If the transition matrix elements from initial to final states are constant, then the photoemission spectrum would reproduce the distribution of occupied states, i.e. the density of states. The inverse photoemission process represents the addition of an electron to the system at an energy E, above the Fermi
sources. In the early spectroscopic studies, the substrates have been close to room temperature during condensation, so that the thin film microstructures probably resemble those discussed by Li et al. [lo] based on their STM investigations. They showed grains of tens to hundreds of Angstroms in size with
hv
e’
level. That
state decays
radiatively,
and the
emitted photon is detected. The distribution of photons replicates the density of conduction band states
in the independent-particle, constant-matrix-element picture. Even in the independent-particle picture there are differences in cross-sections (matrix elements) for the various states so that a given
8 = 5 2.0 1.5
r”
-
-N-
$0
B z 0
0.5 0
0
1
2
3
4
5
6
Energy (ev) W+l)
W-1)
11 -5
I,
0
0
I-
8’s
E,
1
+5
Energy (eV)
Fig. 2. Schematic showing an electron or photon beam incident upon a solid of C,. An electron-hole pair can be created on a molecule by photon absorption or by an electron energy loss process. Such molecular absorption dominates the optical properties and EELS spectra for C,. The results for C, in decalin and solid C, demonstrates the persistence of molecular absorption structure in the solid state (from Eklund et al. [21]). In contrast, photoemission produces a molecular N - 1 electron system and inverse photoemission produces a molecular N + 1 electron system. The separation in energy of HOMO and LUMO of 3.7 represents the N f 1 states. For optical absorption, the lowest energy process involves the creation of an exciton at 1.6 eV. This differs from the N + 1 states by an energy equal to the Hubbard U. -2eV.
Electronic structures of C, and C,O experimental spectrum should not be taken as replicating the density of states [13-181. For the fullerenes, the independent-particle picture encounters problems because the bands are narrow and electron correlation effects are large. This is easily seen from combined photoemission/inverse photoemission studies because these spectroscopies produce (N - 1) and (N + 1) final states by removing or adding an electron. The importance of correlation is most obvious in measurements of the band gap of the condensed fullerenes. Figure 1 depicts the energy levels of C, in the molecular state referenced to the vacuum level. Electron removal yields the ionization potential (IP) and electron addition yields the electron affinity level (EA), producing ionized final states that are then (N - 1) and (N + 1) states. Condensation of the molecules introduces extra-molecular screening so that the separation in energy of EA and IP diminishes. In the independent-particle picture, the wavefunctions describing these states would be sufficiently extended that delocalization would occur, giving a broad band. Electron removal from this band of width W would not have an appreciable effect on the energy level spectra. If the wavefunctions are only weakly delocalized in the solid state, then the band is narrower and the energy needed to remove an electron from one molecule and place it on another is appreciable. This energy corresponds to the Hubbard U. When U is comparable to W, the system is described as being highly correlated [ 191.For conventional (uncorrelated) systems such as Si, the EA and IP would define the conduction band and valence band edges. For correlated systems such as the fullerenes, the measured gap includes the energy U. Note that ground state calculations will yield the energy level spectra for the N-electron system, depicted at the right of Fig. 1. The energy 3.7 eV from the (N + 1) systems in solid C, is the center-to-center energy for the HOMO- and LUMO-derived bands. Figure 2 depicts a collection of C, molecules being illuminated by a photon or electron beam of energy hv. Photon absorption will induce a dipole-allowed excitation, promoting an electron (-) to a higher energy state and creating a hole (+). For the molecule in the upper right, the electron and hole are bound to one another. We term this ‘on-ball’ or molecular excitation. The importance of such on-ball excitations is clear from comparison of optical properties measured for C, in the condensed phase and in solution or in the gas phase [20,21]. The optical absorption spectra at the right of Fig. 2 show such results for solid C, and C,, in decalin from Eklund and coworkers [20]. All such studies show three strong absorption features at about 3.6, 4.6 and
1435
5.8 eV, as first shown by Kriitschmer et al. [20]. The conclusion, then, is that photon absorption produces localized on-ball structures that can be understood in terms of molecular excitations, with very little dependence on the surroundings. It is important to recall the calculations by Rosen and coworkers [22] that examined optical transitions for a large number of molecular configurations, finding good agreement with experiment. The compelling similarity between results for isolated Cm and solid Cso emphasizes the dominant molecular character of the optical structures. At the same time, solid state effects contribute to broadening and background absorption and account for the onset near 2.5 eV. In solid C,, electron-hole bound pairs can hop, behaving like Frenkel excitons. They can also dissociate, producing N + 1 and N - 1 states depicted in Fig. 2, provided the excitation energy is sufficient to produce these states when it decays. The lowest energy excitation for Cso is dipole forbidden, producing an electron in LUMO and a hole in HOMO, but is weakly allowed in the solid, appearing at = 1.6 eV [20,21]. This exciton cannot dissociate and probably decays by direct recombination on the molecule. Figure 2 also depicts the case in which the electron and the hole are on separate molecules. Photoemission produces hole states and inverse photoemission produces electron states, as does the decay of high energy molecular excitons or any process that injects carriers. In all cases, the narrow band molecular character of Cso must be considered when examining the energy level of these N + 1 states. (The production of a separated electron and hole from an exciton requires N 2 eV, the correlation energy of the Hubbard model.) The energy distribution of the electron and hole states follows directly from photoemission (N - 1 state) or inverse photoemission (N + 1 state), as reproduced at the lower left of Fig. 2 from Benning et al. [17]. The energy reference is the Fermi level. As shown, the HOMO-LUMO gap for these states is much greater than the optical absorption (exciton) edge or the gap predicted by various calculations [S, 6, 18,22-261. In the following, we will tacitly assume that all initial state features are shifted relative to the Fermi energy, Er, by the same amount in the (N - 1 electron) final state. We will also assume that all features in the (N + 1 electron) final state are shifted the same amount. Thus, the creation of an electron or hole in a molecular-orbital-derived state produces a rigid shift, regardless of the particular occupied or empty state. This assumption is supported by the fact that the wavefunctions are delocalized on the molecule but have similar spatial extents. Comparison to ground state band calculations should be correct to
J. H. WEAVER
Relative
Energy (eV)
Fig. 3. Photoemission and inverse photoemission processes depicted by electron removal and electron addition producing (N f 1) states. The experimental results reveal the distribution of occupied and empty electronic states of C,, referenced in energy to the Fermi level. The theoretical density of states at the bottom is referenced to the feature nearest Er. The HOMO-LUMO separation is 3.7 eV. The minimum energy needed to produce a separated electron and a hole is 2.6 eV, compared to N 1.6 eV needed to induce the lowest energy molecular excitation in which the electron and hole form a bound pair. when energies are referenced to HOMO or LUMO. This approximation appears to be sufficiently accurate that direct comparison to band calculations can be made. Although the various calculations reflect strengths and weaknesses of the basis functions and calculational schemes, most provide a good facsimile of the photoemission spectra, [5,6, 13, l&22-26] agreement that supports the comparison to experiment. first order
2. C,, C, ELECTRONIC
STRUCTURE
(A) Cw valence and conduction bands Figure 3 provides an overview of the distribution of states for solid C, showing the full valence bands and the conduction bands within 15 eV of EF. Additional spectra and greater detail can be found in Refs 13-15 (see also Ref. 27). The photoemission spectra were obtained with synchrotron radiation with hv = 65 and 170 eV. In general, spectra acquired with low energy photons emphasize the n-states of the fullerenes over the a-states [ 131 while those at higher energy show the growth of the latter. These spectra are referenced in energy to the Fermi level which lies 2.25eV above the center of the HOMOderived band in the (N - 1) electron final state. The IPES spectra of Fig. 3 were obtained with incident electron energies of 19.25 and 32.35 eV [28]. Again, the spectra are referenced to the Fermi level
which lies 1.5 eV below the center of the LUMO band of the (N + 1) electron final state. The IPES spectra are scaled so that the intensity of the LUMO feature is 3/5 the intensity of the HOMO feature. This is the intensity ratio expected from the degeneracies of the two sets of 71,bands [26], but both photoemission and inverse photoemission are affected by matrix elements and neither gives the true density of states. The lower panel of Fig. 2 showed equivalent results for the bands nearest Er. Most of the experimental results reported to date [14,13-17,27,30-321 show good agreement with those of Fig. 3, despite differences in preparation conditions for films thick enough that substrate effects were negligible [9]. We speculate that the position of the Fermi level in the gap is related to H-induced states for H bonded to C,, a common impurity as shown by neutron scattering [29]. One notable exception has been reported by Takahashi et al. [30], where LUMO was much closer to EF. While we have no explanation for their results, we note that impurities in the CM film tend to pin Er closer to LUMO. We also note that charging effects can be important for thick films or for low temperature measurements because of the high intrinsic resistivity of the films. Such effects introduce rigid shifts to greater energies relative to Er but no such effects are important under the measurement conditions used in the experiments discussed here. Finally, we note that caution should be exercised in studies using a high flux, high energy electron beam because it quickly produces a graphite-like carbon surface. (In our studies with 3 mA cm-‘, 1500 eV electrons, we found rapid C, deterioration.) Isolated C, molecules are known to photofragment by dimer loss with an activation energy of - 18 eV, but little is known about the mechanism for destruction in condensed films. For C,, the energy separation between the centers of the HOMO- and LUMO-derived bands is 3.75 eV, as shown in Fig. 3. For a conventional semiconductor, the extrapolation of the leading edges of the valence and conduction band emission to zero intensity would give the band gap. The threshold energy of 2.6 eV (obtained by leading edge extrapolation) would correspond to the minimum energy needed to create a separated electron and hole. This should be close to the transport gap for pure Cm. Transport at lower energy is probably The
electronic
indicative
structure
calculated by several groups generally finding a bandwidth of N 20 eV. Martins et al. distribution of empty states bands in the energy range
of impurities.
Cm has been [5,6, 13, 15, l&22-26], for the occupied states [ 15, 181 calculated the as well, finding * 250 from the base of the
of solid
Electronic structures of C, and C,,, valence band to 15 eV above the conduction band minimum. The bottom curve of Fig. 3 reproduces their calculated densities of states based on their soft pseudopotential local-density method [18]. The structure of the solid was assumed to be fee with one molecule per unit cell and the tetrahedral space group Ti (Fm3). The geometry was optimized using quantum mechanical forces, yielding C-C bond lengths of 1.382 and 1.444 A. The wavefunctions were expanded in a basis set containing all plane waves with energies smaller than 49 Ry; this corresponds to convergence in the total energy to within 0.05 eV per atom. For a molecular crystal with such a small Brillouin zone as C, and small band dispersion of the occupied states, the self-consistent potential can be calculated using the single k-point I to sample the Brillouin zone. For a more accurate sampling, two special k-points have been used to calculate the density of states. Such sampling was required for a description of empty states that have noticeable dispersion. The theoretical density of Fig. 3 was obtained by broadening the discrete energy levels with a Gaussian having a width that scaled in energy as 0.23 eV + 0.021El. This was done to simulate effects related to the experimental energy resolution and lifetime broadening although vibronic broadening is also important [27]. The theoretical results of Fig. 3 are referenced in energy to the center of the HOMOand LUMO-derived bands. Analysis shows that the valence band states and those within N 2.5 eV of the conduction band minimum have well-defined angular momentum and c or n character. Those at higher energy are above the maximum of the self-consistent potential so that they are not ‘confined’ to the molecule. They then extend throughout the crystal and have considerable dispersion. The first two valence band features for solid Cm have rr, and rrr character with 5-fold and P-fold degeneracy, respectively [22,23]. In the photoemission results, the relative emission intensities from the n, and rrg bands change with photon energy because of matrix elements effects. Studies of the hv-modulation of these states [ 141suggest the importance of dipole transitions and the retention of molecular symmetry for states to N 100 eV above Er, well above the limit observed for other solids, including diamond and graphite [31]. The FWHM of the HOMO-derived band is 0.65 eV, consistent with band calculations that give a band width of 0.58 eV [5]. [Even in the gas phase, the FWHM of the HOMO band is = 0.5 eV and vibronic effects are evident [27]. Such effects in the solid state would contribute additional broadening.] States 5-10 eV below Er are of mixed H and u character, and those more than _ 1OeV below EF are u-derived.
1437
The overall valence band width is very nearly the same as for graphite or diamond [34], but the molecular symmetry of Cso assures sharp spectral features. In the empty states, the LUMO feature is derived from three bands with t, symmetry at I. Feature 2 arises from three bands with zr symmetry, and feature 3 represents the superposition of ?r, t,, e8, and ag states at f. The ag state is localized in the center of the C, molecule and does not correspond to any of the canonical tr or n bonds. (This state is likely to be missed in calculations with LCAO basis sets.) The t, and e8 states are practically degenerate and correspond to the icosahedral h, state of the isolated molecule [33]. The t, states in the first and third peaks have an angular nodal structure that corresponds to a spherical harmonic with / = 5, the same as the highest occupied molecular orbital. The tg state of feature 2 and the eB and tg states of feature 3 have nodal structures corresponding to / = 6, and the aB state of feature 3 has an angular nodal structure corresponding to L = 0. Comparison of theory and experiment for the valence band features is very good, particularly if account is taken of an underestimate of the binding energy of the u states relative to the x states in the local density calculations. Comparison in the conduction band is also good with discrepancies smaller than -0.5eV for peaks N 8 eV above the conduction band minimum [18]. (B) C,, valence and conduction bands C,,, appears to resemble a rugby ball with D,, symmetry [35]. In condensed form, C,,, has an fee lattice [36] with van der Waals attraction. While C, exhibits an fee to SCtransition [37] at 249 K, the low temperature phases of Co are less well characterized. Jost et al. [16] have reported photoemission and inverse photoemission studies for C,, films grown by vapor condensation in ultra high vacuum. They showed the distribution of occupied and empty electronic states summarized in Fig. 4. These spectra are plotted in arbitrary units, with no implied normalization to the density of states. Again, energies are referenced to the center of the HOMO and LUMO features, and EF is identified. As for C,, the measured HOMO to LUMO band center separation of N 3.75 eV is the molecular solid equivalent of the difference between the electron affinity and the ionization potential of the molecule. Photoemission from C,,, negative ions [38] gives a smaller HOMO-LUMO gap of N 1.6 eV for the reasons discussed above. Figure 4 shows a variation in relative intensities of the two features on either side of EF as a function of probe energy. There are also changes in relative intensities of detailed features contained within the
J. H.
WEAVER
27.25
Conduction Bonds
Valence Bands 20
IO
0
GO
10
i
Energy (eV)
Fig. 4. Photoemission and inverse photoemission results for solid C,,,. The spectra are plotted in arbitrary units with no implied normalization to the density of states. The energies are referenced to the center of the highest and lowest features of the molecular crystal from which an electron has been removed and one has-been added. The Fermi level is also identified.
first and second valence band structures. As for C,, this modulation can be understood in terms of the non-plane-wave character of the high-lying empty states accessed by photoexcitation or populated by electron addition [14]. Changes introduced by molecular elongation for C70should have little effect on the overall distribution of bands of Q- and n-parentage, but elongation would split degenerate levels of the molecule. For C,, , there would also be 15 new o states and five new n states. Calculations of the electronic states of solid CT0 are more complicated because elongation probably introduces orientational disorder and the bond lengths of the molecule are not fully characterized [25,39,40]. Mintmire and coworkers [25] calculated the photoemission spectra under the assumption of plane-wave final states, showing the general increase in u-derived emission relative to n-derived emission with increased photon energy, as observed in the spectra of Fig. 4. Saito and Oshiyama [39] reported agreement between their calculations and the measured valence and conduction band results. One of the noteworthy differences of Cso and C70 lies in the splitting and broadening of the leading valence band features [ 161. In solid Car these ILderived bands have no discernible underlying structure, even when measured under conditions that gave N 100 meV total resolution at 60 K. In solid C,,,, three resolvable features appear in the first peak and two in the second for C,,. For C,,,, the additional n-derived bands in the vicinity of HOMO probably account for the increase in the intensity of HOMO over the second valence peak when the peak areas are averaged over a range of final state energies.
In a qualitative way, the differences in the valence band structure for C, and CT0 can be understood from the angular momentum character of the wavefunctions. Martins et al. [18] and Saito and Oshiyama [24] described the valence band states with angular momentum quantum numbers that were associated with the spherical harmonies. The e = 0 state then corresponds to electrons with no nodal plane, the / = 1 state has one node @-like), and so forth. States at the bottom of the valence band have e = 0 whereas those at the top have e = 5. As the quantum number ! increases, the number of angular nodal planes passing through the molecule increases. When the spherical harmonics for Cm are replaced by elliptical harmonics for C,,,, the states with the greatest number of nodes should be the most affected. For example, a state with e = 0 (no angular nodal planes) delocalized around the outside of the molecule would be much less affected by elongation of the cage than would a state with several nodal planes passing through the cage. Indeed, this is what is observed in Fig. 4 where the highest valence features have the greatest number of nodes and show the greatest difference. States derived from x orbitals should also be more affected than a-derived states because the K bonds are more sensitive to bond angle and this angle is reduced for C atoms at the equator of C,@. Comparison of the conduction band states of &, and C, shows that the first and third features line up quite well relative to EF but feature 2 is shifted N 0.5 toward feature 1 in &,. The relative positions of
Cso
c Is hv= 1486.6 eVA
I
I
&thre
I- 1.9ev
I
20 Energy (eV) ’
Fig. 5. C 1s features for C, showing the main line and loss features that reflect on-site shake-up structures (labeled 2,3, 7 and 8), dipole energy losses due to scattering of the outgoing photoelectron (3, 4 and 5), and plasmon loss features due to excitation of collective oscillations of individual molecules (6 and 10).
1439
Electronic structures of C, and C,,
%a L
I
I
I
I
I
RL+ive4 Eneriy (eV) Fig. 6. C 1s satellite features, with the main line emission subtracted, compared to EELS spectra from Refs 41 and 42. Structures 3, 4 and 5 reflect dipole-allowed off-site energy losses, with underlying intensity from a II plasmon near -6 eV and n-x* monopole transitions. The feature at 1.9 eV in C, represents the monopole-allowed HOMO-LUMO shake-up. The corresponding (dipole-allowed) feature at 1.2 eV in &Cm reflects a smaller gap.
features
1 and
2
and
their
probable
overlap
would be important in doping to produce metallic, superconducting, and insulating states. The third state feature for C,,, has a shoulder that is not evident in Cso, probably because of reduced symmetry or new states. Features more than N 4eV above EF are similar for Cm and CrO, and we assume that they have contributions from cr and 7c states with increasingly-delocalized character.
empty
(C) C 1s satellites and plasmons for C, Figure 5 shows the C 1s core level spectrum referenced in energy to the center of the C main line [13]. The C 1s binding energy is 285.0 eV and its full width at half maximum (FWHM) is 0.65eV. The latter is almost certainly limited by the resolution of the spectrometer. The main line is symmetric and offers no indication of more than a single C species. There are nine distinguishable satellite features shifted relative to the line. The satellite structures of Fig. 5 are due to both on-site and off-site K-Z* excitations and to plasmon losses. The on-site processes are those that occur on the molecule from which the photoelectron is ejected whereas the off-site lines are due to energy loss events as the electron propagates through the lattice. This satellite region is expanded in Fig. 6
where the main line contribution has been subtracted and results from EELS measurements are shown for comparison [41,42]. The first shake-up peak (labeled 2), located 1.9 eV from the C 1s main line, is due to excitations from HOMO- to LUMOderived molecular states induced by the creation of the core hole. This transition is monopole-allowed (AI = 0) and is likely to appear in a shake-up spectrum. It is dipole-forbidden in the isolated Cso molecule but solid state effects mix the angular momentum quantum numbers. Nonetheless, the transition is weak in optical absorption [20,21] and EELS [41-43] where dipole selection rules are important. The satellite features at 3.7, 5.0 and 6.1 eV originate from n-x* transitions but their prominence in the EELS spectra suggests that they are due to electron-excited dipole transitions. The interpretation in terms of dipole transitions is supported by the agreement between the optical conductivity derived from EELS data [44] and optical absorption measurements [20]. Satellite feature 3 appears to be anomalously strong when compared to the EELS data, probably because of contributions from monopole-allowed transitions involving HOMOderived states and empty t,,-derived states, both with I = 5 symmetry [18,22]. The EELS experiments [42] indicate that the peak at N 6 eV results from n-n * transitions at 5.5 and 5.8 eV and the excitation of a n-plasmon at 6.3 eV. The strength of the plasmon is dependent on the electron energy in EELS, as discussed by Gensterblum et al. [42]. The shoulder labeled 6 is probably due to an underlying broad peak related to this collective oscillation.
---
C
70 XPS EELS (Sohmen et 01.1
a
4
0
Relative Energy (eV) Fig. 7. C 1s features for C,, showing a broadened main line relative to C, because of increased inequivalence for the C atoms (binding energy 285.3 eV). The satellite structures reflect the increased spread in the rt and n * energy levels of C0 compared to C, . The satellites are due to monopole-allowed (2.7 and 3.8 eV) and dipole-allowed x-x* excitations. A distinct HOMO-LUMO feature cannot be resolved.
J. H. WEAVER
1440
LUMO
L-n E,
Energy
t /
l!A
Fig. 8. Schematic of the morphology of a K,C, thin film. The positions of the HOMO- and LUMO-derived bands are shown in relation to Er. For pure C,, Er lies near the middle of the gap. Dilute doping pins Er near the edge of LUMO. Small K,C, grains nucleate, probably in grain boundaries or at imperfections in the film. For K,C,, the Fermi level lies within the LUMO-derived band. Continued incorporation results in polycrystalline K,C,
monopole-allowed ucr* shake-up features for C& and C,, suggests that the elliptic distortion of CT,, leaves the energy distribution of cr molecular orbitals with a given angular momentum character. This is supported by correspondence between features in photoemission, inverse photoemission, and X-ray absorption spectra for the two molecules [16,46]. A distinct HOMO-LUMO transition could not be resolved for C ,,,, probably because these two levels were broadened in C,,, as discussed above. Indeed, the intensity between the main line and the first definite feature at N 2.7 eV remained above the background expected for the main line, based on its shape for C,. This probably indicates unresolved loss features from HOMGLUMO-like transitions. The peak positions of the broad x-n* satellite features are in agreement with those observed in EELS, as shown in Fig. 7. These results compare favorably to the absorption spectrum of C,, in solution [21], suggesting that much of the satellite structure is due to dipole transitions induced by the emitted electron. The XPS features at 2.7 and 3.8 eV appear strong relative to the corresponding EELS features. As with C&, this suggests that the C 1s shake-up features had contributions from on-site z--n * monopole transitions.
3. ALKALI FULLERIDES The satellite region of Fig. 5 is composed of shake-up and inelastic loss features, an interpretation supported by the observation that such processes tend to overlap in the spectra from aromatic molecules [45]. C 1s spectra that extend to _ 40 eV below the main line show the higher energy plasmon at N 28 eV due to a-excitations, as first noted by Weaver et af. [13]. This plasmon is also observed in inverse photoemission [15] and EELS studies t42-441. Additional monopole o--(T* transitions appear at 9.9 and 13.7 eV.
(D) C 1s satellites and plasmons for C,, Figure 7 shows the C 1s main line and satellite structure for C,,. The single feature at 285.3 eV is 0.2 eV broader than for Cso, reflecting the five distinct carbon atoms in the rugby-ball-like structure. The satellite features show broad peaks at 2.7, 3.8 and 5.8 eV. Spectra that span a larger energy range reveal peaks due to U--Q* transitions at 10 and 13.7eV, as well as a broad plasmon loss at N 28 eV. The XPS results for C,, indicate the same energy as for the high energy plasmon of Cm, but the EELS results of Sohmen et al. [42] suggest that the Cyt, plasmon is 1.5 eV lower in energy. The similarity of the
(A) K mixing with C, The observation that alkali atoms could be mixed with Cm to enhance the conductivity [47] and produce superconducting phases [40] stimulated a great deal of activity that focused on the electronic states of the fullerides, as this volume attests. Again the various photon and electron spectroscopies have been particularly valuable because they have been able to observe changes in the electronic states directly, first with the alkaki metals during doping [l-4] and subsequently with other species like Mg, Sr and Ba [7], Yb [49] and Ca [50]. They have also been valuable in demonstrating phase separation [3,4] and determining the stoichiometry of the fulleride films. Figure 8 depicts a Cm film during K incorporation. For the pure fullerene film, the Fermi level lies between the LUMO- and HOMO-derived bands, as discussed above. Exposure to K produces a solid solution with a slightly expanded fee lattice [51]. The K atoms establish new energy levels derived mainly from the LUMO levels, pinning EF close to the LUMO band, as sketched. Continued doping leads to the nucleation and growth of distinct KgCm, K4Cso and K,& phases [51, 521. The calculations have indicated gains of 1.4 eV per atom for K in octahedral
Electronic structures of C, and C,s
I,###
-5
II1II
Er
+5
Energy (eV)
Fig. 9. Representative photoemission and inverse photoemission spectra (hv = 65 eV and E, = 17.25 eV) for K,C,. K incorporation results in a 0.25 eV shift to lower energy of the PES features and a 0.75 eV shift to lower energy of the IPES features due to the movement of Er to the edge of the
LUMO bands and changes in screening in the doped film. The x = 1 spectrum shows emission at Er from grains of K,C,. Adding K results in an increase of emission below Er and a decrease of intensity above Er as the higher stoichiometry phases grow. The top spectrum shows that Er shifts into the gap when the LUMO band is completely filled.
sites for K I C 60, 1.4 eV per atom for K in tetrahedral sites of K2&,, and 1.7 eV per atom for occupancy of tetrahedral and octahedral sites in K,C, [5]. For K, C,, in which the tetrahedral sites of the bee-based lattice are occupied, the energy gain is 1.7 eV per ion. These energies are calculated relative to the standard states for K and Cm, and the K, CM and K, C, phases are hypothetical structures [5]. Atomic intermixing does not appear to be impeded for thin film Cm exposure to an alkali metal flux of K in ultrahigh vacuum under conditions that minimize surface oxide formation. Fulleride formation with other species can require annealing, even for thin films, because of the larger activation energies for diffusion. This is certainly the case for Mg, Sr and Ba [7j, and Yb [49]. In any case, fulleride formation is driven by thermodynamics. Elements with large heats of formation and high ionization energies tend to form metallic clusters on fullerene films rather than the fullerides, as observed for Ti, Cr, In and Au [53]. The third panel of Fig. 8 depicts K,Cso formation and grain growth. For two-phase samples, the spec-
1441
tral features of both phases will be present, as demonstrated by Poirier et al. [3] and Chen et al. [4]. There will also be broadening related to C,-K, Cm interface regions, although the ionic character suggests that the C,--K,C, boundary will be sharp [3]. Ultimately, the grains form a K,C, film, with microstructures that reflect the growth conditions and the structure of the starting film. Additional K-incorporation produces nuclei of bet K,C, [52]. The final K,C, phase has each Cso coordinated with 24 potassium ions [54]. Although this K, C, phase is insulating, [ 1,2, 17,551, substoichiometric K,C, is characterized by Fermi level pinning by holes near the top of the nearly-filled LUMO band of the bee compound [17]. The Fermi level moves into the gap upon complete filling of those bands. For fulleride films, the near-surface stoichiometry should be very nearly the same as the bulk because the fullerides are ionic materials with very high heats of formation [l, 5,6]. In general, stoichiometries at the vacuum surface do not deviate from those of the bulk for ionic compounds, and surface relaxation or reconstruction is exceptional. For a vacuum-exposed K,C6, (111) surface, the K atoms would be found in the surface-equivalent tetrahedral and octahedral sites, but not all of these sites would be occupied because of charge neutrality requirements. STM images for K,&, show ordered (111) surfaces in which only the C, molecules are imaged [lo]. We note that XPS studies have been done for Kr C, and K,C, films in which the take-off angle of the photoelectrons was varied from near-normal emission (75”) to neargrazing emission (20”). This had the effect of changing the surface sensitivity of the measurements so that the probe depth varied from 72 to 24A (probe depth = 31 sin 0). The kinetic energies of the K 2p and C Is electrons differed by only N 12 eV but they have the same mean free path. Superimposing the different spectra showed identical results, giving no evidence of a ‘surface phase’. Even so, the samples are composed of a very large number of small grains and the measurements average over those grains. It remains to be proved that growth of fullerides from thin samples will produce a single phase K3Cso sample.
valence and conduction bands (B) KG, Figure 9 summarizes photoemission and inverse photoemission results for K,C, [17]. They demonstrate that the filling of LUMO-derived bands with electrons donated from alkali metal atoms does not result in simple rigid band shifts. This is particularly evident in the empty states because the separation between the first and second conduction band features changed from 1 eV in pure Cso to 1.3 eV in
J. H. PES (-6 A
WGo
IPES
I ,
I
-!
Energy (eV)
Fig. 10. Photoemission and inverse photoemission spectra (hv = 65 eV and Ei = 17.25 eV) for K,C,O. The x = 1.8 spectrum shows a split-off band entirely below Er, lahelled
LUMO-A. Higher K concentrations produce emission at
EF, LUMO-B, and a valence band shift toward EF. The top
spectrum shows complete filling of LUMO. The inset summarizes the intensities of LUMO-A and LUMO-B. I&&, to 1.6 eV for K6C6,,. The differences reflect a modification in the underlying density of states. Such effects are greatest for the extended empty states. The empty state structure probed with X-ray absorption spectroscopy [4] and EELS [41] shows similar development with K addition with slight differences in the relative positions of peaks that result from the presence of the core hole. The spectral broadening evident in Fig. 9 is a combination of several processes. Changes associated with K doping are observed in the occupied state spectra because the n-derived features shift 0.15 eV more toward Er than the lower-lying a-derived features upon transformation from C, to K3Cso. There is also structural disorder related to grain boundaries and imperfections and, hence, differences in local bonding configurations in the mixed-phase samples. The FWHM of the HOMO feature changes from 0.65 eV to l.OeV to 0.9 eV for C,, K,Cso, and K,C,. Changes in the width of the LUMO feature are even larger since the FWHM of the half-filled LUMO band in K,C,, is 1.1 eV compared to 0.75 eV for K,Cso [l, 4, 171. The calculations show relatively little change in width during fulleride formation [5,6]. Figure 9 shows that the now-occupied LUMO band shifts away from EF whenit is fully occupied at x = 6. This implies that the solid, defect-ridden as it is, forms the local geometry needed to fill the LUMOderived molecular states of Cm. Were this not the case, Er would be pinned at the top of the LUMO. The IPES spectra demonstrate such pinning for x slightly below 6. The fact that an insulating state is reached with EF in the gap of the (new) molecular solid implies that structural imperfections do not introduce levels that can pin EF near the band edges.
WEAVER
No evidence was found for the filling of the LUMO + 1 band upon further K exposure but the valence bands showed evidence for metallic K growth on the surface for excessive K exposure. Electrical resistivity measurements [17] with photoemission studies have shown a sharp drop in the resistivity with doping, a broad minimum for stoichiometries of 1.5-5, and then an increase in the resistivity as the K,C,,, phase was reached. The gross features of the resistivity behavior can be understood by considering a granular metal model in which metallic K,Cso (or K,C,) grains are imbedded in an insulating C,, (or K,C,) matrix [56,57]. In a granular metal model, the resistivity dependence on x can be separated into dielectric, transition and metallic regions. In the dielectric region, conduction results from tunneling between metallic grains through the insulating medium. Hence, the resistivity scales as exp((iV/x)“3), where N is the metallic grain density [56]. In the fully metallic region, the resistivity is determined by electron scattering. In the transition region, transport is accomplished by a combination of tunneling and metallic conduction. The number of direct pathways for conduction increases with K concentration. Hence, the resistivity varies as (x - xc)-0, where x, is the threshold composition between the metallic and dielectric regions and the exponent p varies between 1 and 2, depending on geometry used to model the morphology [57]. Calculations which model the system with spherical metallic K,C, grains on the lattice points of a simple cubic array growing in an insulating C, medium [17] give a grain density of - 10” cmm3. The calculations also predict that conduction pathways will form when x - 1, corresponding to grains that are - 100 A in diameter. Such grain sizes are similar to those in pure Cm films deduced from the X-ray diffraction analyses of Hebard et al. [20] and STM analyses of Li et al. [lo]. The leveling-off of the resistivity where the K,C@ grains form conduction pathways near x = 1 is in agreement with the model calculations. The broad minimum in p(x) suggests that the grain size is much larger than the scattering length of electrons in K3C&. This can be understood qualitatively by realizing that films with large grains have less insulator surface area and, hence, electron scattering relative to small grains with the same nominal stoichiometry. Enhanced scattering in films with small grains would produce a faster decrease in resistivity and hence a sharper minimum when x approaches 3 and the insulating C, phase is consumed. Note that the behavior of p(x) reported by Benning et al. was determined K content.
by direct spectroscopic assessment of the They argued that one should not rely on
Electronic structures of C, and C0
Fig. 11. Photoemission spectra for Li,C, and Rb,C,. The nonmetallic behavior of Li,C, for all x is indicated by the lack of emission at Er. In &trast, Rb,C, films exhibit metallic Fermi edges, as for K,C,. The dashed lines for L&C, provide a guide to the eye for a band A and band B. Those for Rb,, C, show the effect of enhanced experimental resolution. time of exposure in the evolving
because the sticking coefficient
of K
film varies with x.
(C) K-C,,, valence and conduction bands Figure
10 shows the distribution
of occupied
and
empty states for K,C,, [17]. Upon K exposure, the valence features shift 0.2 eV to lower binding energy
due to improved screening. There is a shift of 0.3 eV to higher binding energy when the system reaches K,C,, and is again insulating. The final shift is analogous to that for C&, fullerides but is smaller because the gap between the C,, LUMO and LUMO + 1 levels is smaller [15]. For K,&, , the separation between the centers of the two leading bands (formerly HOMO and LUMO) is 1.9 eV. This separation agrees reasonably well with gas phase photoemission results for the negative ion of C,,, [38], with account taken of the influence of the K ions. In K,C,, , the new HOMO-LUMO gap is larger than the separation between the LUMO and LUMO + 1 bands of pure C,, (0.9 eV), again because of the nature of the (N + 1) states. Perhaps the most remarkable aspect of the photoemission spectra of Fig. 10 is that a band forms completely below Er during the initial stages of doping [17]. This band does not have a counterpart in the K-C, system [l&l, 171. For x < 1.8, a single feature 1.2 eV below EF is clearly evident and there is no emission near EF. For x = 2.7, two distinct features appeared centered 1.2 and 0.5 eV below Ep and the emission at EF demonstrates metallic character. For x = 4.2, there is distinct emission at EF. The spectrum for K,C,, reveals that the emission intensity
1443
of the now-filled LUMO-derived feature is N 0.3 times the intensity of the HOMO-derived feature, consistent with predictions of band degeneracies [40]. The inset in Fig. 10 shows an increase in LUMO-A until it reaches a maximum at x E 1.8 and then decreases. Feature B increases after x s 1.8 until the saturated phase is reached. As the first insulating phase is formed, the sample is probably separated into a solid solution and K,C,,,-like phase. The formation of an insulating K,C,,,-like phase may indicate that the octahedral sites are so large that a K,C,,,-like phase is not energetically favorable. A metallic phase nucleates and grows at the expense of the phase of lower stoichiometry when the K concentration increases. By analogy to K-C&, it may be that this metallic phase has K,C,,-like structure with CT0 molecules in a distorted bee lattice and K in tetrahedral sites. In contrast, the K,C& phase is characterized by emission from a single LUMO feature. KgC7,, may be a bee phase with full occupation of tetrahedral sites. Despite these speculations about the phase diagram and crystal structures for K-C,, , care should be exercised in using photoemission results to draw conclusions about structures until such studies have been completed. The assumption that the low component phase is K,CO is based on the appearance of a distinct band derived from a LUMO level that can accommodate two electrons. The alternative would be to suppose that a correlated impurity-like band developed in the gap at low concentration, as appears to be the case for Li,&, and Na,C,. (D) Fullerides of Li, Na, and Rb Superconductivity has been conspicuously absent in L&C,, Na,C,, and the C,,-based fullerides. The Li- and Na-fullerides have resistivities l-2 orders of magnitude higher than K,C, [47], suggesting that these narrow band materials may be close to a Mott-insulator transition [19]. Photoemission and inverse photoemission [SS] indicate that this is the case with Li,C, on the insulating side and K,&, and Rb,C, on the metallic side. Figure 11 shows valence band spectra for LiX&,. Li deposition to x = 0.5 yields a photoemission peak HOMO band centered 1.1 eV above the (FWHM N 0.8 eV). This HOMO-to-A separation is smaller than any estimate of the separation between centers of the HOMO and LUMO bands or the band gap of fee Cso [5,6, 13, 18,23-261. Peak A increased with exposure until x E 2. Feature B appeared with continued incorporation, centered 0.6 eV closer to EF (FWHM 0.7 eV), and this feature grew at the expense of feature A. When saturation was reached, x = 6, the spectral features sharpened and shifted away from
J. H. WEAVER
1444 I
I
I8
I
I
I
!
30
I
N% c60 PES IPES El = 14.25 N hv*65cN
-5
+5
Fig. 12. Photoemission and inverse photoemission results for Na,C,. Feature A corresponds to Na,C, and feature B reflects conversion to the Na,C, phase. Splitting is evident in the leading conduction band feature for Na,,C, . The movement of spectral features relative to EF reflects changes in screening with pinning of EF at the conduction band minimum.
Er. This is consistent with improved sample homogeneity, the filling of the LUMO levels, the loss of defects that pin Er near the top of peak B, and the molecular character of A,Cso solids. Throughout LX, mixing, the density of states at EF was negligible. Comparison shows a striking similarity between the saturated phase and K,Cso as far as the electronic signatures are concerned [l&4, 171. The right panel of Fig. 11 summarizes photoemission results for Rb,C6,, where the behavior is analogous to that for K,C,. A distinct Fermi edge was evident for x = 0.2, and the LUMO-derived valence feature grew monotonically with x, with no change in binding energy or general lineshape until after x = 3. This is consistent with phase separation into Rb,C, and a solid solution. The instrumental resolution for the solid curves in Fig. 11 was 0.34 eV and that for the dashed curve for x = 2.8 was 0.16 eV. The width of the Fermi edge was equal to that expected when account is taken of thermal broadening at 300 K. Figure 12 summarizes the valence and conduction band behavior for Na,C,. In this case, the samples were annealed at -100°C for 10min after each deposition. The photoemission results reveal the formation of band A well below EF for x S 2 and the formation of band B, shifted 0.6 eV for x 2 2. The IPES spectra show that small amounts of Na produced a rigid shift of the empty state features toward
Er, with Fermi level pinning near the conduction band minimum. With increased Na incorporation, the empty state features broadened and there was reduced emission from the LUMO-derived band. Two distinct empty state peaks separated by N 0.5 eV can be. resolved for x r 2. The emission from these bands diminished and ultimately was very small, as shown for x = 5.8. These results demonstrate very clear differences in the distribution of the electronic states of the alkali metal fullerides. For K, C, and Rb3&,, the occupation of the LUMO-derived bands reflects complete charge transfer from K to the LUMO level for a structure having ions in the tetrahedral and octahedral sites of the fee lattice. [5,6]. Complete filling of the LUMO-derived band for x = 6 occurs, most likely because the alkali ions occupy all of the possible tetrahedral interstices of the bee structure. In contrast, the Liz&, and Na,C, results show a single band well below EF and splitting of the empty states. Based on the structural data for the other alkali fullerides [52,54], L&C, could form with Li ions in tetrahedral sites of the fee lattice (anti-fluorite structure). This would be different from the A,&, structure since the octahedral sites would be empty, presumably because the Li+ ions are too small to stabilize the L&C, structure. Another structural possibility would be a bee-derived structure similar to the observed A,C, phases with partial tetrahedral site occupancy or multiple occupancy of the octahedral sites. The observation of semiconducting L&C, and Na,C, phases raises the question of whether they are band insulators or whether their insulating character is due to electron correlation effects. The calculated band structures of Cm and K,C, show only a rigid shift of the LUMO-derived states with alloying [5,6], so that a large crystal field splitting of those levels in L&C, and Na,C, appears unlikely. If the Li and Na atoms occupy the small tetrahedral interstitials of an fee crystal, such splitting is ruled out by group theory arguments. There are several indications that the alkali fullerides have strongly correlated electrons and could be close to the metal-insulator transition. First, the measured conductivities of the alkali fullerides [47] are quite low and the mean free paths derived from those values are a few Angstroms. Measurements for Rb,C, suggest a mean free path of lS2OA [59]. Mean free paths close to the C.&Z, intermolecular distance are an indication of proximity to a metal-insulator transition [ 191. Another measure of the importance of correlation effects is the magnitude of the electron-electron interaction parameter U. As noted above, the combination of photoemission and
Electronic structures of C, and C,
B%Go
ShGo
hv =70eV
hv=48eV
‘;;i
Srd
1
Binding Energy (eV1 Fig. 13. Valence band spectra for Ba,C, and Sr,C, grown under a variety of conditions. Variations in the intensity of the band at Er reflect surface stoichiometries. This band reflects hybridization of the LUMO and the s-state of the alkaline earth. Metallic character is evident in all cases. The top left spectrum shows the result of deposition of 9 8, of Ba on solid C, at 300 K where a Ba-rich surface layer is produced. inverse photoemission
gives a center-to-center
separ-
ation of N 3.7 eV for the HOMO and LUMO bands.
This is N 2 eV greater than the lowest energy for HOMO-LUMO on-site excitations and the difference is a measure of the electron-electron interaction parameter U in solid C,. From Fig. 12, the separation between feature A and the lowest conduction band feature for Na,C, is N 1.6 eV. This is close to U in magnitude and is therefore consistent with a band split by correlation effects.
4. ALKALINE EARTH EULLERIDES Most alkali
studies metals,
of fullerides Chen
have
focused
on the
et al. [7] have demonstrated
recently that alkaline earth deposition onto Cso also produces fullerides. Such mixing was anticipated because the alkaline earths have relatively small cohesive energies, small ionization energies, and they are found with formal 2 + valency in compounds with electronegative elements. The most significant change in the valence band spectra for Mg,&, is the appearance of emission from a band entirely below EF, a band attributed to states derived from the LUMO of Cso and the s states of Mg. Analysis shows a feature centered 1.1-1.2 eV above HOMO that has a FWHM similar to that of HOMO, i.e. 1.0-1.1 eV. The peak-to-peak energy separation between it and HOMO is close to that for semiconducting Li2Cso and Na,C, where a new band of states developed below EF [B]. It is considerably smaller than the corresponding separation for K,C, (1.9 eV) or K,C&
1445
(1.6 eV) [l-4] and Chen et al. [7] concluded that Mg doping produced only non-metallic fullerides. Figure 13 shows valence band spectra for Ba, Cso. The deposition of 12 A at 475 K produced a band centered 1.9-2.0 eV above HOMO that was cut by the Fermi level, and there was broadening of the rcderived bands. Spectra acquired with higher resolution showed an asymmetric lineshape related to the convolution of the Ba-induced structure with the Fermi function. The band EF grew with Ba deposition at 475 K, and the HOMO peaks continued to broaden. The LUMO-derived peak was centered 1.8 eV above HOMO by 30A deposition. The Ba 4d core level intensity for this coverage suggests a stoichiometry of x = 1 f 0.3. Further deposition at 475 K resulted in much stronger Fermi level emission but the intensity was time dependent, demonstrating that the Ba atoms were kinetically trapped near the surface. The highest Ba concentration before metal cluster formation (as judged by the Ba 4d core level lineshape) was x = 6 f 2 and was reached after 9 A Ba deposition at 300 K. The valence band spectrum for 9 A Ba coverage is shown in the top left of Fig. 13. The right panel of Fig. 13 shows photoemission spectra for Sr deposited on a solid Cso film. Sr deposition of 3 8, at 300 K produced a feature centered = 1.6 eV above HOMO. The Sr-induced peak was stronger for 10 8, but it was also broader. The Sr 3d core level intensities suggest a composition of x = 5 f 1.5 at this stage. Annealing to 475 K allowed Sr diffusion into the bulk. The separation between HOMO and the Sr-induced feature also increased to 1.8 eV and the Sr 3d core level intensity gave a composition of x = 0.6 f 0.2. For the alkaline earth fullerides, Sr,C, and Ba,C, were always metallic and Mg,Cso was never metallic. Hence, a simple picture in which electrons are transferred to occupy the six-fold degenerate LUMO levels is not applicable. For alkaline earth fullerides, pure ionic bond formation requires the transfer of two s-electrons. Analysis based on the ionization energies of alkaline earths, the electron affinity of Cso, and the electrostatic (Madelung) energy of the crystal demonstrates that two-electron transfer is not favorable. Therefore, bonding must involve hybridization between Cso states and alkaline earth states. Note that the two electrons in each alkaline earth atom will be equally involved in the bonding. Mixing of the LUMO-derived and the s-derived states of the alkaline earths is favored because they are close in energy and because the LUMO is unoccupied. In the fullerides, it is not known whether hybridization will result in separation of bonding and antibonding bands, but we speculate that they will overlap because the respective wave functions are not
J. H. WEAVER
1446
very localized. LUMO + 1 is likely to mix with alkaline earth s states, and the bands probably overlap with the LUMO-derived bands. Therefore, it is even less probable that a band gap can exist. For the same reason, a fortuitous band splitting driven by crystal symmetry is not likely to occur over the entire Brillouin zone. Superconductivity is closely related to distribution of electronic states and those at EF are derived almost entirely from the LUMO levels. Several studies have focused on electron-electron coupling via C, phonons although they have not specifically considered the dopant [60]. Every C,, fulleride that exhibits metallic character also shows superconductivity at remarkably high temperature. SrXCGOand Ba,C,, the only metallic fullerides found outside the alkali family, provide an example of a hybrid conduction band. MgX& stands in sharp contrast because EF is pinned at the valence band maximum. The existence of a gap is confirmed by inverse photoemission and current-voltage measurements using scanning tunneling microscopy [61]. We propose that the electronic structure of Mg,C& also reflects strong electronelectron repulsion, noting that the center-to-center separation between the occupied and unoccupied LUMO-s hybrid bands is N 2 eV [61]. This is close to the ZJ value for the insulating fullerides. The atomic and ionic sizes of Mg are much smaller than those for Sr and Ba, showing a similar trend when one compares Li and Na to K, Rb and Cs. The small Li and Na ions might not occupy the large octahedral interstitial sites of the fee Cm lattice. The structure of Mg,&, could also be different than Sr,C, and Ba,C,. Such structural changes may not be large enough to split the conduction band in the independent-electron band description, but the system could be pushed to the insulating side of the metal-insulator transition by electron correlation.
2. Wertheim G. K., Rowe J. E., Buchanan D. N. E., Chaban E. E.. Hebard A. F., Kortan A. R., Makhija A. V. and Haddon R. C: Science 252, 1419 (1991). 3. Poirier D. M., Ohno T. R., Kroll G. H., Chen Y., Benning P. J., Weaver J. H., Chibante L. P. F. and Smalley R. E., Science 252, 6464 (1991). 4. Chen C. T. et al., Nature 352, 603 (1991) showed very high resolution valence band spectra with a distinct F&mi level cutoff for intermediate stoichiometries. 5. Troullier N. and Martins J. L.. Phvs. Rev. B 46. 1754 (1992); Martins J. L. and Troulher N., Phys. Rev: B 46, 1766 (1992); Troullier N, PhD thesis, University of Minnesota (1991). 6. Saito S. and Oshiyama A., Phvs. Rev. B 44, 11536 (1991); Xu Y.-N.,.Huang M.-Z., and Ching W. Y., Phvs. Rev. 844. 13171 (1991): Erwin S. C. and Pederson M.* R., Phys. &a. I&. 67i.1610 (1991); Satpathy S., Antropov V. P., Andersen 0. K., Jepsen O., Gunnarson 0. and Liechtenstein A. I., Phys. Rev. 846, 1773 (1992). 7. Chen Y., Stepniak F., Weaver J. H., Chibante L. P. F. and Smalley R. E., Phys. Rev. B 45, 8845 (1992). 8. Ohno T. R., Kroll 6. H., Weaver J. H., Chibante L. P. F. and Smalley R. E.. Nature 355. 401 (1992). 9. Ohno, T. R., Chen- Y., Harvey S. E.,’ Kroli G. ‘H., Weaver J. H., Haufler R. E. and Smalley R. E., Phys. Rev. B 44, 13747 (1991). 10. STM results are discussed by Li Y. Z., Chander M. Patrin J. C., Weaver J. H.,.Chibante L. P. F. and Smallev R. E.. Science 253. 429 (1991) and Li Y. Z.. Chandkr M., Patrin J. C., Weaver J. H.: Chibante L. P: F. and Smalley R. E., Science 252, 547 (1991). STM studies of monolayer films have been reported by Wilson R. J. et al., Nature 348, 621 (1990) and Wragg J. L., Chamberlain J. E., White H. W., Kritschmer W. and Huffman D. R., Nature 348, 623 (1990). 11. See, for example, Cardona M. and Ley L., Photo-
Acknowledgements-This
14.
work was supported by the Office of Naval Research and the National Science Foundation. The synchroton radiation photoemission studies were conducted at Aladdin, a user facility operated by the University of Wisconsin and funded bv the National Science Foundation. We are pleased to acknowledge stimulating discussions and collaborations with J. L. Martins, N. Troullier, Y. Z. Li, J. C. Patrin, T. R. Ohno, G. H. Kroll, D. M. Poirier, P. J. Benning, Y. Chen, M. B. Jost, F. Stepniak, R. E. Smalley and L. P. F. Chibante. Correspondence and discussions with A. F. Hebard, A. Rosen, S. Saito, J. Bernholc, A. A. Lucas, G. Sawatzky, J. R. Chelikowsky and J. E. Fischer contributed to this work.
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Electronic structures of C, and C,,
21.
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