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Localization of charge carriers in the c-axis electronic transport of YBa2Cu3Oχ
PHYSlCA® ELSEVIER
Physica C 270 (1996) 311-316
Localization of charge carders in the c-axis electronic transport of YBa2Cu30 x J. M ~ n z e l *'a H.P. G e s e r i c h a Th. W o l f b a Institutffir angewandte Physik, Unioersit~t Karlsruhe, D-76128 Karlsruhe, Germany b Institutffir Technische Physik, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany Received 28 December 1995; revised manuscript received 22 August 1996
Abstract
Reflectance measurements with EII c on a YBa2Cu3Ox single crystal where the oxygen content was varied between x ~ 6.8 and x ~ 6.98 are presented in the far infrared range (5 meV < h w < 100 meV) at temperatures between 10 K and 300 K. Performing a Kramers-Kronig transformation we derived the optical conductivity Orllc(hto). A n analysis of the spectral weight shows that the main contribution of the electronic transport is due to localized carders. With decreasing the oxygen content, the spectral weight of free carders decreases whereas the spectral weight of localized carriers is enhanced. Keywords: Far infrared spectra; Anisotropic superconductor; Normal state properties; c-Axis conductivity
1. Introduction The far infrared properties of YBa2Cu30 x for E II c are determined both by lattice vibrations and by charge carriers, i.e. holes hopping between adjacent CuO2-double layers. Both contributions are strongly temperature-dependent: The outstanding phenomenon of the electronic system is the development of an reflectivity edge in the far infrared regime upon cooling below the superconducting transitiort temperature, [1-11]. Homes et al. [1] have shown that, in the case of non fully doped YBa2Cu30 x ( x < 6.92), a decrease of the optical conductivity o-iic(hto) with decreasing temperature occurs in a broad energy range below 50 meV. This so-called pseudogap depends on the doping concentration. It is most prominent at an oxygen content of about x =
* Corresponding author. Fax: + 4 9 721 607 593.
6.85, and disappears completely both, in the fully doped and overdoped samples ( x > 6.92), and in the non metallic samples ( x < 6.3). In the phonon spectrum, the development of Fano-like lineshapes at low temperatures is reported both in infrared and Raman investigations [12,13], giving evidence for coupling between phonons and some electronic background in the energy range of the lattice vibrations. Nevertheless, the separation between electronic and phononic contributions to o-ii c in the energy range between 10 meV and 100 meV remained as a still open question. Independently from the pseudogap a broad excitation arises with decreasing temperature which also turns out to be doping dependent: centered at about 60 meV for x = 6.85 this feature shifts to lower energies with decreasing oxygen content [1-3]. It was argued that this new excitation is of phononic origin as simultanouesly a loss of spectral weight in the energy range of the two upper phonon modes can
0921-4534/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S 0 9 2 1 - 4 5 3 4 ( 9 6 ) 0 0 5 1 1 - 4
312
J. M~nzel et aL /Physica C 270 (1996) 311-316
be observed. However, the developing of a broad, quasi glass-like phonon band should be attended by strong changes of the underlying structure, which is not observed in YBa2Cu30 x. As a substantial outcome of the present paper it turns out that this excitation can be ascribed to the electronic contribution of the conductivity function and it is related to localized carriers.
2. Experimental
tO00 60
¢00
~'
~
7 ~S-~
4-0
600 x=6.98
~:~..__.~
.
2O 100
80
,~"~ ~
N 40 ~ 20
x=6.92 -"
~ 100
'-, 8o ¢,
Single crystals of YBa2Cu30 x with a typical size of 2.5 X 2.5 X 2 mm 2 were grown by a technique described earlier [15]. AI203 crucibles were used to get a sufficient sample thickness. This results in a replacement of Cu Ions by A1 Ions in the order of one percent which decreases T~ by about 2 - 3 K, and additionally it flattens out the parabolic lineshape of the dependence of Tc on the oxygen content x [16]. It may also cause a decrease of the optical conductivity, as investigations on samples grown in ZrO crucibles show a strong enhancement of o-II c, compared to samples from A1203 crucibles [1]. A maximum value of the oxygen content of x = 6.98 was attained by annealing the samples in an atmosphere of flowing oxygen in two steps, at a temperature of 400°C and 380°C for 140 h and 280 h, respectively. The superconducting transition temperature of these samples was 88.5 K. After obtaining the polarized spectra RIIc at this oxygen content, in a next step the crystals underwent a procedure of decreasing the oxygen content to x = 6.92 (T~ = 89 K). Again the FIR spectra werde taken. Subsequently, the crystals were reduced in a final annealing process to an oxygen content of x = 6.80 (T~ = 79 K), and the corresponding spectra were attained. The procedure of lowering the oxygen content is described in more detail in [5]. For comparison, reflectivity measurements were also performed on crystals of different batches with oxygen contents of x = 6.95 and x = 6.3, respectively. The data obtained from the samples with x = 6.95 coincide with the above 6.93-composition. The reflectance spectra were obtained on (010) surfaces using a Fourier transform spectrometer (Bruker l13v) in the spectral range between 4 meV and 1 eV. The temperature of the samples was varied between 10 K and 300 K using a
•~ ( c m -1)
200
02
z',
x=6.80
40 20
6o~
i00 8o 40 20
I
x=&30
~,.
0
''
0
r
0.02
0.040.06 h~a ( e V )
0.08
Fig. I. Polarized reflectance spectra RII c of Y B a 2 C u 3 0 x with different oxygen content x at T = 10 K ( - ) , T = 100 K ( - . - ) and T = 300 K ( . . . . ) in the highly doped regime ( x > 6.8) (upper panels) and at T = l0 K and T = 300 K for x = 6.3 (lower panel).
helium-flow cryostat (Oxford 1204). At each temperature the sample spectrum was compared to a reference gold mirror using a turning mechanism within the cryostat. This procedure and the calibration with the data obtained by a single beam setup at room temperature yield a photometric accuracy better than one percent. We derived the optical conductivity Giic(h~) from the reflectivity data performing a Kramers-Kronig transformation. As lattice vibrations play a predominant role in the conductivity spectra, additionally a Drude-Lorentz fit was used to separate the contribution of the lattice vibrations from that of the charge carders, and to calculate the plasma energies for different temperatures.
3. Results and discussion In the upper panels of Fig. 1 the reflectance spectra RIIc of a crystal are shown where the oxygen content was varied between x = 6.98 and x = 6.80. The spectra were taken at room temperature, T = 100
313
J. Mr,nzel et al./Physica C 270 (1996) 311-316
K, and T = 10 K. All spectra are dominated by phonons: six phonon lines can be distinguished, separated into three bands each of them containing two phonon modes. With the exception of a transfer of spectral weight from the phonon mode at 560 c m - ' to the mode at 630 cm- 1, a behaviour that continues even to lower oxygen content [1], no significant changes in the phonon lines with decreasing oxygen content can be observed [20]. Compared to the spectra obtained at high oxygen content, the spectrum of a sample with x = 6.3 displayed in the lower panel of Fig. 1, shows distinct differences, both, in eigenfrequencies and oscillator strength of the phonon modes. Upon cooling the phonon modes are almost unchanged and can be described within a good approximation by Lorentzian lineshapes. The phonon lines are superimposed by a broad electronic background, which shows above T~ in the samples with high oxygen content a strongly damped plasma edge around 0.1 eV known from earlier investigations [19,22]. Below T~, however, this smooth plasma edge disappears, and a steep reflectivity edge develops in the energy range of the far-infrared which reflects the condensation of free carriers into the superconducting phase [5,6,14]. Depending sensitively on the oxygen content this low temperature plasma edge is found at top IIc = 10 meV for x = 6.80 and top ll c = 14 meV for x = 6.98. That means, it represents only a small fraction of those carriers which contribute to the plasma edge observed at room temperature. With decreasing oxygen content the low temperature plasma edge shifts to lower energy and disappears for x < 6.5 [4]. As the lowest panel of Fig. 1 shows, the electronic background of the reflectance spectrum for x = 6.3 is drastically reduced and nearly independent of temperature, indicating that the free carrier contribution in this composition has completly disappeared. The conductivity spectra trll~, calculated from the reflectivity by a Kramers-Kronig transformation, are shown in Fig. 2. Above the superconducting transition temperature, the spectra of the lower doped compositions ( x - - 6 . 8 0 and x = 6.92) show in a broad energy range below 50 meV a distinct decrease of the conductivity with decreasing temperature. This behaviour can be related to a pseudo-gap, as it is known from earlier investigations [1,4]. This
(cm -1) 400 0 300 -
200
,~oo
I
I
600 t
1
x=6.g8
200 i
II
100
~
400
"~ 300;
;
X=6-g2
~.~..~ ~
u~ 2oo
.
i00 •~ 400
300 E-
/
x=6.8o
200 LO)Io0 4OO 300 -
x=6.30
200 i00 i 0
'
o
0.02
0.04 o.oe h~J ( e V )
0.08
Fig. 2. Optical conductivity ~rll c calculated from the data of Fig. 1 by a Kramers-Kronig transformation at T = 10 K (-), T = 100 K ( - - - ) and T = 300 K ( . . . . ). The arrows mark the beginning of the region where the low temperature data exceed that of the higher temperature.
pseudo-gap appears to be more prominent in x = 6.80, and still exists at least at x = 6.70 and x -- 6.5 [1], but is obviously not longer observed in x = 6.3. In contrast to the behaviour of the 'underdoped' samples, the conductivity spectra of the composition with the highest oxygen content, YBaECU306.98, show neither a decrease with decreasing temperature for T > Tc nor a "metallic like" behaviour as is known from the results of Homes et al. [1], and of Schtitzmann et al. [4] at corresponding high oxygen contents. As mentioned above (Sec. II), this discrepancy may be caused by the small differences of the chemical compositions of the samples: The use of AI20 3 crucibles leads to a replacement of Cu ions by Al by a small amount, which predominantly takes place within the CuO-chains. As the CuO-chains play an essential role in the interchange of carriers between adjacent CuO 2 layers it may be possible that the A1 ions within the chains yield a suppression of the electronic transport along the c axis. In tum, doping with Ca which increases the carrier concen-
314
J. MiJnzel et aL /Physica C 270 (1996) 311-316
:2°V00 Irl~ ~ ~ ~,, TT00K
6o[
o.b:
'o.bs'oi:
o,oi 6.3
'1
T:300K
o.s':
/
~
6.8
6.9
_f- j 6.~-
6.5
6.6 6.7 oxygen conten[ x
30
/ , ::%
:o?
~p¢)2
Fig. 3. Square of the low temperature plasma energy (h and the extrapolated dc conductivity as a function of oxygen content ( T = 3 0 0 K). Inset: Extrapolated dc conductivity O'd
tration within the CuO 2 layers [17], enhances the o'11c as well remarkably [4,18]. As the conductivity function o'llc at 300 K of all samples is almost constant at low energies, the extrapolation to tO ~ 0 yields reasonable values of O'd
anisotropic reflecting the transition from a 3-D to a 2-D metal. As mentioned earlier the low temperature plasma energies of all samples are much lower than the plasma energies obtained from a Drude-Lorentz fit of the room temperature data. It seems to be obvious that only a small fraction of the carriers which contribute to the strongly damped room temperature plasma edge take part in the superconducting transition. On the other hand, in the presented samples the following condition is fulfilled [2]: h % << 2z~,
(1)
where top denotes the low temperature plasma frequency and 2 A is the maximum value of the superconducting gap. Furthermore, the free carrier scattering rate shows a strong decrease with temperature for T < Tc [2]. Therefore, it can be assumed that, at sufficient low temperatures the entire free carrier contribution condensates into the superconducting state [ 14]. Under these special conditions the plasma frequency at low temperature and the dc conductivity at room temperature are determined both by the total number of the carriers N: tOp: IIc(T
= 10 K) = N e 2 / e o m ,
o'a, , c( T = 300 K ) = N e 2 / m r ,
(2)
with the optical mass m and the scattering rate 3'. ThUS, tOp2IIc and o-a
J. M~nzel et a l . / Physica C 270 (1996) 311-316
0
200
(cm-1) 400
600
200 1so t
I
I
loo
~200 ~
x=~.uz I
ls0L
I
./A 200 ~
I x=6.98
150~\"t
5°°o
~ ~w (meV)
Fig. 4. Electronic contribution of the optical conductivity O'tlc for T = 300 K (dashed line) and T = 10 K. The shadowed area represents the spectral weight of the condensed carriers at low temperatures.
maximum shift almost linearly to lower energies. Simultanouesly, in all compositions a loss of spectral weight with temperature can be observed in the energy range of the two highest phonon lines indicating that an excitation arises or narrows at low temperature which is hidden in the broad electronic background at room temperature. A similar excitation is also found at corresponding lower energies in the spectra of Y B a 2 C u 3 0 6 . 5 and YBa2Cu306. 7, respectively [4,1]. Analogeous to the lack of free carrier contribution at the oxygen content x = 6.3 no cross-over is observed in this composition (Fig. 2). Because of the clear dependence on the carrier concentration we think that this effect is of electronic origin, in contrast to the assumptions given by the above mentioned authors. An analysis of the spectral weight of the electronic contribution shown in Fig. 4 supports the assumption of the coexistence of free and loalized carriers within the samples. The free carrier contribution calculated from the low temperature plasma edge is symbolized by the shadowed areas. While the spectral weight of the free carriers condensed into the superconducting phase decreases with decreasing doping concentration, the contribution of the localized carriers increases slightly, indicated by the shift of spectral weight from the free carriers to the
315
localized carriers. At the same time, within the contribution of localized carriers, spectral weight is transferred from lower to higher energy, giving evidence for a decrease of the mean localization length of the carriers in the c direction. These experimental results suggest the following explanation: As a comparison between the Bi and T1 based high T c superconductors and the Y based superconductors YBa2Cu30 x and YBa2Cu308 shows that the conductivity along the c axis depends essentially on the existence of CuO chains between the CuO 2 double layers [22]. Additionally to this role as acceptors introducing holes into the bilayers, the CuO chains carry the charge transport of carriers between adjacent bilayers. To give an idea how localization may occur in this system, we regard cells which are adjacent in c direction as independent channels of c axis conductivity. Following this simple model chain oxygen sites which are not occupied would act as backscatterers for transport in c direction leading to an amount of completely localized carriers in all not fully oxygenated compositions of YBa2Cu30 x. This barriers can be bypassed via the (highly metallic) bilayers and thus the c axis transport is reenabled, but this bypassing will enhance the resistance of the sample in c direction. Thus, the strong doping dependence of O'dcll c (even at T = 300 K) is due to the decrease of the total number of charge carriers in the CuO 2 bilayers with decreasing oxygen content but also to the increase of "blocking" sites in the electronic transport along c direction, i.e. the decrease of the mean cross-section area. A combination of both effects would result in a power law for the dependency of O'dcllc on the oxygen deficiency ~, as seen in the inset of Fig. 3. It would explain in addition the behaviour seen in Fig. 4 as with decreasing the oxygen content the probability of blocking will increase and thus, the spectral weight of localized carriers will increase compared to that of the itinerant carriers. At low oxygen contents ( x < 6.5), however, O'd~IIc decreases rapidly and breaks down when the system crosses a percolation threshhold. In compositions with x < 6.3 all carriers are entirely localized. It should be noted that in this model no effects occurring due to a transition from coherent to incoherent transport nor due to the influence of the pseudo-gap are taken into account. They both would
316
J. M~nzel et aL /Physica C 270 (1996) 311-316
yield a stronger doping dependence, in the overdoping regime, and at low temperatures, respectively. As our samples r e m a i n in the " i n c o h e r e n t " regime e v e n in the highest o x y g e n concentration, only the effect of the latter can be seen in the inset of Fig. 3.
4. Conclusions D e t e r m i n i n g the reflectance spectra RII c and the conductivity function trll c of Y B a 2 C u 3 0 x at low temperature and different o x y g e n content x, we were able to separate the contributions o f free and localized carriers to the transport properties. With decreasing o x y g e n content, the spectral weight of free carriers decreases whereas that of the localized carriers is enhanced, thus the anisotropy of the compositions increases. At room temperature, the contribution of both types of carriers merge into a weak spectral dependence of trll c resulting in a smooth reflectivity edge. At low temperatures, both contributions are separated. The free carriers c o n d e n s e d into the superconducting state yield a steep low temperature plasma edge, the excitation o f localized carriers results in a peak of the the conductivity function o-iic.
Acknowledgements This work was supported b y the S o n d e r p r o g r a m m zur G r u n d l a g e n f o r s c h u n g auf d e m Gebiet der H o c h t e m p e r a t u r s u p r a l e i t u n g des L a n d e s B a d e n Wiirttemberg, b y the C o m m i s s i o n o f the E u r o p e a n C o m m u n i t i e s under Contract No. C 11-0526-M(CD), and by the Deutsche Forschungsgemeinschaft.
References [1] C.C. Homes, T. Timusk, D.A. Bonn, R. Liang and W.N. Hardy, Physica C 254 (1995) 265. [2] J. M~nzel, K. Widder, H.P. Geserich, P. W~lfle, W. Widder, H.G. Braun and Th. Wolf, Physica C 235-240 (1994) 1087.
[3] J. Schiitzmann, S. Tajima, S. Miyamato and S. Tanaka, Phys. Rev. Lett. 73 (1994) 174. [4] J. Schiitzmann, S. Tajima, S. Miyamato, Y. Sato and R. Hauff, Phys. Rev. B 52 (1995) 13665. [5] J. Miinzel, A. Zibold, H.P. Geserich and Th. Wolf, to be published in Europhys. Lett. [6] B. Koch, M. Diirrler, H.P. Geserich, Th. Wolf, G. Roth and G. Zachmann, in: Electronic Properties of High-Tc Superconductors and Related Compounds, eds. H. Kuzmany, M. Mehring and J. Fink (Springer, Berlin, 1990). [7] M. Diirrler, B. Koch, H.P. Geserich and Th. Wolf, in: Electronic Properties of High-Tc Superconductors and Rela~d Compounds, eds. H. Kuzmany, M. Mehring and J. Fink (Springer, Berlin, 1990). [8] K. Tamasaku, Y. Nakamura and S. Uchida, Phys. Rev. Lett. 69 (1992) 1455. [9] A.V. Bazhenov, Sov. Phys, JETP 95 (1992) 566. [10] C.C. Homes, T. Timusk, R. Liang, D.A. Bonn and W.N. Hardy, Phys. Rev. Lett. 71 (1993) 1645. [11] J.H. Kim, H.S. Somal, M.T. Czyzik, D. Van der Marel, A.M. Gerrits, A. Wittlin, V.H.M. Duijn, N.T. Hien and A.A. Menovsky, Physica C 247 (1995) 297. [12] V.M. Burlakov, K.F. Renk, A. Gaymann, J. Mfinzel and H.P. Geserich, Physica C 221 (1994) 269. [13] C. Thomsen, in: Light scattering in Solids IV: Topics in Applied Physics 68, eds. M. Cardona and G. Ghntherrodt (Springer, Berlin, 1991). [14] P. W6lfle, J. Low Temp. Phys. 95 (1994) 191. [15] Th. Wolf, private communication. [16] Th. Wolf, W. Goldacker, B. Obst, G. Roth and R. Fliikiger, J. Crystal Growth 96 (1989) 1110. [17] K. Widder et al., to be published. [18] J. Miinzel et al., unpublished. [19] S.L. Cooper, P. Nyhus, D. Reznik, M.V. Klein, W.C. Lee, D.M. Ginsberg, B.W. Veal and A.P. Paulinkas, J. Phys. Chem. Sol. 54 (1992) 1307. [20] A strong change of the phonon lines is first observed in samples with even smaller oxygen content (x _<6.5) [9,4]. [21] S.L. Cooper, D. Reznik, A. Kotz, M.A. Karlow, R. Liu, M.V. Klein, W.C. Lee, J. Giapintzakis, D.M. Ginsberg, B,W. Veal and A.P. Paulikas, Phys. Rev. B 47 (1993) 8233. [22] For a review see: S.L. Cooper, K.E. Gray, in: High-Temperature Superconductivity, Vol. IV, ed. D. Ginsburg (World Scientific, Singapore, 1994) p. 61. [23] J. Orenstein, G.A. Thomas, A.J. Millis, S.L. Cooper, D.H. Rapkine, T. Timusk, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. B 42 (1990) 6342. [24] A. Zibold, K. Widder, H.P. Geserich, G. Bfiiuchle, H. Claus, H.v. Lbhneysen, N. Niicker, A. Erb and G. Miiller-Vogt, Physica C 212 (1993) 365.
Physica C 270 (1996) 311-316
Localization of charge carders in the c-axis electronic transport of YBa2Cu30 x J. M ~ n z e l *'a H.P. G e s e r i c h a Th. W o l f b a Institutffir angewandte Physik, Unioersit~t Karlsruhe, D-76128 Karlsruhe, Germany b Institutffir Technische Physik, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany Received 28 December 1995; revised manuscript received 22 August 1996
Abstract
Reflectance measurements with EII c on a YBa2Cu3Ox single crystal where the oxygen content was varied between x ~ 6.8 and x ~ 6.98 are presented in the far infrared range (5 meV < h w < 100 meV) at temperatures between 10 K and 300 K. Performing a Kramers-Kronig transformation we derived the optical conductivity Orllc(hto). A n analysis of the spectral weight shows that the main contribution of the electronic transport is due to localized carders. With decreasing the oxygen content, the spectral weight of free carders decreases whereas the spectral weight of localized carriers is enhanced. Keywords: Far infrared spectra; Anisotropic superconductor; Normal state properties; c-Axis conductivity
1. Introduction The far infrared properties of YBa2Cu30 x for E II c are determined both by lattice vibrations and by charge carriers, i.e. holes hopping between adjacent CuO2-double layers. Both contributions are strongly temperature-dependent: The outstanding phenomenon of the electronic system is the development of an reflectivity edge in the far infrared regime upon cooling below the superconducting transitiort temperature, [1-11]. Homes et al. [1] have shown that, in the case of non fully doped YBa2Cu30 x ( x < 6.92), a decrease of the optical conductivity o-iic(hto) with decreasing temperature occurs in a broad energy range below 50 meV. This so-called pseudogap depends on the doping concentration. It is most prominent at an oxygen content of about x =
* Corresponding author. Fax: + 4 9 721 607 593.
6.85, and disappears completely both, in the fully doped and overdoped samples ( x > 6.92), and in the non metallic samples ( x < 6.3). In the phonon spectrum, the development of Fano-like lineshapes at low temperatures is reported both in infrared and Raman investigations [12,13], giving evidence for coupling between phonons and some electronic background in the energy range of the lattice vibrations. Nevertheless, the separation between electronic and phononic contributions to o-ii c in the energy range between 10 meV and 100 meV remained as a still open question. Independently from the pseudogap a broad excitation arises with decreasing temperature which also turns out to be doping dependent: centered at about 60 meV for x = 6.85 this feature shifts to lower energies with decreasing oxygen content [1-3]. It was argued that this new excitation is of phononic origin as simultanouesly a loss of spectral weight in the energy range of the two upper phonon modes can
0921-4534/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S 0 9 2 1 - 4 5 3 4 ( 9 6 ) 0 0 5 1 1 - 4
312
J. M~nzel et aL /Physica C 270 (1996) 311-316
be observed. However, the developing of a broad, quasi glass-like phonon band should be attended by strong changes of the underlying structure, which is not observed in YBa2Cu30 x. As a substantial outcome of the present paper it turns out that this excitation can be ascribed to the electronic contribution of the conductivity function and it is related to localized carriers.
2. Experimental
tO00 60
¢00
~'
~
7 ~S-~
4-0
600 x=6.98
~:~..__.~
.
2O 100
80
,~"~ ~
N 40 ~ 20
x=6.92 -"
~ 100
'-, 8o ¢,
Single crystals of YBa2Cu30 x with a typical size of 2.5 X 2.5 X 2 mm 2 were grown by a technique described earlier [15]. AI203 crucibles were used to get a sufficient sample thickness. This results in a replacement of Cu Ions by A1 Ions in the order of one percent which decreases T~ by about 2 - 3 K, and additionally it flattens out the parabolic lineshape of the dependence of Tc on the oxygen content x [16]. It may also cause a decrease of the optical conductivity, as investigations on samples grown in ZrO crucibles show a strong enhancement of o-II c, compared to samples from A1203 crucibles [1]. A maximum value of the oxygen content of x = 6.98 was attained by annealing the samples in an atmosphere of flowing oxygen in two steps, at a temperature of 400°C and 380°C for 140 h and 280 h, respectively. The superconducting transition temperature of these samples was 88.5 K. After obtaining the polarized spectra RIIc at this oxygen content, in a next step the crystals underwent a procedure of decreasing the oxygen content to x = 6.92 (T~ = 89 K). Again the FIR spectra werde taken. Subsequently, the crystals were reduced in a final annealing process to an oxygen content of x = 6.80 (T~ = 79 K), and the corresponding spectra were attained. The procedure of lowering the oxygen content is described in more detail in [5]. For comparison, reflectivity measurements were also performed on crystals of different batches with oxygen contents of x = 6.95 and x = 6.3, respectively. The data obtained from the samples with x = 6.95 coincide with the above 6.93-composition. The reflectance spectra were obtained on (010) surfaces using a Fourier transform spectrometer (Bruker l13v) in the spectral range between 4 meV and 1 eV. The temperature of the samples was varied between 10 K and 300 K using a
•~ ( c m -1)
200
02
z',
x=6.80
40 20
6o~
i00 8o 40 20
I
x=&30
~,.
0
''
0
r
0.02
0.040.06 h~a ( e V )
0.08
Fig. I. Polarized reflectance spectra RII c of Y B a 2 C u 3 0 x with different oxygen content x at T = 10 K ( - ) , T = 100 K ( - . - ) and T = 300 K ( . . . . ) in the highly doped regime ( x > 6.8) (upper panels) and at T = l0 K and T = 300 K for x = 6.3 (lower panel).
helium-flow cryostat (Oxford 1204). At each temperature the sample spectrum was compared to a reference gold mirror using a turning mechanism within the cryostat. This procedure and the calibration with the data obtained by a single beam setup at room temperature yield a photometric accuracy better than one percent. We derived the optical conductivity Giic(h~) from the reflectivity data performing a Kramers-Kronig transformation. As lattice vibrations play a predominant role in the conductivity spectra, additionally a Drude-Lorentz fit was used to separate the contribution of the lattice vibrations from that of the charge carders, and to calculate the plasma energies for different temperatures.
3. Results and discussion In the upper panels of Fig. 1 the reflectance spectra RIIc of a crystal are shown where the oxygen content was varied between x = 6.98 and x = 6.80. The spectra were taken at room temperature, T = 100
313
J. Mr,nzel et al./Physica C 270 (1996) 311-316
K, and T = 10 K. All spectra are dominated by phonons: six phonon lines can be distinguished, separated into three bands each of them containing two phonon modes. With the exception of a transfer of spectral weight from the phonon mode at 560 c m - ' to the mode at 630 cm- 1, a behaviour that continues even to lower oxygen content [1], no significant changes in the phonon lines with decreasing oxygen content can be observed [20]. Compared to the spectra obtained at high oxygen content, the spectrum of a sample with x = 6.3 displayed in the lower panel of Fig. 1, shows distinct differences, both, in eigenfrequencies and oscillator strength of the phonon modes. Upon cooling the phonon modes are almost unchanged and can be described within a good approximation by Lorentzian lineshapes. The phonon lines are superimposed by a broad electronic background, which shows above T~ in the samples with high oxygen content a strongly damped plasma edge around 0.1 eV known from earlier investigations [19,22]. Below T~, however, this smooth plasma edge disappears, and a steep reflectivity edge develops in the energy range of the far-infrared which reflects the condensation of free carriers into the superconducting phase [5,6,14]. Depending sensitively on the oxygen content this low temperature plasma edge is found at top IIc = 10 meV for x = 6.80 and top ll c = 14 meV for x = 6.98. That means, it represents only a small fraction of those carriers which contribute to the plasma edge observed at room temperature. With decreasing oxygen content the low temperature plasma edge shifts to lower energy and disappears for x < 6.5 [4]. As the lowest panel of Fig. 1 shows, the electronic background of the reflectance spectrum for x = 6.3 is drastically reduced and nearly independent of temperature, indicating that the free carrier contribution in this composition has completly disappeared. The conductivity spectra trll~, calculated from the reflectivity by a Kramers-Kronig transformation, are shown in Fig. 2. Above the superconducting transition temperature, the spectra of the lower doped compositions ( x - - 6 . 8 0 and x = 6.92) show in a broad energy range below 50 meV a distinct decrease of the conductivity with decreasing temperature. This behaviour can be related to a pseudo-gap, as it is known from earlier investigations [1,4]. This
(cm -1) 400 0 300 -
200
,~oo
I
I
600 t
1
x=6.g8
200 i
II
100
~
400
"~ 300;
;
X=6-g2
~.~..~ ~
u~ 2oo
.
i00 •~ 400
300 E-
/
x=6.8o
200 LO)Io0 4OO 300 -
x=6.30
200 i00 i 0
'
o
0.02
0.04 o.oe h~J ( e V )
0.08
Fig. 2. Optical conductivity ~rll c calculated from the data of Fig. 1 by a Kramers-Kronig transformation at T = 10 K (-), T = 100 K ( - - - ) and T = 300 K ( . . . . ). The arrows mark the beginning of the region where the low temperature data exceed that of the higher temperature.
pseudo-gap appears to be more prominent in x = 6.80, and still exists at least at x = 6.70 and x -- 6.5 [1], but is obviously not longer observed in x = 6.3. In contrast to the behaviour of the 'underdoped' samples, the conductivity spectra of the composition with the highest oxygen content, YBaECU306.98, show neither a decrease with decreasing temperature for T > Tc nor a "metallic like" behaviour as is known from the results of Homes et al. [1], and of Schtitzmann et al. [4] at corresponding high oxygen contents. As mentioned above (Sec. II), this discrepancy may be caused by the small differences of the chemical compositions of the samples: The use of AI20 3 crucibles leads to a replacement of Cu ions by Al by a small amount, which predominantly takes place within the CuO-chains. As the CuO-chains play an essential role in the interchange of carriers between adjacent CuO 2 layers it may be possible that the A1 ions within the chains yield a suppression of the electronic transport along the c axis. In tum, doping with Ca which increases the carrier concen-
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J. MiJnzel et aL /Physica C 270 (1996) 311-316
:2°V00 Irl~ ~ ~ ~,, TT00K
6o[
o.b:
'o.bs'oi:
o,oi 6.3
'1
T:300K
o.s':
/
~
6.8
6.9
_f- j 6.~-
6.5
6.6 6.7 oxygen conten[ x
30
/ , ::%
:o?
~p¢)2
Fig. 3. Square of the low temperature plasma energy (h and the extrapolated dc conductivity as a function of oxygen content ( T = 3 0 0 K). Inset: Extrapolated dc conductivity O'd
tration within the CuO 2 layers [17], enhances the o'11c as well remarkably [4,18]. As the conductivity function o'llc at 300 K of all samples is almost constant at low energies, the extrapolation to tO ~ 0 yields reasonable values of O'd
anisotropic reflecting the transition from a 3-D to a 2-D metal. As mentioned earlier the low temperature plasma energies of all samples are much lower than the plasma energies obtained from a Drude-Lorentz fit of the room temperature data. It seems to be obvious that only a small fraction of the carriers which contribute to the strongly damped room temperature plasma edge take part in the superconducting transition. On the other hand, in the presented samples the following condition is fulfilled [2]: h % << 2z~,
(1)
where top denotes the low temperature plasma frequency and 2 A is the maximum value of the superconducting gap. Furthermore, the free carrier scattering rate shows a strong decrease with temperature for T < Tc [2]. Therefore, it can be assumed that, at sufficient low temperatures the entire free carrier contribution condensates into the superconducting state [ 14]. Under these special conditions the plasma frequency at low temperature and the dc conductivity at room temperature are determined both by the total number of the carriers N: tOp: IIc(T
= 10 K) = N e 2 / e o m ,
o'a, , c( T = 300 K ) = N e 2 / m r ,
(2)
with the optical mass m and the scattering rate 3'. ThUS, tOp2IIc and o-a
J. M~nzel et a l . / Physica C 270 (1996) 311-316
0
200
(cm-1) 400
600
200 1so t
I
I
loo
~200 ~
x=~.uz I
ls0L
I
./A 200 ~
I x=6.98
150~\"t
5°°o
~ ~w (meV)
Fig. 4. Electronic contribution of the optical conductivity O'tlc for T = 300 K (dashed line) and T = 10 K. The shadowed area represents the spectral weight of the condensed carriers at low temperatures.
maximum shift almost linearly to lower energies. Simultanouesly, in all compositions a loss of spectral weight with temperature can be observed in the energy range of the two highest phonon lines indicating that an excitation arises or narrows at low temperature which is hidden in the broad electronic background at room temperature. A similar excitation is also found at corresponding lower energies in the spectra of Y B a 2 C u 3 0 6 . 5 and YBa2Cu306. 7, respectively [4,1]. Analogeous to the lack of free carrier contribution at the oxygen content x = 6.3 no cross-over is observed in this composition (Fig. 2). Because of the clear dependence on the carrier concentration we think that this effect is of electronic origin, in contrast to the assumptions given by the above mentioned authors. An analysis of the spectral weight of the electronic contribution shown in Fig. 4 supports the assumption of the coexistence of free and loalized carriers within the samples. The free carrier contribution calculated from the low temperature plasma edge is symbolized by the shadowed areas. While the spectral weight of the free carriers condensed into the superconducting phase decreases with decreasing doping concentration, the contribution of the localized carriers increases slightly, indicated by the shift of spectral weight from the free carriers to the
315
localized carriers. At the same time, within the contribution of localized carriers, spectral weight is transferred from lower to higher energy, giving evidence for a decrease of the mean localization length of the carriers in the c direction. These experimental results suggest the following explanation: As a comparison between the Bi and T1 based high T c superconductors and the Y based superconductors YBa2Cu30 x and YBa2Cu308 shows that the conductivity along the c axis depends essentially on the existence of CuO chains between the CuO 2 double layers [22]. Additionally to this role as acceptors introducing holes into the bilayers, the CuO chains carry the charge transport of carriers between adjacent bilayers. To give an idea how localization may occur in this system, we regard cells which are adjacent in c direction as independent channels of c axis conductivity. Following this simple model chain oxygen sites which are not occupied would act as backscatterers for transport in c direction leading to an amount of completely localized carriers in all not fully oxygenated compositions of YBa2Cu30 x. This barriers can be bypassed via the (highly metallic) bilayers and thus the c axis transport is reenabled, but this bypassing will enhance the resistance of the sample in c direction. Thus, the strong doping dependence of O'dcll c (even at T = 300 K) is due to the decrease of the total number of charge carriers in the CuO 2 bilayers with decreasing oxygen content but also to the increase of "blocking" sites in the electronic transport along c direction, i.e. the decrease of the mean cross-section area. A combination of both effects would result in a power law for the dependency of O'dcllc on the oxygen deficiency ~, as seen in the inset of Fig. 3. It would explain in addition the behaviour seen in Fig. 4 as with decreasing the oxygen content the probability of blocking will increase and thus, the spectral weight of localized carriers will increase compared to that of the itinerant carriers. At low oxygen contents ( x < 6.5), however, O'd~IIc decreases rapidly and breaks down when the system crosses a percolation threshhold. In compositions with x < 6.3 all carriers are entirely localized. It should be noted that in this model no effects occurring due to a transition from coherent to incoherent transport nor due to the influence of the pseudo-gap are taken into account. They both would
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J. M~nzel et aL /Physica C 270 (1996) 311-316
yield a stronger doping dependence, in the overdoping regime, and at low temperatures, respectively. As our samples r e m a i n in the " i n c o h e r e n t " regime e v e n in the highest o x y g e n concentration, only the effect of the latter can be seen in the inset of Fig. 3.
4. Conclusions D e t e r m i n i n g the reflectance spectra RII c and the conductivity function trll c of Y B a 2 C u 3 0 x at low temperature and different o x y g e n content x, we were able to separate the contributions o f free and localized carriers to the transport properties. With decreasing o x y g e n content, the spectral weight of free carriers decreases whereas that of the localized carriers is enhanced, thus the anisotropy of the compositions increases. At room temperature, the contribution of both types of carriers merge into a weak spectral dependence of trll c resulting in a smooth reflectivity edge. At low temperatures, both contributions are separated. The free carriers c o n d e n s e d into the superconducting state yield a steep low temperature plasma edge, the excitation o f localized carriers results in a peak of the the conductivity function o-iic.
Acknowledgements This work was supported b y the S o n d e r p r o g r a m m zur G r u n d l a g e n f o r s c h u n g auf d e m Gebiet der H o c h t e m p e r a t u r s u p r a l e i t u n g des L a n d e s B a d e n Wiirttemberg, b y the C o m m i s s i o n o f the E u r o p e a n C o m m u n i t i e s under Contract No. C 11-0526-M(CD), and by the Deutsche Forschungsgemeinschaft.
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[3] J. Schiitzmann, S. Tajima, S. Miyamato and S. Tanaka, Phys. Rev. Lett. 73 (1994) 174. [4] J. Schiitzmann, S. Tajima, S. Miyamato, Y. Sato and R. Hauff, Phys. Rev. B 52 (1995) 13665. [5] J. Miinzel, A. Zibold, H.P. Geserich and Th. Wolf, to be published in Europhys. Lett. [6] B. Koch, M. Diirrler, H.P. Geserich, Th. Wolf, G. Roth and G. Zachmann, in: Electronic Properties of High-Tc Superconductors and Related Compounds, eds. H. Kuzmany, M. Mehring and J. Fink (Springer, Berlin, 1990). [7] M. Diirrler, B. Koch, H.P. Geserich and Th. Wolf, in: Electronic Properties of High-Tc Superconductors and Rela~d Compounds, eds. H. Kuzmany, M. Mehring and J. Fink (Springer, Berlin, 1990). [8] K. Tamasaku, Y. Nakamura and S. Uchida, Phys. Rev. Lett. 69 (1992) 1455. [9] A.V. Bazhenov, Sov. Phys, JETP 95 (1992) 566. [10] C.C. Homes, T. Timusk, R. Liang, D.A. Bonn and W.N. Hardy, Phys. Rev. Lett. 71 (1993) 1645. [11] J.H. Kim, H.S. Somal, M.T. Czyzik, D. Van der Marel, A.M. Gerrits, A. Wittlin, V.H.M. Duijn, N.T. Hien and A.A. Menovsky, Physica C 247 (1995) 297. [12] V.M. Burlakov, K.F. Renk, A. Gaymann, J. Mfinzel and H.P. Geserich, Physica C 221 (1994) 269. [13] C. Thomsen, in: Light scattering in Solids IV: Topics in Applied Physics 68, eds. M. Cardona and G. Ghntherrodt (Springer, Berlin, 1991). [14] P. W6lfle, J. Low Temp. Phys. 95 (1994) 191. [15] Th. Wolf, private communication. [16] Th. Wolf, W. Goldacker, B. Obst, G. Roth and R. Fliikiger, J. Crystal Growth 96 (1989) 1110. [17] K. Widder et al., to be published. [18] J. Miinzel et al., unpublished. [19] S.L. Cooper, P. Nyhus, D. Reznik, M.V. Klein, W.C. Lee, D.M. Ginsberg, B.W. Veal and A.P. Paulinkas, J. Phys. Chem. Sol. 54 (1992) 1307. [20] A strong change of the phonon lines is first observed in samples with even smaller oxygen content (x _<6.5) [9,4]. [21] S.L. Cooper, D. Reznik, A. Kotz, M.A. Karlow, R. Liu, M.V. Klein, W.C. Lee, J. Giapintzakis, D.M. Ginsberg, B,W. Veal and A.P. Paulikas, Phys. Rev. B 47 (1993) 8233. [22] For a review see: S.L. Cooper, K.E. Gray, in: High-Temperature Superconductivity, Vol. IV, ed. D. Ginsburg (World Scientific, Singapore, 1994) p. 61. [23] J. Orenstein, G.A. Thomas, A.J. Millis, S.L. Cooper, D.H. Rapkine, T. Timusk, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. B 42 (1990) 6342. [24] A. Zibold, K. Widder, H.P. Geserich, G. Bfiiuchle, H. Claus, H.v. Lbhneysen, N. Niicker, A. Erb and G. Miiller-Vogt, Physica C 212 (1993) 365.