- Email: [email protected]
Transport properties of localized states in Bi2Sr2CuO6 single crystals
PHYSICA ELSEVIER
Physica C 263 (1996) 321-324
Transport properties of localized states in Bi2SrECuO 6 single crystals Katsuhiko Inagaki *, Kazuhiko Yamaya, Satoshi Tanda Department of Applied Physics, Hokkaido University, Sapporo 060, Japan
Abstract Transport properties, such as electric conductivity, magnetoresistance, and Hall coefficient are measured in Bi 2Sr2CuO6 single crystals. The conductivity drops at low temperature proportional to log T. This behavior is interpreted as the weakly localized regime of Anderson localization, since we observe log T, log E and log H dependences of the conductivity. The coefficients of log T and log E come close to the expected values by treating the sample as consisting of stacked two-dimensional conduction planes. However, the coefficient of log H is much less than the universal value which is expected from theories of the weakly localized regime. From the results of Hall measurement, we show that electron-electron interaction does not play a major role.
1. Introduction The normal state transport of high-Tc superconducting cuprates is still far from being completely understood, though many years have passed since the first discovery of the superconducting cuprate. In particular, the relation between the localization of carders due to the randomness and the Mott transition has remained unknown, and is an important issue in investigating the mechanism of high-temperature superconductivity. Electric conduction of the cuprates occurs by doping carders into the two-dimensional CuO 2 planes. Since the doped carriers also introduce random potentials into the CuO 2 planes, the doped cuprates can be regarded as inherently disordered two-dimensional systems. Indeed, localization phenomena have been observed in various kinds of cuprates [1-5]. Among them,
Bi2Sr2CuO 6 is one o f the ideal materials for studying the normal state transport of high-T~ cuprates because of its lower Tc( < 9 K). The localized states of Bi2Sr2CuO 6 have previously been studied in relation to the dimensionality of localization [1] and the anomalous scattering rate observed in highly doped crystals [2]. In our current work, we synthesize lower-doped crystals of Bi2Sr2CuO 6, and measure electric field dependence, magnetic field dependence, and temperature dependence of in-plane conductivity of the Bi2Sr2CuO 6 single crystals. We find the new results that the coefficient of log H is much smaller than those of log E and log T, and that the difference in coefficients is not caused by electron-electron interaction.
2. Experimental * Corresponding author. Fax: + 8 1 11 706 6075; e-mail: [email protected].
The single crystals of Bi2Sr2CuO 6 were synthesized by a self-flux method [6]. The starting compo-
0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 3 4 ( 9 6 ) 0 0 0 8 4 - 6
K. lnagaki et al./ Physica C 263 (1996) 321-324
322 sition
consisted
of
Bi203: S r C O
3 "CuO
=- 1 . 0 : 1 . 0
:
1.5 (mol). The mixture was melted in the furnace at 950°C for 10 h, then cooled at the rate of 5°C/h from 950°C to 800°C. All the processes were carried out under standard air. The typical geometry is 1 × 0.5 × 0.01 mm 3. The number of CuO 2 layers stacked in the Bi2Sr2CuO6 sample is calculated as 8000 by considering the spacing between the CuO 2 layers, 12 .~. We determine the carrier density of the sample n = 2 × 1021 cm -3 from the measurement of the Hall coefficient. We mention here that the carrier density of the Bi2Sr2CuO6 crystals used in Ref. [2] is 4 × 1021 cm -3, and that of the optimally doped Bi2Sr2CuO6, which has the highest Tc, is found near 3 × 1021 cm -3 [7]. To measure electrical conductivity, we use a four-probe method. The flowing DC electric current is 100 p,A. The direction of the current is periodically reverted in order to minimize the effect of thermoelectric power. We also use pulsed current to measure the voltage dependence of conductivity at higher voltage. Magnetoconductivity due to the orbital motion of carriers is obtained as Atr=b(H)= ( p~ (H) - pllab(H))/(p=b(0)) 2, where Pa~ (H)pllab(H) are the magnetoresistance with applied magnetic field perpendicular and parallel to the CuO 2 planes, respectively. Fig. 1 shows the in-plane conductivity O'~b observed as a function of temperature T, electric field E, and magnetic field H. No superconducting transition is observed in the whole temperature range from room temperature to 1.6 K. The observed in-plane conductivity has logarithmic dependence on T, E and H. We obtain sheet conductance per one CuO 2 plane by dividing the observed conductivity by the number of stackings. Sheet conductances in the localized regime can be written as follows:
morab(Z) ~--2.5 X
10 -6
log
Z(~~-l),
Atrab(E ) = 1.2 × 10 -6 log E ( l q - ' ) , ACrab(H ) = 4 . 8 × 10 - 8 l o g H ( • - ' ) .
160
-(a)
i
.
.
.
.
.
.
.
.
.
.
.
cry/
Bi2Sr2CuO6
~ 140 7
single
~120
E.1o
f
1=0.1 mA
~100 80
E 0
300
100
10 T (K) (hi ........................
'
T=4.2K
.........
/
/
/ /
'7
/ /a> / / /
200 o •d , i
/ I ........
i
,
.......
i
.......
,i
10 -2
........
¢
.
100
E (V/cm) .... i
........
:(c)
_
~E
i
........
i
•
- -
T=1.6K 1
0
<3
.
.
102
103
..:
104
H (G) Fig. 1. In-plane conductivity as a function of (a) temperature, (b) electric field, and (c) magnetic field. All data are obtained by DC measurement, except for the high-field data of electric field dependence which are obtained by pulse measurement (open circles). Details of least-square firing are described in the text.
In the weakly localized regime (WLR), the conductance depends only upon the size of the system, L, e2
Note that the universal c o n d u c t a n c e appearing in the localization phenomena is given by e2/27r2h = 1.2 × 10 -5 (lq-J). The coefficients of Acr~b(T) and Ao'ao(E) are in reasonable agreement with the universal conductance, whereas A O'ab(H) disagrees by a factor of 50 with that of Ao'.o(T).
Art(L) = a~-~log
L,
(1)
where a is a constant of the order of unity. The size of the system is determined by various scattering processes, such as L t I T - p / 2 , H-1/2, and E-P/(1 + p / 2 ) [8,9]. Therefore, the factor of logarith-
K. lnagaki et aL / Physica C 263 (1996) 321-324
323
mic dependence changes only by the order of unity. In the case of the in-plane conductivity in question, the log T and log E dependence is consistent with that of WLR. However, the log H dependence has much smaller coefficient by a factor of 50. Our results suggest extra contributions to the in-plane conductivity. To discuss the difference in coefficients of log T and log H, we consider the effect of electron-electron interaction on transport properties. The electron-electron interaction also gives a log T decrease of conductivity. The coefficient of log T due to the interaction is ( 1 - F ) / ( e 2 / 2 ~ r 2 h ) , where F is a screening factor [10]. While the temperature dependence of conductivity is similar to that of the localization, the electron-electron interaction is expected to cause remarkably different magnetic field dependences in magnetoresistance and Hall coefficient [ 11]. The magnetoresistance due to localization is negative, and purely transverse for a thin film, whereas for the electron-electron interaction the magnetoresistance becomes positive, isotropic for spin splitting and transverse for the orbital part. We have shown that no trace of positive magnetoresistance due to the electron-electron interaction is observed in our sample (Fig. 1). Moreover, the Hall coefficient of the sample also shows that the interaction has a smaller contribution to the sample conductivity, because its correction is proportional to the resistance increase:
where the resistance varies from 2 to 7 II. We conclude that the effect of electron-electron interaction in Bi2Sr2CuO6 can be ignored, and hence does not explain the small coefficient of log H. The origin of the difference in coefficients of log T and log H has remained an unsolved problem. The localized state of Bi2Sr2CuO 6 seems to have a different nature from that of conventional metal films. The difference in the carder density might be a candidate to understand our results: our samples have slightly smaller carrier density, whereas the samples used in Ref. [2] have one larger than that of the optimally doped sample.
~ R . / R . = 2~R/R.
Acknowledgement
(2)
Fig. 2 shows that the Hall coefficient of the sample is almost constant from room temperature to 4.2 K,
.
.
.
.
.
.
.
.
i
.
.
.
.
.
.
.
.
i
•
To summarize, we have investigated the electric transport phenomena of Bi2Sr2CuO 6 single crystals. We compare the coefficients of log T, log E and log H dependences of the conductivity in the weakly localized regime. In conventional metal films, these coefficients are in accordance with a universal value of e2/2"rr2h. In the case of the Bi2Sr2CuO6 crystals, however, the coefficient of log H does not follow this rule. The effect of electron-electron interaction is negligible.
One of the authors (KI) is grateful for a Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists.
•
4 v
3. Summary
E "7 O
References
O
tr J
10
2 ~ -r tr
100
T (K) Fig. 2. In-plane resistance and the Hall coefficient as a function of temperature. The resistance varies from 2 to 7 fl, while the Hall coefficient remains almost constant. The broken line is a guide to the eye.
[1] A.T. Fiory, S. Martin, R.M. Fleming, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. B 41 (1990) 2627. [2] T.W. Jing, N.P. Ong and T.V. Ramakrishnan, Phys. Rev. Lett. 67 (1991) 761. [3] N.W. Preyer, M.A. Kastner, C.Y. Chen, RJ. Birgenau and Y. Hidaka, Phys. Rev. B 44 (1991) 407. [4] S. Tanda, M. Honma and T. Nakayama, Phys. Rev. B 43 (1991) 8725; S. Tanda, S. Ohzeki and T. Nakayama, Phys. Rev. Lett. 69 (1992) 530. [5] S.J. Hagen, X.Q. Xu, W. Jiang, J.L. Peng, Z.Y. Li and R.L. Greene, Phys. Rev. B 45 (1992) 515.
324
K. lnagaki et aL / Physica C 263 (1996) 321-324
[6] E. Sonder, B.C. Chakoumakos and B.C. Sales, Phys. Rev. B 40 (1989) 6872. [7] J. Hejtmanek, M. Nevriva, E. Pollert, D. Scdmidubsky and P. Vasck, Physica C 235-240 (1994) 1389. [8] P.W. Anderson, E. Abrahams and T.V. Ramakrishnan, Phys. Rev. Lett. 43 (1979) 728.
[9] M. Kaveh, M.J. Uren, R.A. Davies and M. Pepper, J. Phys. C: Solid State Phys. 14 (1981) L413. [10] B.L. Aitshuler, A.G. Aronov and P.A. Lee, Phys. Rev. Lett. 44 (1980) 1288. [l l] P.A. Lee and T.V. Ramakrishnan, Rev. Mod. Phys. 57 (1985) 287; Phys. Rev. Lett. 60 (1988) 2194.
Physica C 263 (1996) 321-324
Transport properties of localized states in Bi2SrECuO 6 single crystals Katsuhiko Inagaki *, Kazuhiko Yamaya, Satoshi Tanda Department of Applied Physics, Hokkaido University, Sapporo 060, Japan
Abstract Transport properties, such as electric conductivity, magnetoresistance, and Hall coefficient are measured in Bi 2Sr2CuO6 single crystals. The conductivity drops at low temperature proportional to log T. This behavior is interpreted as the weakly localized regime of Anderson localization, since we observe log T, log E and log H dependences of the conductivity. The coefficients of log T and log E come close to the expected values by treating the sample as consisting of stacked two-dimensional conduction planes. However, the coefficient of log H is much less than the universal value which is expected from theories of the weakly localized regime. From the results of Hall measurement, we show that electron-electron interaction does not play a major role.
1. Introduction The normal state transport of high-Tc superconducting cuprates is still far from being completely understood, though many years have passed since the first discovery of the superconducting cuprate. In particular, the relation between the localization of carders due to the randomness and the Mott transition has remained unknown, and is an important issue in investigating the mechanism of high-temperature superconductivity. Electric conduction of the cuprates occurs by doping carders into the two-dimensional CuO 2 planes. Since the doped carriers also introduce random potentials into the CuO 2 planes, the doped cuprates can be regarded as inherently disordered two-dimensional systems. Indeed, localization phenomena have been observed in various kinds of cuprates [1-5]. Among them,
Bi2Sr2CuO 6 is one o f the ideal materials for studying the normal state transport of high-T~ cuprates because of its lower Tc( < 9 K). The localized states of Bi2Sr2CuO 6 have previously been studied in relation to the dimensionality of localization [1] and the anomalous scattering rate observed in highly doped crystals [2]. In our current work, we synthesize lower-doped crystals of Bi2Sr2CuO 6, and measure electric field dependence, magnetic field dependence, and temperature dependence of in-plane conductivity of the Bi2Sr2CuO 6 single crystals. We find the new results that the coefficient of log H is much smaller than those of log E and log T, and that the difference in coefficients is not caused by electron-electron interaction.
2. Experimental * Corresponding author. Fax: + 8 1 11 706 6075; e-mail: [email protected].
The single crystals of Bi2Sr2CuO 6 were synthesized by a self-flux method [6]. The starting compo-
0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 3 4 ( 9 6 ) 0 0 0 8 4 - 6
K. lnagaki et al./ Physica C 263 (1996) 321-324
322 sition
consisted
of
Bi203: S r C O
3 "CuO
=- 1 . 0 : 1 . 0
:
1.5 (mol). The mixture was melted in the furnace at 950°C for 10 h, then cooled at the rate of 5°C/h from 950°C to 800°C. All the processes were carried out under standard air. The typical geometry is 1 × 0.5 × 0.01 mm 3. The number of CuO 2 layers stacked in the Bi2Sr2CuO6 sample is calculated as 8000 by considering the spacing between the CuO 2 layers, 12 .~. We determine the carrier density of the sample n = 2 × 1021 cm -3 from the measurement of the Hall coefficient. We mention here that the carrier density of the Bi2Sr2CuO6 crystals used in Ref. [2] is 4 × 1021 cm -3, and that of the optimally doped Bi2Sr2CuO6, which has the highest Tc, is found near 3 × 1021 cm -3 [7]. To measure electrical conductivity, we use a four-probe method. The flowing DC electric current is 100 p,A. The direction of the current is periodically reverted in order to minimize the effect of thermoelectric power. We also use pulsed current to measure the voltage dependence of conductivity at higher voltage. Magnetoconductivity due to the orbital motion of carriers is obtained as Atr=b(H)= ( p~ (H) - pllab(H))/(p=b(0)) 2, where Pa~ (H)pllab(H) are the magnetoresistance with applied magnetic field perpendicular and parallel to the CuO 2 planes, respectively. Fig. 1 shows the in-plane conductivity O'~b observed as a function of temperature T, electric field E, and magnetic field H. No superconducting transition is observed in the whole temperature range from room temperature to 1.6 K. The observed in-plane conductivity has logarithmic dependence on T, E and H. We obtain sheet conductance per one CuO 2 plane by dividing the observed conductivity by the number of stackings. Sheet conductances in the localized regime can be written as follows:
morab(Z) ~--2.5 X
10 -6
log
Z(~~-l),
Atrab(E ) = 1.2 × 10 -6 log E ( l q - ' ) , ACrab(H ) = 4 . 8 × 10 - 8 l o g H ( • - ' ) .
160
-(a)
i
.
.
.
.
.
.
.
.
.
.
.
cry/
Bi2Sr2CuO6
~ 140 7
single
~120
E.1o
f
1=0.1 mA
~100 80
E 0
300
100
10 T (K) (hi ........................
'
T=4.2K
.........
/
/
/ /
'7
/ /a> / / /
200 o •d , i
/ I ........
i
,
.......
i
.......
,i
10 -2
........
¢
.
100
E (V/cm) .... i
........
:(c)
_
~E
i
........
i
•
- -
T=1.6K 1
0
<3
.
.
102
103
..:
104
H (G) Fig. 1. In-plane conductivity as a function of (a) temperature, (b) electric field, and (c) magnetic field. All data are obtained by DC measurement, except for the high-field data of electric field dependence which are obtained by pulse measurement (open circles). Details of least-square firing are described in the text.
In the weakly localized regime (WLR), the conductance depends only upon the size of the system, L, e2
Note that the universal c o n d u c t a n c e appearing in the localization phenomena is given by e2/27r2h = 1.2 × 10 -5 (lq-J). The coefficients of Acr~b(T) and Ao'ao(E) are in reasonable agreement with the universal conductance, whereas A O'ab(H) disagrees by a factor of 50 with that of Ao'.o(T).
Art(L) = a~-~log
L,
(1)
where a is a constant of the order of unity. The size of the system is determined by various scattering processes, such as L t I T - p / 2 , H-1/2, and E-P/(1 + p / 2 ) [8,9]. Therefore, the factor of logarith-
K. lnagaki et aL / Physica C 263 (1996) 321-324
323
mic dependence changes only by the order of unity. In the case of the in-plane conductivity in question, the log T and log E dependence is consistent with that of WLR. However, the log H dependence has much smaller coefficient by a factor of 50. Our results suggest extra contributions to the in-plane conductivity. To discuss the difference in coefficients of log T and log H, we consider the effect of electron-electron interaction on transport properties. The electron-electron interaction also gives a log T decrease of conductivity. The coefficient of log T due to the interaction is ( 1 - F ) / ( e 2 / 2 ~ r 2 h ) , where F is a screening factor [10]. While the temperature dependence of conductivity is similar to that of the localization, the electron-electron interaction is expected to cause remarkably different magnetic field dependences in magnetoresistance and Hall coefficient [ 11]. The magnetoresistance due to localization is negative, and purely transverse for a thin film, whereas for the electron-electron interaction the magnetoresistance becomes positive, isotropic for spin splitting and transverse for the orbital part. We have shown that no trace of positive magnetoresistance due to the electron-electron interaction is observed in our sample (Fig. 1). Moreover, the Hall coefficient of the sample also shows that the interaction has a smaller contribution to the sample conductivity, because its correction is proportional to the resistance increase:
where the resistance varies from 2 to 7 II. We conclude that the effect of electron-electron interaction in Bi2Sr2CuO6 can be ignored, and hence does not explain the small coefficient of log H. The origin of the difference in coefficients of log T and log H has remained an unsolved problem. The localized state of Bi2Sr2CuO 6 seems to have a different nature from that of conventional metal films. The difference in the carder density might be a candidate to understand our results: our samples have slightly smaller carrier density, whereas the samples used in Ref. [2] have one larger than that of the optimally doped sample.
~ R . / R . = 2~R/R.
Acknowledgement
(2)
Fig. 2 shows that the Hall coefficient of the sample is almost constant from room temperature to 4.2 K,
.
.
.
.
.
.
.
.
i
.
.
.
.
.
.
.
.
i
•
To summarize, we have investigated the electric transport phenomena of Bi2Sr2CuO 6 single crystals. We compare the coefficients of log T, log E and log H dependences of the conductivity in the weakly localized regime. In conventional metal films, these coefficients are in accordance with a universal value of e2/2"rr2h. In the case of the Bi2Sr2CuO6 crystals, however, the coefficient of log H does not follow this rule. The effect of electron-electron interaction is negligible.
One of the authors (KI) is grateful for a Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists.
•
4 v
3. Summary
E "7 O
References
O
tr J
10
2 ~ -r tr
100
T (K) Fig. 2. In-plane resistance and the Hall coefficient as a function of temperature. The resistance varies from 2 to 7 fl, while the Hall coefficient remains almost constant. The broken line is a guide to the eye.
[1] A.T. Fiory, S. Martin, R.M. Fleming, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. B 41 (1990) 2627. [2] T.W. Jing, N.P. Ong and T.V. Ramakrishnan, Phys. Rev. Lett. 67 (1991) 761. [3] N.W. Preyer, M.A. Kastner, C.Y. Chen, RJ. Birgenau and Y. Hidaka, Phys. Rev. B 44 (1991) 407. [4] S. Tanda, M. Honma and T. Nakayama, Phys. Rev. B 43 (1991) 8725; S. Tanda, S. Ohzeki and T. Nakayama, Phys. Rev. Lett. 69 (1992) 530. [5] S.J. Hagen, X.Q. Xu, W. Jiang, J.L. Peng, Z.Y. Li and R.L. Greene, Phys. Rev. B 45 (1992) 515.
324
K. lnagaki et aL / Physica C 263 (1996) 321-324
[6] E. Sonder, B.C. Chakoumakos and B.C. Sales, Phys. Rev. B 40 (1989) 6872. [7] J. Hejtmanek, M. Nevriva, E. Pollert, D. Scdmidubsky and P. Vasck, Physica C 235-240 (1994) 1389. [8] P.W. Anderson, E. Abrahams and T.V. Ramakrishnan, Phys. Rev. Lett. 43 (1979) 728.
[9] M. Kaveh, M.J. Uren, R.A. Davies and M. Pepper, J. Phys. C: Solid State Phys. 14 (1981) L413. [10] B.L. Aitshuler, A.G. Aronov and P.A. Lee, Phys. Rev. Lett. 44 (1980) 1288. [l l] P.A. Lee and T.V. Ramakrishnan, Rev. Mod. Phys. 57 (1985) 287; Phys. Rev. Lett. 60 (1988) 2194.