PHYSICAL REVIEW B

VOLUME 53, NUMBER 14

1 APRIL 1996-II

Transport properties of Bi2Sr2CuO6 single crystals: Possibility of interplane couplingin the weakly localized regime
Katsuhiko Inagaki and Satoshi Tanda
Department of Applied Physics, Hokkdaido University, Sapporo 060, Japan~Received 23 June 1995; revised manuscript received 18 January 1996!
Transport properties of Bi2Sr2CuO6 single crystals, including the electric conductivity magnetoresistance,and Hall coefficient, were measured. Characteristics of the conductivity in the weakly localized regime, which
includes temperature, electric field, and magnetic field, were also measured. The coefficient of ln H was foundto be much smaller than the theoretical value predicted for the weakly localized regime. Measurement of theHall coefficient indicates that the electron-electron interaction does not play a significant role in the conductivity. Rather, interplane coupling appears to play a role in the transport properties of this system.

The nature of normal-state conduction in high-T c superconducting cuprates remains unknown, although many years
have passed since the discovery of superconducting cuprates.
Previous studies reported a ln T upturn in resistance at low
temperature in various kinds of cuprates, such as
La22x Srx CuO41y ~Ref. 1!, Bi2Sr2CuO6 ~Refs. 2,3!,
Nd22x Cex CuOy ~Refs. 4,5!, Nd2CuO42x2 d F ~Ref. 6!, andPr22x Cex CuO4.7 This upturn is thought to be due to theweakly localized regime ~WLR! of Anderson localization.
The reasons are that electric conduction in cuprate occurs in
the two-dimensional CuO2 plane and that the doped carriers
introduce random potential into the plane. Tanda et al. demonstrated that the localized states of Nd22x Cex CuOy ~Ref. 4!
and Nd2CuO42x2 d F ~Ref. 6! can best be described as a disordered Fermi-liquid system, i.e., essentially the same as thelocalized states in conventional metal films. However, otherstudies have reported different phenomena in the localizedstate of cuprates: these differences include isotropic magnetoresistance observed in La22x Srx CuO41y ~Ref. 1! andanomalous temperature dependence of the dephasing rate,t f }T 21/3, observed in Bi2Sr2CuO6 .3
The present paper reports the electric-field, temperature,and magnetic-field dependences of conductivity in the localized state of Bi2Sr2CuO6 single crystals. We also measured
the Hall coefficient of the sample. Theories of localization
phenomena for metal films predict these dependences, which
are represented as ln T, ln H, and ln E, and the coefficientsare related to each other. We observed ln T, ln E, and ln H
dependences in the localized regime of the Bi2Sr2CuO6single crystals and found that the coefficient of ln H is muchsmaller than the others. One may consider that this discrepancy in the coefficient of ln H is caused by electron-electroninteraction. However, the effect of the electron-electron interaction was found to be negligible, since the Hall coefficient was independent of temperature. The results suggestthat interplane coupling between the conducting planes plays
an important role in the transport phenomena in
Bi2Sr2CuO6 .
The Bi2Sr2CuO6 single crystals used in this study weresynthesized by the self-flux method.8 A composite powder
consisting of Bi2O3 , SrCO3 , and CuO was placed in an alumina crucible and the mixture was reacted in a furnace at
950 °C for 4 h. The furnace was cooled at the rate of 1 °C/h.
0163-1829/96/53~14!/8902~4!/$10.00

53

All the processes were carried out under standard atmosphere. The resulting crystals were black and slab shaped.
Typical sample size was 0.53130.01 mm3. Electric conductivity of the sample was measured by the standard four-probe
technique. Voltage drop across the sample was measured using a nanovoltmeter ~Keithley 182!. Typical current was 100
mÅ for 1 V measurement. Electrical contacts were fabricatedby the following method: gold thin film was sputtered onto
the sample, and silver wires were attached with silver pasteand cured at 160 °C for 2.5 h. Resistance of the contacts was
typically 10 V.
To prevent Joule heating from raising the temperature of
the sample during I-V measurements, a short pulse current
was applied to the sample instead of direct current.9 A transformer was inserted between the pulse generator and sample
circuit to prevent a ground loop from forming the measurement equipment. Current flowing in the circuit was determined by monitoring the voltage drop across a 10 V shunt
resistor connected in series with the sample. Both voltage
and current were measured by a digitizing oscilloscope. The
sampling ratio was 256 kHz, and the sampled data were averaged 256 times in order to reduce background noise. The
pulse width was 3 ms with a 1 s interval. The duty cycle ofthese pulse currents was 1:300. By using this arrangement,
the amount of Joule heating produced by the current could be
reduced to 1/300, compared with the amount of heat produced by direct current of the same strength.
Figure 1 shows the temperature dependence of the electric
conductivity of the sample. Conductivity increases linearly
from room temperature to 100 K. Maximum conductivity
was observed around 100 K, below which conductivity decreased proportionally to ln T. In the WLR, conductance canbe represented10 as

Ds~ T !5a pe2ln T
2 p 2\~1!

where a is a constant of an order of unity, and p is a parameter that takes into account the scattering process, t i }T 2 p .
The number of CuO2 layers stacked in the Bi2Sr2CuO6sample was then calculated based on sample thickness andthe spacing between the layers of the sample. Given a sample
R8902© 1996 The American Physical Society

53R8903

TRANSPORT PROPERTIES OF Bi2Sr2CuO6 SINGLE . . .

FIG. 1. Conductivity of sample decreases by ln T. The coefficient of ln T is discussed in the text.

thickness of 10 mm and a lattice spacing of 12 Å the sample
was determined to contain 8000 layers. Using only the number of layers to calculate the conductance per unit sheet, weobtained ap50.2.
Figure 2 shows the electric-field dependence of the resistance at 4.2 K. Dots and open circles represent dc ~100%
duty cycle! and pulse measurement ~0.3% duty cycle!, respectively. As shown in the figure, resistance R remains constant below 2 mV ~corresponding to an electric field of 0.1
V/cm!, and decreases by ln E above the threshold. The datafrom different duty cycles are in agreement. This resultshows that the observed nonlinearity in resistance is notcaused simply by a temperature increase due to Joule heating, but rather to the nature of Bi2Sr2CuO6 . The relation
between temperature T and electric field E in the WLR has
been proposed.10 In the nonlinear resistance regime, the effective temperature of the carriers T eff can be higher than thetemperature of the lattice system. Effective temperature is
proportional to the electric field E as

FIG. 3. ~a! The transverse and longitudinal magnetoresistancesof sample. Note that the sign of magnetoresistances is negative forboth directions. ~b! The component of orbit motion contributing tomagnetoconductivity, Ds52(D r T 2D r L )/ r 20 . Solid lines show thefit with theory.
2p/ ~ 11p/2!
T 2p.
eff }EBy substituting T eff for T in Eq. ~1!, the nonlinear conductivity can be represented as
Ds~ E !5FIG. 2. I-V characteristics of the sample at 4.2 K, plotting
R~5V/I!. Dots and open circles represent data obtained by dc andpulse measurement, respectively. Both values agree around 10 22 V.
Resistance R remains constant below the threshold electric field, atwhich R begins increasing by ln T.

~2!

e2apln E.
11 p/2 2 p 2 \~3!

From the coefficient of ln E, as shown in Fig. 2, we obtained
ap/~11p/2!50.1. When it is noted that we have ap50.2, theobserved data yields a p value of approximately 2. This is areasonable value and the assumption expressed in relation~2! is considered to be valid.
Figure 3~a! shows the magnetoresistance of the sample,
when the magnetic field is applied parallel, and perpendicular, to the CuO2 planes. The magnitude of the transverse
magnetoresistance is about twice as large as the longitudinalvalue. The signs of the magnetoresistance are negative forboth the parallel and perpendicular fields. Anisotropic negative magnetoresistance is a significant characteristic of theWLR. Figure 3~b! shows the orbital component of the magnetoconductivity defined by D s 52(D r T 2D r L )/ r 20 , where
D r T and D r L denote transverse and longitudinal magnetoresistance; and r 0 signifies zero-field resistivity, respectively.
The magnetoconductivity in the WLR is thus given as
D s ~ H ! 52

FSD S

D S DG1
1a *e 2
11tc 12c 12ln
22p \2 Vt
2 Vtf
tf~4!

KATSUHIKO INAGAKI AND SATOSHI TANDA

R8904

53TABLE I. Coefficients of logarithmic dependences for temperature, electric field, and magnetic field observed in same sample.
Note small value for ln H.

Coefficients (V 21 )e 2 /2p 2 \ unit

ln T

ln Eln H

2.531026
ap50.21.231026
ap/~11p/2!50.1

4.831028
a*50.005

where c is the digamma function, V54eDH/\, D is the diffusion constant, and a* is a constant of the order of unity.11The content between the brackets of Eq. ~4! reaches an asymptotic value for ln H when H is large. Therefore,e2ln H.
~5!
Ds~ H !5a*2 p 2\By fitting the magnetoconductivity shown in Fig. 3~b! to Eq.
~5!, we obtained a*50.005. This is much smaller than theexpected value of the order of unity. Table I shows a summary of the coefficients obtained for ln T, ln E, and ln H. The
discrepancy in ln H is different from the localized states ofmetal films. Scaling theory predicts that conductivity in theWLR is determined only by system size. At finite temperature, the system size is replaced by a cutoff length which is afunction of T, E, and H, and the coefficients of these dependences must be related to each other. Therefore, the observed
discrepancy in ln H is not explained in terms of the WLR
theory.
We considered the effect of the electron-electron interaction. The electron-electron interaction also shows a ln T dependence in the conductivity. The coefficient of ln T attributable to this interaction is ~12F!(e 2 /2p 2 \), where F is thescreening factor.12 While the temperature dependence of conductivity is similar to that of localization, the interaction effect has a remarkably different magnetic-field dependencewith respect to the magnetoresistance and Hall coefficient.13
The magnetoresistance in the WLR is negative, and purelytransverse for a thin film, whereas the interaction effectshows a positive magnetoresistance and is isotropic for spin
splitting and transverse for the orbital part. Figure 3~a! showsthat the positive magnetoresistance due to the electronelectron interaction was not observed in our sample. Moreover, the Hall coefficient of the sample also shows that theinteraction contributes very little to the sample conductivity.
The interaction correction for the Hall resistance R H is proportional to the resistance increased R H /R H 52 d R/R.
~6!
Figure 4 shows that the observed Hall coefficient of thesample is almost constant in the localized regime where theresistance varies 2 to 7 V. It is therefore reasonable to con-1

N. W. Preyer, M. A. Kastner, C. Y. Chen, R. J. Birgenau, and Y.
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FIG. 4. Temperature dependence of Hall coefficients ~solidcircles! and resistance ~solid line! of the sample. The Hall coefficients is almost independent of temperature ~see text!.

clude that the effect of the electron-electron interaction isnegligible in our sample, and that the very small value forthe coefficient of ln H can not be attributed to the electronelectron interaction.
We have noted that the coefficient of ln H is significantly
different from that of ln T and ln E in the localized state of
Bi2Sr2CuO6 . This suggests the existence of interplane coupling between the CuO2 planes. The interplane coupling increases the number of conducting paths, hence the conductivity might have a different value from that expected for asingle plane. Moreover, since the relation ~2! is valid in thenonlinear resistance regime @ T eff(E).T # , as we discussed
before, both temperature and electric field play the same rolein contributing to the conductivity. Hence the coefficients ofln T and ln E are still thought to be in agreement. However,
the orbital component of magnetoresistance is caused by thesuppression of interference between the partial wave functions of a carrier. This interference occurs independently ineach plane. The magnitude of the orbital component of magnetoresistance is determined separately in each plane, hence
the coefficient of ln H may possibly be different from thoseof ln T and ln E. In conclusion, we suggest that interplane
coupling plays an important role in the electric transport
properties in the localized state in Bi2Sr2CuO6 single crystals.
The authors wish to thank Professor T. Nakayama
and Professor K. Yamaya for their thoughtful discussions.
Thanks are also due to Dr. H. Tamura, NTT Nano-electronics Laboratory, for his stimulating discussions. One ofthe authors ~K.I.! wishes to thank the Japan Society for thePromotion of Science for Young Scientists for financial support. This work was partly supported by a Kurata ResearchGrant.

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TRANSPORT PROPERTIES OF Bi2Sr2CuO6 SINGLE . . .

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