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In-plane and out-of-plane resistivities of PrBa2Cu3O7−δ and Y0.47Pr0.53Ba2Cu3O7−δ single crystals
PHYSICA ELSEVIER
Physica C 282-287 (1997) 1127-1128
In-Plane and Out-of-Plane Resistivities of PrBa2CuaOr- and Yo.47Pro.saBa ,CuaOr-5 Single Crystals.* G. A. Levin, a T. Stein, a C. N. Jiang, a C. C. Almasan a, D. A. Gajewski, b S. H. Han, b and M. t3. Maple b ~Department of Physics, Kent State University, Kent OH 44242, USA b D e p a r t m e n t of Physics and Institute for Pure and Applied Physical Sciences, University of California at San Diego, La Jolla, CA 92093, USA We report out-of-plane and in-plane normal-state resistivities of twinned, fully-oxygenated single crystals of insulating PrBa2CuaOr-e and superconducting Yo.4vPro.5aBa2CuaOv-~ (To ~ 18K) measured by the flux transformer method. In the latter specimen, the onset of superconductivity was suppressed by a magnetic field of 9 T. The anisotropy pc/Pab = a + bT -2/3 for both samples, increasing monotonically at low temperatures with no sign of saturation. The absence of saturation and the T -2/3 dependence indicate two-dimensional transport. These data also represent a direct observation of hopping conduction in a homogeneous superconductor.
We present experimental results which att e m p t to address two outstanding questions of the physics of cuprates: the dimensionality of hopping conduction [two-dimensional (2-D) vs. three-dimensional (3-D)] and the possibility of superconductor-insulator transition. We measured the t e m p e r a t u r e dependence of out-of-plane Pc and in-plane Pab resistivities of insulating P r B a 2 C u 3 0 7 - ~ and lowTc Y l - x P r x B a 2 C u 3 0 7 - e single crystals. In cont r a s t to previous inconclusive efforts to elucidate the dimensionality of hopping conduction by discerning between the exponents v -- 1/3 and 1/4 in Pab ,cA exp{(To/T)~}, we find t h a t the Tdependence of the anisotropy Pc/Pab is a much more effective indicator of the hopping transport and its dimensionality. The normal state resistivities Pc and Pab of two twinned, fully-oxygenated single crystals of P r B a 2 C u 3 0 7 - ~ and Yo.47Pro.53Ba2Cu307-6 were measured by the six-terminal technique as described in Refs. [1,2]. Figure 1 exhibits the main results for the insulating specimen. The onset of a variable range hopping regime (VRH) is evident below ~ 25 K . However, within one * T h e w o r k a t K S U w a s s u p p o r t e d b y D O E G r a n t No. DE-FG02-90ER45427 through Midwest Superconductivi t y C o n s o r t i u m a n d b y N S F G r a n t No. D M R - 9 6 0 1 8 3 9 , a n d a t U C S D b y D O E G r a n t No. D E - F G 0 3 - 8 6 E R - 4 5 2 3 0 . 0921-4534/97/$17.00 © E l s e v i e r PI1 S0921-4534(97)00686-2
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decade of temperatures, it is impossible to distinguish between v = 1/3 and 1/4. Moreover, if we rely solely on in cr vs. T -~ graphs, we would have to conclude t h a t the apparent Mort parameters To (determined by the slopes d l n c r / d T - ' ) are different for crc and Crab by approximately a factor of 2.
10 3 10 2 101 --:
10 o
X
,
,
,
i • '250' , .,
10°
,. , . i
10-1 Q
\ \
2I
10-2
1o-3 ~ 10 .2 1 0 -3
0.1
PrBa2Cu 307_8 •
,
0.2
.
,
0.3
.
,
.
,
~ , 3 : ) .
,
0.4 0.5 0.6 T -1/3 (K-1/3)
.
,
0.7
.
K t
0.8
10-4 0.9
Figure 1. Semi-log plot of conductivities of P r B a 2 C u 3 0 7 - ~ vs. T -1/3. T h e straight lines are guides to the eye. The inset is a linear plot of the anisotropy Pc/Pab vs. T -2/3.
G.A. Levin et al./Physica C 282-287 (1997) 1127-1128
1128
The benefits of measuring both ac and Grab on the same sample become evident when we analyze the anisotropy Pc/Pab. The inset to Fig. 1. shows that there is a simple and elegant relationship between the two conductivities:
10 4 10 3
a+
ac,
(1)
with a = 122.7 and b = 171.4 K 2/3. When this T-dependent pre-exponential factor in Crab is taken into account, the exponential dependence e x p { - ( T o / T ) ~} for both Grab and ac is the same. The absence of saturation of Pc/Pab at low T, as well as its characteristic T -2/3 dependence, point unambiguously towards 2-D localization and hopping in this system. One can show that, when the localized states are highly anisotropic so that their wave functions spread across several unit cells in the in-plane direction but are confined to a single bilayer in the c-direction, the ratio 2 2 where (Rab 2 } and (Rc2) are aab/ac ~ {Rab}/(Rc), the mean square hopping distances in the respective directions. Equation (1) indicates that (R2ab) o( a + bT -2/3 which increases at low temperature and crosses over into Mott's VRH T -2/3 limit; the average step in the c-direction remains T-independent, equal to the spacing between the neighboring bilayers. The normal-state conductivities of the superconducting Yo.47Pro.53Ba2Cu307-6 crystal were measured by suppressing the onset of superconductivity with a magnetic field H of 9 T. The T-dependences of Pc and Pab above Tc (in zero field) are discussed in Refs. [1,3]. Figure 2 shows that, although ac and Grabexhibit a crossover into the VRH regime, the deviation from the straight line below 2.3 K is obvious. We attribute this to the fact that H = 9 T is not large enough to completely eliminate the enhancement of conductivity by superconducting fluctuations. However, the anisotropy (inset to Fig. 2) shows a remarkably persistent T -2/3 dependence similar to t h a t in Fig. 1 with parameters a = 439 and b = 487 g 2/3. Apparently, the relatively weak enhancement of both ac and Grab cancels out. The fact that Eq. (1) describes the normal-state anisotropies of both insulating and superconducting systems means that the suppression of su-
%00
10 2 "7
~ab =
101
~10 ]
~ % %
r~=°.
~Q
o o,2 o,4 o.6 o
10o "~
l0 ° 14~5K
10 -1 0.l
0.2
H=9T
0.3 0.4 0.5 0.6 0.7 T q/3 (K-1/3)
0.8
| 0 "1 0.9
Figure 2. Conductivities and anisotropy (inset) of Yo.47Pro.53Ba2Cu307-~ crystal in a magnetic field H = 9 T. The onset of superconductivity at 14.5 K in a low field of 0.2 T is also shown.
perconductivity in low-To Y l - x P r x B a 2 C u 3 0 7 - ~ cuprates reveals a 2-D insulating ground state. The monotonic increase of the anisotropy at lowT (Fig. 2) is in stark contrast with the saturation of Pc/Pab in L a l - x S r x C u 0 4 [4]. Such a difference is especially peculiar given the fact that the anisotropy of underdoped Y I - x P r z B a 2 C u 3 0 7 - 6 is smaller or comparable to that of underdoped L a l - x S r ~ C u 0 4 . For example, judging by the data of Ref. 4 and those shown in Fig. 2, Yo.47Pro.53Ba2Cu307-5 is substantially less anisotropic than Lao.92Sro.osCu04 and yet, appears to be more two-dimensional. REFERENCES
1. C. N. Jiang et al., Phys. Rev. B 55, R3390 (1997). 2. G . A . Levin et al., Physica C: these proceedings. 3. C . C . Ahnasan et al., Physica C: these proceedings. 4. Y. Ando et al., Phys. Rev. Lett. 75, 4662 (1995).
Physica C 282-287 (1997) 1127-1128
In-Plane and Out-of-Plane Resistivities of PrBa2CuaOr- and Yo.47Pro.saBa ,CuaOr-5 Single Crystals.* G. A. Levin, a T. Stein, a C. N. Jiang, a C. C. Almasan a, D. A. Gajewski, b S. H. Han, b and M. t3. Maple b ~Department of Physics, Kent State University, Kent OH 44242, USA b D e p a r t m e n t of Physics and Institute for Pure and Applied Physical Sciences, University of California at San Diego, La Jolla, CA 92093, USA We report out-of-plane and in-plane normal-state resistivities of twinned, fully-oxygenated single crystals of insulating PrBa2CuaOr-e and superconducting Yo.4vPro.5aBa2CuaOv-~ (To ~ 18K) measured by the flux transformer method. In the latter specimen, the onset of superconductivity was suppressed by a magnetic field of 9 T. The anisotropy pc/Pab = a + bT -2/3 for both samples, increasing monotonically at low temperatures with no sign of saturation. The absence of saturation and the T -2/3 dependence indicate two-dimensional transport. These data also represent a direct observation of hopping conduction in a homogeneous superconductor.
We present experimental results which att e m p t to address two outstanding questions of the physics of cuprates: the dimensionality of hopping conduction [two-dimensional (2-D) vs. three-dimensional (3-D)] and the possibility of superconductor-insulator transition. We measured the t e m p e r a t u r e dependence of out-of-plane Pc and in-plane Pab resistivities of insulating P r B a 2 C u 3 0 7 - ~ and lowTc Y l - x P r x B a 2 C u 3 0 7 - e single crystals. In cont r a s t to previous inconclusive efforts to elucidate the dimensionality of hopping conduction by discerning between the exponents v -- 1/3 and 1/4 in Pab ,cA exp{(To/T)~}, we find t h a t the Tdependence of the anisotropy Pc/Pab is a much more effective indicator of the hopping transport and its dimensionality. The normal state resistivities Pc and Pab of two twinned, fully-oxygenated single crystals of P r B a 2 C u 3 0 7 - ~ and Yo.47Pro.53Ba2Cu307-6 were measured by the six-terminal technique as described in Refs. [1,2]. Figure 1 exhibits the main results for the insulating specimen. The onset of a variable range hopping regime (VRH) is evident below ~ 25 K . However, within one * T h e w o r k a t K S U w a s s u p p o r t e d b y D O E G r a n t No. DE-FG02-90ER45427 through Midwest Superconductivi t y C o n s o r t i u m a n d b y N S F G r a n t No. D M R - 9 6 0 1 8 3 9 , a n d a t U C S D b y D O E G r a n t No. D E - F G 0 3 - 8 6 E R - 4 5 2 3 0 . 0921-4534/97/$17.00 © E l s e v i e r PI1 S0921-4534(97)00686-2
Science
B.~d
All
rights
reserved.
decade of temperatures, it is impossible to distinguish between v = 1/3 and 1/4. Moreover, if we rely solely on in cr vs. T -~ graphs, we would have to conclude t h a t the apparent Mort parameters To (determined by the slopes d l n c r / d T - ' ) are different for crc and Crab by approximately a factor of 2.
10 3 10 2 101 --:
10 o
X
,
,
,
i • '250' , .,
10°
,. , . i
10-1 Q
\ \
2I
10-2
1o-3 ~ 10 .2 1 0 -3
0.1
PrBa2Cu 307_8 •
,
0.2
.
,
0.3
.
,
.
,
~ , 3 : ) .
,
0.4 0.5 0.6 T -1/3 (K-1/3)
.
,
0.7
.
K t
0.8
10-4 0.9
Figure 1. Semi-log plot of conductivities of P r B a 2 C u 3 0 7 - ~ vs. T -1/3. T h e straight lines are guides to the eye. The inset is a linear plot of the anisotropy Pc/Pab vs. T -2/3.
G.A. Levin et al./Physica C 282-287 (1997) 1127-1128
1128
The benefits of measuring both ac and Grab on the same sample become evident when we analyze the anisotropy Pc/Pab. The inset to Fig. 1. shows that there is a simple and elegant relationship between the two conductivities:
10 4 10 3
a+
ac,
(1)
with a = 122.7 and b = 171.4 K 2/3. When this T-dependent pre-exponential factor in Crab is taken into account, the exponential dependence e x p { - ( T o / T ) ~} for both Grab and ac is the same. The absence of saturation of Pc/Pab at low T, as well as its characteristic T -2/3 dependence, point unambiguously towards 2-D localization and hopping in this system. One can show that, when the localized states are highly anisotropic so that their wave functions spread across several unit cells in the in-plane direction but are confined to a single bilayer in the c-direction, the ratio 2 2 where (Rab 2 } and (Rc2) are aab/ac ~ {Rab}/(Rc), the mean square hopping distances in the respective directions. Equation (1) indicates that (R2ab) o( a + bT -2/3 which increases at low temperature and crosses over into Mott's VRH T -2/3 limit; the average step in the c-direction remains T-independent, equal to the spacing between the neighboring bilayers. The normal-state conductivities of the superconducting Yo.47Pro.53Ba2Cu307-6 crystal were measured by suppressing the onset of superconductivity with a magnetic field H of 9 T. The T-dependences of Pc and Pab above Tc (in zero field) are discussed in Refs. [1,3]. Figure 2 shows that, although ac and Grabexhibit a crossover into the VRH regime, the deviation from the straight line below 2.3 K is obvious. We attribute this to the fact that H = 9 T is not large enough to completely eliminate the enhancement of conductivity by superconducting fluctuations. However, the anisotropy (inset to Fig. 2) shows a remarkably persistent T -2/3 dependence similar to t h a t in Fig. 1 with parameters a = 439 and b = 487 g 2/3. Apparently, the relatively weak enhancement of both ac and Grab cancels out. The fact that Eq. (1) describes the normal-state anisotropies of both insulating and superconducting systems means that the suppression of su-
%00
10 2 "7
~ab =
101
~10 ]
~ % %
r~=°.
~Q
o o,2 o,4 o.6 o
10o "~
l0 ° 14~5K
10 -1 0.l
0.2
H=9T
0.3 0.4 0.5 0.6 0.7 T q/3 (K-1/3)
0.8
| 0 "1 0.9
Figure 2. Conductivities and anisotropy (inset) of Yo.47Pro.53Ba2Cu307-~ crystal in a magnetic field H = 9 T. The onset of superconductivity at 14.5 K in a low field of 0.2 T is also shown.
perconductivity in low-To Y l - x P r x B a 2 C u 3 0 7 - ~ cuprates reveals a 2-D insulating ground state. The monotonic increase of the anisotropy at lowT (Fig. 2) is in stark contrast with the saturation of Pc/Pab in L a l - x S r x C u 0 4 [4]. Such a difference is especially peculiar given the fact that the anisotropy of underdoped Y I - x P r z B a 2 C u 3 0 7 - 6 is smaller or comparable to that of underdoped L a l - x S r ~ C u 0 4 . For example, judging by the data of Ref. 4 and those shown in Fig. 2, Yo.47Pro.53Ba2Cu307-5 is substantially less anisotropic than Lao.92Sro.osCu04 and yet, appears to be more two-dimensional. REFERENCES
1. C. N. Jiang et al., Phys. Rev. B 55, R3390 (1997). 2. G . A . Levin et al., Physica C: these proceedings. 3. C . C . Ahnasan et al., Physica C: these proceedings. 4. Y. Ando et al., Phys. Rev. Lett. 75, 4662 (1995).