Physica C 317–318 Ž1999. 600–602
In-plane thermal conductivity of single crystals of Zn-doped
YBCO in the mixed state
Michiaki Matsukawa
a,)
, Hiroyuki Furusawa a , Koshichi Noto a , Xin Yao b,
Yu Siohara b, Norio Kobayashi c
a
b
Faculty of Engineering, Iwate UniÕersity, 4-3-5 Ueda, Morioka 020, Japan
Superconducting Research Laboratory, ISTEC Shinonome, Tokyo 135, Japan
c
Institute for Materials Research, Tohoku UniÕersity, Sendai 980, Japan
Abstract
The in-plane thermal conductivity Ž k ab . of single crystals of YBa 2 ŽCu 1yx Zn x . 3 O y ŽZn-doped YBCO. has been studied
as functions of temperature and magnetic field. The k ab value of pure YBCO shows a rapid enhancement below Tc but a
small amount of Zn doping into the CuO 2 plane suppresses dramatically the observed superconducting enhancement in k a b .
The thermal conductivity value of the Zn-doped crystals exhibits the weak field dependence compared with that of pure
crystals. The k ab behavior of pure and Zn-doped YBCO in the superconducting state has been discussed on the basis of the
carrier–carrier scattering model. q 1999 Elsevier Science B.V. All rights reserved.
Keywords: High-Tc cuprates; Thermal conductivity; Impurity effect
The thermal conductivity measurement on superconductors gives rise to significant information about
quasiparticle scattering rate and symmetry of superconducting gap w1x. In high-Tc cuprates, the rapid
enhancement of k below Tc has been widely reported by many authors. It is believed that the origin
of the observed peak is mainly ascribed to the electron component because both measurements of Hall
thermal conductivity and a.c. conductivity for high-Tc
cuprates strongly support such electronic scenario
w2,3x. To make clear the origin of the observed peak
of k , it is probably needed to examine the impurity
effect on the thermal conductivity behaviors of highTc cuprates.
)
Corresponding author. Tel.: q81-19-621-6358; Fax: q81-19621-6373; E-mail: matsukawa@iwate-u.ac.jp
In this paper, the in-plane thermal conductivity of
YBa 2 ŽCu 1yx Zn x . 3 O y ŽZn-doped YBCO. single
crystals has been studied in the superconducting and
mixed states as functions of temperature and field.
The used crystals were prepared by the Czochralski
ŽSRL-CP. method w4x. The sample dimensions are
typically 6 = 2.6 mm2 in the ab-plane and 1.5 mm
along the c-axis. As-grown samples were annealed
on the same condition at 5208C for 2 weeks in the
oxygen flow to attain optimum and homogeneous
distribution of oxygen concentration. The optimum
value of Tc reaches 92 K for pure crystals. The Zn
concentration ranged from 0 to 1.55%. The thermal
conductivity was measured with steady-state heatflow method using the differential thermocouples of
Chromel–Au q 0.07 at.% Fe alloy and Chromel–
Constantan types in the zero and magnetic fields,
respectively. The heat flow is directed to the ab-plane
0921-4534r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 1 4 0 - 9
M. Matsukawa et al.r Physica C 317–318 (1999) 600–602
while the field is applied along the c-axis of the
samples up to 14 T.
The in-plane thermal conductivity k a b of Zndoped YBCO single crystals is shown in Fig. 1 as a
function of temperature down to 10 K. For comparison, the k a b value of the as-grown sample with
x s 0.71% is also shown. The pure sample shows a
rapid enhancement in k a b below Tc whereas for the
lightly Zn-doped samples, the small peak is observed
in k a b . However, the normal-state k a b behavior of
the Zn-doped sample is similar to that of the pure
sample, which is in contrast with the superconducting cases. Next, the in-plane thermal conductivity of
Zn-doped YBCO single crystal with x s 0.71% is
shown in Fig. 2 as a function of field up to 14 T
applied to the c-axis direction of the sample. For
comparison, the k a b Ž H . data of the pure YBCO is
also cited at 40 K, where the k a b value reaches a
maximum value in the zero field. For the pure
sample, the value of k a b Ž H . shows a strong field
dependence while k a b Ž H . of the Zn-doped sample
weakly decreases at 40 K down to about 7% even at
the maximum field of 14 T. For the x s 0.71%
sample, the small enhancement below Tc is consistent with the result of the weak field dependence of
kab.
The measured thermal conductivity is separated
into the electron and phonon components k el and
k ph . In our previous papers, it is shown that the main
reason for the superconducting peak in k a b of YBCO
Fig. 1. The in-plane thermal conductivity k a b of Zn-doped YBCO
single crystals as a function of temperature down to 10 K. For
comparison, the k a b value of the as-grown sample with x s 0.71%
is also shown. The arrow marks denote the positions of Tc .
601
Fig. 2. The in-plane thermal conductivity of Zn-doped YBCO
single crystal with x s 0.71% as a function of field up to 14 T,
parallel to the c-axis of the sample. For comparison, the k a b Ž H .
data of pure YBCO at 40 K is also cited.
is ascribed to an electron contribution w5,6x. The
electron component in the superconducting-state is
calculated in terms of the Kadanoff–Martin expression as follows:
k es s
2p
H0
df
3
2p 2p
`
2
H0 d ´´
t
2
sech2
E
1qa
2
´rE q at n
ž /
,
with E s '´ 2 q D 2 , t s TrTc and DŽ t, f . s
xD BCS Ž t . cd Ž f ., where k es is normalized by the k e
value at Tc w1,7x. The variables of ´ and DŽT .
normalized by kT denote the quasiparticle energy
measured from Fermi-level and the superconducting
energy gap according to the Bardeen Cooper and
Schrieffer ŽBCS. theory, respectively. In this expression, we take account of the following effect; the
mean free path of quasiparticles is largely enhanced
below Tc in comparison with that in the normal state
since the strongly carrier–carrier scattering is freezed
out in the superconducting state. In the integrand, the
parameter a represents the ratio of a power-law
scattering rate to the residual scattering rate, which
roughly corresponds to the value of residual resistivity ratio ŽR.R.R... In calculation for the d-wave
pairing-states, the wave functions are taken as cd Ž f .
s '2 cosŽ2 f ., where f is the azimuthal angle of
wave number k in the ab-plane. The x value is a
scaling parameter for the superconducting gap to the
value of the BCS gap. The calculated result of the
superconducting k e for both the pure and Zn-doped
samples is shown in Fig. 3, where the fitted parame-
602
M. Matsukawa et al.r Physica C 317–318 (1999) 600–602
Fig. 3. The calculated curves of the superconducting k e for both
the pure and Zn-doped samples. Here, the fitted parameters are
x s1, ns 4 and as 28 for the pure sample, and x s 0.7,
ns 2.5 and as 20 for the impure sample with x s 0.71%.
ters are listed as below; for the pure sample x s 1,
n s 4 and a s 28, and for the impure sample with
x s 0.71%, x s 0.7, n s 2.5 and a s 20. It is found
that a considerable decrease of the power-law value
from 4 to 2.5 dominates the strong suppression of the
observed peak due to the Zn-doping effect in comparison with a reduction of the gap parameter or the
R.R.R value. The scattering rate of quasiparticle in
the superconducting state is radically enhanced due
to the light doping of Zn into the CuO 2 plane. The
field dependence of the superconducting k e originates from quasiparticle scattering due to magnetic
vortices. Thus, the weak field dependence of k a b for
the doped sample indicates the scattering rate of
quasiparticles has become stronger than that for the
pure sample so that it is considered that the vortices
are made less effective as the scattering centers of
quasiparticles in the Zn doping into the CuO 2 plane.
This interpretation is reasonably consistent with the
present calculation result on the superconducting k e .
In summary, the in-plane thermal conductivity
Ž k a b . of single crystals of YBa 2 ŽCu 1yx Zn x .O y ŽZndoped YBCO. has been studied as functions of
temperature and magnetic field. A small amount of
Zn doping into the CuO 2 plane suppresses dramatically the observed superconducting enhancement in
k a b and causes the weak field dependence of k a b .
The k a b behavior of pure and Zn-doped YBCO in
the superconducting state has been discussed on the
basis of the carrier–carrier scattering model.
Acknowledgements
This work was partially supported by NEDO.
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