PHYSICA
ELSEVI[:R Physica C 282-287 (1997) 1851-1852
Impurity Effects on the Tc suppression in the Pair Tunneling Mechanism
for High-Tc Superconductors
Yunkyu Bang ~ *
~Dept. of Physics, Chonnam National University, Kwangju 500-757, Korea
We consider the impurity effects on the Tc suppression of the d-wave state in Anderson's Pair Tunneling
Mechanism for High-Tc superconductors, including explicitly strong inelastic scattering (P," ~ a(hw + rksT)).
Using a self-consistent T-matrix approximation, we solve the gap equation of the Pair Tunneling Mechanism with
non-magnetic impurity in the plane, with and without the inelastic scattering. As expected, the effect of impurities
for the Tc suppression is strongly reduced by inelastic scattering and the results can fit most of experimental data
with impurities by varying impurity scattering strength.
1. Introduction
While there are accumulating experimental evi-
dences which indicate the d-wave symmetry of the
order parameter (OP) in high-Tc superconduc-
tors (HTSC) [1], the Tc suppression upon dop-
ing with various impurities like Zn, Ni, Fe, Co,
AI, Ga etc. does not well fit into the conven-
tional Abrikosov-Gorkov theory of the impure su-
perconductors with the d-wave OP. In general,
those data show the much slower suppression of
Tc with impurities than the prediction of the con-
ventional theory. One possible reason for such a
slow suppression of Tc with impurity doping is
that already existing strong inelastic scattering
in the cuprate superconductors would mask the
effect of elastic scattering due to impurities [2].
While most of the scenarios for high-Tc su-
perconductors are focusing on the single layer of
Cu-O plane and can eventually be wound up to
the BCS- or Eliashberg-type gap equation, the
Interlayer Pair Tunneling (IPT) mechanism pro-
posed by Anderson and coworkers [3] results in
the gap equation different from the BCS one. The
main feature of the IPT gap equation is the in-
terlayer pair tunneling process which strongly en-
hances any intra-plane pairing interaction. De-
pending on the nature of the intra-plane pairing
"This work was supported by the Chonnam National Uni-
versity Research Grant, 1996 and by the Korea Science
and Engineering Foundation through the SRC program of
SNU-CTP
0921-4534/97/$17.00 © Elsevier Science B.M All rights reserved.
PII S0921-4534(97)01085-X
interaction, the IPT mechanism can flexibly sup-
port both d-wave and anisotropic s-wave OPs[4].
In this paper, we study the Tc suppression due
to non-magnetic potential scatterers in the d-
wave superconductivity of the IPT mechanism,
in particular with strong inelastic scattering in-
cluded. The results show that the experimen-
tal data are well in the range of the prediction
of the IPT mechanism with a d-wave OP when
the strong inelastic scattering is included. In or-
der to simulate the strong inelastic scattering,
which is the origin of various anomalous normal
state properties in the cuprate superconductors,
we explicitly include the self-energy of the form
E" ~ cr(hw + 7rkBT) in the gap equation.
2. Formalism
Because there is an additional pairing interac-
tion, Hint = EkTJ(k)C+,( +
1)C k,(1)Ck,(2)C-k,(2) -'["
h.c., due to the inter-layer pair tunneling pro-
cess in otherwise BCS-like Hamiltonian for planar
electrons, the usual BCS anomalous decoupling
leads to two anomalous self-energies as follows.
m ~k n t er
Aintra
k
= - + a;","°)(1)
= Tj(k)x(k)(a "'°r + "'to) (2)
where x(k) = tanh(Ek/2T)/2Ek, with E~ = ~ +
A -,ro)2
~k + , is the pair susceptibility.