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.