Ž . Physica C 299 1998 83–90 Restricted pair tunneling model in the context of high-T cuprates c A.N. Das a, ) , S. Sil b a Saha Institute of Nuclear Physics, 1 r AF Bidhannagar, Calcutta 700 064, India b Institut fur Theoretische Physik, UniÕersitat zu Koln, Zulpicher Strasse 77, 50937, Germany ¨ ¨ ¨ Received 13 November 1997; revised 26 December 1997; accepted 27 January 1998 Abstract Based on the experimental suggestion that the normal state pseudo gap in cuprates suppresses the interlayer single-par- ticle hopping we propose a restricted tunneling model where we have considered interlayer hopping of single particles as well as pair tunneling with complementary probabilities which are determined by the value of the normal state pseudo gap Ž . E . For underdoped systems where E is large our model would be equivalent to Anderson’s pair tunneling model. g g However at optimum doping or overdoped systems, where E is comparable or less than the transition temperature, the g results, obtained from our model, are different from the Anderson’s model. We have studied the superconducting gap ratio, transition temperature at optimum doping as a function of interlayer coupling and the variation of the gap parameter with temperature, for different values of E . The relevance of these results in the context of high-T cuprates is discussed. q 1998 g c Elsevier Science B.V. PACS: 74.20.yz; 74.62.yc; 74.62.Dh Keywords: Pair tunneling; Cuprates; Single-particle hopping 1. Introduction High-T cuprates have layered structures where c the charge carriers move in the CuO planes. The 2 quasi two-dimensional nature of the system has been indicated in many experimental results, e.g., large resistivity anisotropy, short coherence length along the c axis, etc. Angle-resolved photoemission experi- w x ments 1–3 also indicate that high-T cuprates have c an extended van Hove singularity in the electronic density of states which is a characteristic of two-di- mensional systems. Consequently, most of the theo- ) Corresponding author. retical studies regarding high-T cuprates consider c isolated CuO planes and ignore the interlayer cou- 2 pling to capture the essential physics of the system. However, one of the important problems in the theory of high-T superconductivity is to what extent c the properties of these superconductors are bound to two dimensionality of the CuO planes and how 2 important is the role of the interlayer coupling in the superconductivity of cuprates. A number of studies have been made focusing on the role of interlayer w x coupling in high-T superconductors 4–10 . The c normal state electrical conductivity measurements provide us useful information regarding interlayer coupling in cuprates. For underdoped cuprates the absence of Drude peak in the optical conductivity 0921-4534r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. Ž . PII S0921-4534 98 00075-6