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The effect of interlayer interaction on transition temperature (T c ) with number of layers (n) has been investigated in layered high T c superconductors within the BCS theory, irrespective of the pairing mechanism. The expression for interlayer correlation (γ) has been obtained and its implications have been studied. T c has been calculated numerically for n = 1, 2 and 3. Interlayer interactions have been found crucial for superconductivity and enhancing T c . It is also found that mere addition of layers does not increase T c , but the density of states (N 0 ) should also increase with addition of layers. The results are in general agreement with experiments and explain the trend of T c with n satisfactorily. IntroductionThe discovery of high T c cuprates [1] raised the question whether BCS theory continues to be applicable with exceptionally strong coupling or a completely new framework must be developed [2][3][4][5]. As the question of mechanism of superconductivity remains unsettled, many new ideas and proposals have been generated for a possible new mechanism but little consensus has been reached so far. However, the class of high T c superconductors provides useful information, which could give insight into the unconventional nature of superconductivity in these systems.It is now well recognized that all high T c cuprates are based on structures with square planar copper oxide layers [6]. The superconducting phase occurs near a metal insulator transition with the destruction of long-range antiferromagnetic order of Cu spins [7]. These CuO 2 layers are found to be responsible for conduction and increase in their number per unit cell increases T c , being maximum for n = 3 [8,9], and then decreases. They are considered key to the understanding of Physics in these compounds and must be incorporated in any final high T c theory.Beside high T c cuprates, recent years witnessed discovery of many layered superconductors. Fullerides, borocarbides, ruthenates, MgB 2 , intercalated Na x CaO 2 , Ba 1-x K x BiO 3 [10-12] to name a few. The layered structure seems to support high T c and can be a favorable hunting ground for obtaining higher bounds of T c .Several workers [13][14][15][16][17][18][19][20] have studied the role of layered structure on the unusual properties of these compounds and proposed interlayer interactions to play significant role in the enhancement of T c and stabilizing superconducting order with respect to fluctuations. This coupled with the fact that increase in number of layers (for high T c cuprates), increases T c , is a clear indication that layered structure is crucial to high T c superconductors and plays dominant role in establishing superconducting order. Further it is also known that long-range order is impossible in 1D and 2D systems with an order parameter that has a continuous symmetry [22]. Therefore to obtain a real phase transition with long-range order and a homogenous order parameter, one needs to take into account the interlayer coupling. Recently quantum tunneling of cooper ...

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