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Abstract
The effects of the electronic density of states (DOS) on superconductivity are studied within the BCS theory using a one-electron anisotropic tight-binding model for the energy band. By tuning the ratio of the interlayer to intralayer couplings, the model interpolates the two-dimensional and three-dimensional cases. The transition temperature T c and the isotope effect exponent α are studied as a function of the position of the Fermi energy for various degrees of anisotropy. The transition temperature is highest for uncoupled layers with the Fermi energy near to the logarithmic singularity in the 2D DOS, while the corresponding value of α shows a minimum. As the interlayer coupling is increased, the singularity in the DOS is rounded-off. The enhancement in T c is suppressed and α approaches the BCS value of 0.5.
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