Layered superconductors with anisotropic energy gap: specific heat and infrared absorption

Abstract

New oxide superconductors with layered structure are expected to have anisotropic energy gap in the generalized BCS pairing theory. The gap parameter 2Δ(k^{^}) can be quite different for (k^{^}) perpendicular to the plane of the layers as compared tok parallel to layer planes. Because of short coherence lengths ξ, quite small compared to the normal state carrier meanfree pathl, the effect of these anisotropies do not average out, as in many of the conventional superconductors. For a proper comparison of experimental results with the correct predictions of the pairing theory, a formulation is developed to obtain important physical quantities like specific heat and infrared absorption in the superconducting state of such anisotropic systems. This includes a brief account of the pairing theory generalized to layered crystals with arbitrary number of layers per unit cell, not necessarily equidistant. In an explicit model for the anisotropy of the gap parameter ink-space, with a simple form for the nonspherical Fermi-surface, it is shown that the low-temperature specific heat can have even a linear or a power-law temperature-dependence in the superconducting state. Even if the gap parameter does not vanish anywhere, its smeared-out exponential temperature-dependence may be difficult to be distinguished experimentally from a power-law behaviour. Similarly, it is shown that in the case of appreciable anisotropy, infrared absorption can take place much below the in-plane gap parameter 2Δ_t(k^{^})_t), where k_t is the wavevector in the plane of the layers.