Gap anisotropy in layered superconductors due to Rashba and Dresselhaus spin-orbit interactions

Abstract

The theory of layered superconductors is extended in the presence of Rashba and Dresselhaus spin-orbit interactions (SOIs). Using the intralayer BCS-like pairing interaction and employing the Gor'kov formalism, we obtain analytical expressions for the temperature Green's functions and determine the gap function A which becomes complex in the presence of SOIs. In the absence of SOIs, A is isotropic at both zero and finite temperatures, but it becomes anisotropic even in the presence of a single SOI. This anisotropy is related to the extra cos kz factors in which the kz momentum along the z direction contributes to the magnitude of the gap function. It is also found that SOIs suppress A at both zero and finite temperatures, and for certain critical values of SOIs and beyond A vanishes. Analytical expressions for the critical values of SOIs at zero temperature are obtained. Additionally, how the BCS equation for layered superconductors changes in the presence of SOIs is determined.