Gap Anisotropy in Layered Superconductors Due to Rashba and Dresselhaus Spin-Orbit Interactions

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 $\Delta$ which becomes complex in the presence of SOIs. In the absence of SOIs, $\Delta$ 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 $\cos{k_z}$ factors in which the $k_z$ momentum along the $z$ direction contributes to the magnitude of the gap function. It is also found that SOIs suppress $\Delta$ at both zero and finite temperatures, and for certain critical values of SOIs and beyond $\Delta$ 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.