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

TL;DR

This paper extends the theory of layered superconductors to include Rashba and Dresselhaus spin-orbit interactions, revealing how these interactions induce gap anisotropy and suppress the superconducting gap.

Contribution

It provides analytical expressions for the gap function and critical SOI values, showing how spin-orbit interactions affect superconducting properties in layered materials.

Findings

SOIs induce anisotropy in the superconducting gap.

SOIs suppress the gap magnitude at various temperatures.

Critical SOI values lead to vanishing superconducting gap.

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 $\Delta$ 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.