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 $\mathrm{\Delta }$ which becomes complex in the presence of SOIs. In the absence of SOIs, $\mathrm{\Delta }$ 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 $\mathrm{\Delta }$ at both zero and finite temperatures, and for certain critical values of SOIs and beyond $\mathrm{\Delta }$ 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.

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• Dresselhaus coupling
• Rashba coupling
• Spin-orbit coupling
• Superconducting gap
• Superconductivity
• Green's function methods
• Mathematical physics methods
• Methods in superconductivity
• Real & complex analysis