Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials

We theoretically investigate how the Berry curvature, which arises in multiband structures when electrons can be described by an effective single-band Hamiltonian, affects superconducting properties of two-dimensional electronic systems. Generically, curvature is coupled to electric fields beyond those created periodic crystal potential. A potential source such fields, vary slowly on lattice scale, mutual interaction between electrons. show that provides additional terms Hamiltonian describing interacting within a single band. When these are taken into account framework usual BCS weak-coupling treatment generic attractive allows for formation Cooper pairs, coupling constant modified. In pure singlet and triplet superconductors, we find generally lowers thus gap critical temperature as function doping. From experimental point view, measured deviation from expected upon doping, e.g., doped transition-metal dichalcogenides, may unveil strength curvature.