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

TL;DR

This paper explores how Berry curvature influences superconductivity in two-dimensional materials, showing it generally reduces the superconducting gap and critical temperature, with implications for experimental detection in doped systems.

Contribution

It introduces a theoretical framework incorporating Berry curvature effects into BCS superconductivity in 2D materials, revealing its impact on coupling strength and critical temperature.

Findings

Berry curvature modifies the electron interaction Hamiltonian.

It generally lowers the superconducting gap and critical temperature.

Experimental deviations in T_c can indicate Berry curvature effects.

Abstract

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