Functional renormalization and mean-field approach to multiband systems with spin-orbit coupling: Application to the Rashba model with attractive interaction

TL;DR

This paper develops a combined functional renormalization group and mean-field approach to analyze multiband systems with spin-orbit coupling, revealing an unconventional superconducting phase in a Rashba model with attractive interactions.

Contribution

It introduces a novel method combining RG and mean-field theory for multiband spin-orbit coupled systems, fully implementing spin dependence and band contributions.

Findings

Identifies a superconducting phase with a singlet-type interaction.

Reveals an unconventional superconducting order parameter with mixed singlet and triplet characteristics.

Demonstrates the importance of including both bands in the RG flow for accurate analysis.

Abstract

The functional renormalization group (RG) in combination with Fermi surface patching is a well-established method for studying Fermi liquid instabilities of correlated electron systems. In this article, we further develop this method and combine it with mean-field theory to approach multiband systems with spin-orbit coupling, and we apply this to a tight-binding Rashba model with an attractive, local interaction. The spin dependence of the interaction vertex is fully implemented in a RG flow without SU(2) symmetry, and its momentum dependence is approximated in a refined projection scheme. In particular, we discuss the necessity of including in the RG flow contributions from both bands of the model, even if they are not intersected by the Fermi level. As the leading instability of the Rashba model, we find a superconducting phase with a singlet-type interaction between electrons with opposite momenta. While the gap function has a singlet spin structure, the order parameter indicates an unconventional superconducting phase, with the ratio between singlet and triplet amplitudes being plus or minus one on the Fermi lines of the upper or lower band, respectively. We expect our combined functional RG and mean-field approach to be useful for an unbiased theoretical description of the low-temperature properties of spin-based materials.