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

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.

consistent with published version in Physical Review B (2016)

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• The nonperturbative functional renormalization group and its applications
• Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model
• Rashba spin-orbit coupling in the square lattice Hubbard model: A truncated-unity functional renormalization group study
• Truncated unity functional renormalization group for multiband systems with spin-orbit coupling
• Bond-ordered states and $f$-wave pairing of spinless fermions on the honeycomb lattice
• Derivation of a Ginzburg-Landau free energy density containing mixed gradient terms of a $p+ip$ superconductor with spin-orbit coupling
• Ab initio materials physics and microscopic electrodynamics of media
• Response Theory of the Electron-Phonon Coupling
• Consistent combination of truncated-unity functional renormalization group and mean-field theory
• Superconductivity in a two-dimensional repulsive Rashba gas at low electron density