Electron Correlation Effects in Non-Centrosymmetric Metals in the Weak Coupling Regime

TL;DR

This study investigates how electron correlations affect Rashba spin-orbit coupling and Fermi momentum spin-splitting in non-centrosymmetric metals, revealing that correlations enhance RSOC but leave SFM largely unaffected due to a cancellation effect.

Contribution

It demonstrates that electron correlations enhance RSOC without significantly altering SFM in non-centrosymmetric metals, highlighting a cancellation mechanism.

Findings

RSOC is enhanced by electron correlation.

Spin-splitting of the Fermi momentum remains robust.

Cancellation of effects is nearly perfect in common models.

Abstract

The two-dimensional Rashba-Hubbard model is investigated in order to clarify the electron correlation effects in non-centrosymmetric metals. The renormalization effect on Rashba spin-orbit coupling (RSOC) is calculated on the basis of second-order and third-order perturbation theories. We show that RSOC is enhanced by the electron correlation. On the other hand, the spin-splitting of the Fermi momentum (SFM) is robust against the electron correlation effect because the enhancement of RSOC is cancelled by the $k$-mass renormalization. The cancellation is almost perfect in often adopted models in which the momentum dependence of RSOC is linear in the quasiparticle velocity. A small correction to the SFM appears otherwise. We show that the same results are obtained for other antisymmetric spin-orbit couplings in non-centrosymmetric systems, such as the synthetic spin-orbit coupling in cold atoms.