Comparing the effective enhancement of local and non-local spin-orbit couplings on honeycomb lattices due to strong electronic correlations

TL;DR

This study compares how electronic correlations differently enhance local and non-local spin-orbit couplings in honeycomb lattice models, revealing that correlations more strongly increase local SOC effects.

Contribution

It introduces a comparative analysis of correlation effects on local versus non-local SOC in honeycomb lattices using TRILEX and DMFT methods.

Findings

Correlations increase the effective SOC in both models.

The enhancement of SOC is weaker for non-local SOC.

TRILEX formulas for broken SU(2) symmetry are developed.

Abstract

We investigate the interplay of electronic correlations and spin-orbit coupling (SOC) for a one-band and a two-band honeycomb lattice model. The main difference between the two models concerning SOC is that in the one-band case the SOC is a purely non-local term in the basis of the $p_z$ orbitals, whereas in the two-band case with $p_x$ and $p_y$ as basis functions it is purely local. In order to grasp the correlation effects on non-local spin-orbit coupling, we apply the TRILEX approach that allows to calculate non-local contributions to the self-energy approximatively. For the two-band case we apply dynamical mean-field theory. In agreement with previous studies, we find that for all parameter values in our study, the effect of correlations on the spin-orbit coupling strength is that the bare effective SOC parameter is increased. However, this increase is much weaker in the non-local than in the local SOC case. Concerning the TRILEX method, we introduce the necessary formulas for calculations with broken SU(2) symmetry.