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

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