Correlation Renormalized and Induced Spin-Orbit Coupling

Interplay of spin-orbit coupling (SOC) and electron correlation generates a bunch of emergent quantum phases and transitions, especially topological insulators and topological transitions. We find that electron correlation will induce extra large SOC in multi-orbital systems under atomic SOC and change ground state topological properties. Using the Hartree-Fock mean field theory, phase diagrams of p(x) /p(y) orbital ionic Hubbard model on honeycomb lattice are well studied. In general, correction of strength of SOC delta lambda proportional to (UMODIFIER LETTER PRIME-J). Due to breaking down of rotation symmetry, form of SOC on multi-orbital materials is also changed under correlation. If a non-interacting system is close to fermionic instability, spontaneous generalized SOC can also be found. Using renormalization group, SOC is leading instability close to quadratic band-crossing point. Mean fields at quadratic band-crossing point are also studied.