Random phase approximation for superconducting states in multi-orbital Hubbard models with spin-orbit coupling

Abstract

To better understand electronic and magnetic properties of superconducting (SC) states in 5d transition metal oxides, we derive an analytical formula of the dynamical correlation function for multi-orbital systems with the spin-orbit coupling (SOC), which is accessible to the experimental responses. Starting with a multi-orbital BCS Hamiltonian including the SC gap function, we introduce the dynamical correlation function in the non-interacting case. Based on the diagrammatic techniques, we derive the dynamical correlation function for the interacting case within the random phase approximation. With the help of a numerical calculation, we also show the temperature dependence of the magnetic susceptibility for two different SC states in the presence of the SOC.