Conductivity for a Spin-Split 2D Electron System

Recent research on spintronic systems has examined a wide variety of their transport and optical properties from both a theoretical and experimental perspective. By including spin-orbit interaction (SOI) in a model Hamiltonian, we calculate the low-frequency local conductivity, starting with Kubo's formula. For long mean-free paths, we obtain a closed-form analytical result which is a generalization of the Drude conductivity. By adding vertex corrections using maximally crossed Feynman diagrams to our result, we also obtain, to lowest order in the scattering parameter, the non-local conductivity is given in terms of function which shows that there is an ``interference" effect due to the SOI. This means that the electrons do not diffuse through the sample when the SOI is neglected, as it demonstrated several years ago.