Green's function of the magnetic topological insulator in a gradient expansion approach

Abstract

We study theKeldysh Green's function of theWeyl fermion surface state of the three-dimensional topological insulator coupled with a space-time dependent magnetization in the gradient expansion. Based on this, we analyze the electric charge and current densities as well as the energy density and current induced by spatially and temporally slowly varying magnetization fields. We show that all the above quantities except the energy current are generated by the emergent electromagnetic fields. The energy current emerges as the circular current reflecting the spatial modulation of an induced gap of theWeyl fermion.