Green's Function of Magnetic Topological Insulator in Gradient Expansion Approach

TL;DR

This paper derives the Green's function for the surface states of a magnetic topological insulator with slowly varying magnetization, revealing how electromagnetic fields and gap modulations induce charge, current, and energy densities.

Contribution

It provides a gradient expansion approach to analyze the Green's function and related physical quantities in magnetic topological insulators.

Findings

Charge and current densities are generated by emergent electromagnetic fields.

Energy current is associated with the spatial modulation of the induced gap.

All quantities except the energy current are driven by electromagnetic fields.

Abstract

We study the Keldysh Green's function of the Weyl-fermion surface state of the three-dimensional topological insulator coupled with a space-time dependent magnetization in the gradient expansion. Based on it 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 the Weyl fermion.