Linear response theory of interacting topological insulators

Abstract

Chiral surface states in topological insulators are robust against interactions, non-magnetic disorder and localization, yet topology does not yield protection in transport. This work presents a theory of interacting topological insulators in an external electric field, starting from the quantum Liouville equation for the many-body density matrix. Out of equilibrium, topological insulators acquire a current-induced spin polarization. Electron-electron interactions renormalize the non-equilibrium spin polarization and charge conductivity, and disorder in turn enhances this renormalization by a factor of two. Topological insulator phenomenology remains intact in the presence of interactions out of equilibrium, and an exact correspondence exists between the mathematical frameworks necessary for the understanding of the interacting and non-interacting problems.