Pole expansion of self-energy and interaction effect on topological insulators

TL;DR

This paper introduces a pole expansion method for self-energy to analyze the effects of interactions on topological insulators, simplifying calculations and providing a clear picture of interaction-driven phase transitions.

Contribution

It establishes a connection between interacting topological indices and an auxiliary noninteracting system using pole expansion of the self-energy, aiding practical calculations.

Findings

Simplifies the calculation of interacting topological indices.

Provides a noninteracting picture of interaction-driven topological phase transitions.

Bridges correlated topological insulators with dynamical mean-field theory.

Abstract

We study effect of interactions on time-reversal-invariant topological insulators. Their topological indices are expressed by interacting Green's functions. Under the local self-energy approximation, we connect topological index and surface states of an interacting system to an auxiliary noninteracting system, whose Hamiltonian is related to the pole-expansions of the local self-energy. This finding greatly simplifies the calculation of interacting topological indices and gives an noninteracting pictorial description of interaction driven topological phase transitions. Our results also bridge studies of the correlated topological insulating materials with the practical dynamical-mean-field-theory calculations.