Green's Function Method for Line Defects and Gapless Modes in Topological Insulators : Beyond Semiclassical Approach

TL;DR

This paper introduces a comprehensive quantum Green's function approach to analyze line defects and gapless modes in topological insulators, surpassing semiclassical methods and revealing new topological invariants and effects of interactions.

Contribution

It develops a full quantum formulation for topological invariants in defected topological insulators, enabling analysis beyond semiclassical approximations and including interaction effects.

Findings

Identifies a nontrivial topological invariant in topological insulator-ferromagnet junctions.

Demonstrates failure of semiclassical methods in certain topological phases.

Shows how interactions influence topological responses in inhomogeneous systems.

Abstract

Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)]. A standard approach for the calculation of topological invariants associated with defects is to deal with the spatial inhomogeneity raised by defects within a semiclassical approximation. In this paper, we propose a full quantum formulation for the topological invariants characterizing line defects in three-dimensional insulators with no symmetry by using the Green's function method. On the basis of the full quantum treatment, we demonstrate the existence of a nontrivial topological invariant in the topological insulator-ferromagnet tri-junction systems, for which a semiclassical approximation fails to describe the topological phase. Also, our approach enables us to study effects of electron-electron interactions and impurity scattering on topological insulators with spatial inhomogeneity which gives rise to the Axion electrodynamics responses.