Gauge theory of topological phases of matter

TL;DR

This paper develops a gauge theory framework to analyze topological phases of matter, providing insights into their transport properties, effective actions, and surface modes in various quantum systems.

Contribution

It introduces a gauge theory approach to topological phases, offering a new perspective complementary to Landau theory and deriving effective actions for various topological materials.

Findings

Derived gauge-invariant effective actions for topological superconductors and insulators.

Provided a theoretical understanding of surface modes in topological systems.

Connected gauge responses to observable transport phenomena.

Abstract

We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our analysis leads to a "gauge theory of states of matter" complementary to the well known Landau theory of order parameters. We illustrate the power of our approach by deriving and interpreting the gauge-invariant effective actions of (topological) superconductors, 2D electron gases exhibiting the quantized Hall- and spin-Hall effect, 3D topological insulators, as well as axion electrodynamics. We also use the theory to elucidate the structure of surface modes in these systems.