Gauge theory of topological phases of matter

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.

arXiv commentPublished version

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Cited by in corpus (12)

• Magnetohydrodynamics of Chiral Relativistic Fluids
• On Nonrelativistic Diffeomorphism Invariance
• ${\mathbb{Z}}_2$ invariants of topological insulators as geometric obstructions
• Mirror Anomaly in Dirac Semimetals
• Tracing the nonequilibrium topological state of Chern insulators
• Cancellation of quantum anomalies and bosonization of three-dimensional time-reversal symmetric topological insulators
• Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-like terms
• Chiral Anomaly, Topological Field Theory, and Novel States of Matter
• Spontaneous mass generation due to phonons in a two-dimensional Dirac fermion system
• Gauge Invariance and Anomalies in Condensed Matter Physics
• From colored gravity to electromagnetism
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure