Gauge theory of topological phases of matter
1 Theoretische Physik, ETH Zurich - 8093 Zürich, Switzerland
2 Department of Physics, University of Fribourg - 1700 Fribourg, Switzerland
Received: 28 December 2012
Accepted: 7 February 2013
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.
PACS: 71.10.-w – Theories and models of many-electron systems / 73.43.-f – Quantum Hall effects / 14.80.Va – Axions and other Nambu-Goldstone bosons (Majorons, familons, etc.)
© EPLA, 2013