TKNN formula for general Hamiltonian
Abstract
Topological insulators in odd dimensions are characterized by topological numbers. We prove the wellknown relation between the topological number given by the Chern character of the Berry curvature and the ChernSimons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including nonminimal couplings by an explicit calculation. A series of WardTakahashi identities are crucial to relate the ChernSimons level to a winding number, which could then be directly reduced to Chern character of Berry curvature by carrying out the integral over the temporal momenta.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.11852
 Bibcode:
 2019arXiv190311852F
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 High Energy Physics  Lattice
 EPrint:
 revised version, 23 pages