Thouless-Kohmoto-Nightingale-den Nijs formula for a general Hamiltonian

Hidenori Fukaya (Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan) ; Tetsuya Onogi (Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan) ; Satoshi Yamaguchi (Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan) ; Xi Wu (Physics Department, Ariel University, Ariel)

Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons 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 Ward-Takahashi identities are crucial to relate the Chern-Simons 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.

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Published on:
10 April 2020
Publisher:
APS
Published in:
Physical Review D , Volume 101 (2020)
Issue 7
DOI:
https://doi.org/10.1103/PhysRevD.101.074507
arXiv:
1903.11852
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: