Streda Formula for the Hofstadter–Wilson–Dirac Model in Two and Four Dimensions

Takahiro Fukui, Takanori Fujiwara
2016 Journal of the Physical Society of Japan  
We rederive the spectral asymmetry of the Wilson-Dirac model in external fields, paying attention to the Chern number due to the Berry connection. We interpret the smooth part of the spectral asymmetry as the Streda formula that is originally derived for the two-dimensional quantum Hall effect (QHE). We show by numerical calculations that the Streda formula reproduces the known first and second Chern numbers in a weak magnetic field limit. We conjecture that the Streda formula is valid even for
more » ... stronger fields and for more generic systems in higher dimensions.
doi:10.7566/jpsj.85.124709 fatcat:jnbwk2tz5rbf5p2sbvd3hs5fxu