Streda formula for the Hofstadter-Wilson-Dirac model in two and four dimensions

Abstract

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 stronger fields and for more generic systems in higher dimensions.

arXiv comment7 pages, 5 figures, Final version

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Cited by in corpus (4)

• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Topological magnetoelectric pump in three dimensions
• Real-space representation of the second Chern number