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We know that $\sigma_{xy}$ in the integer quantum Hall effect (or quantum anomalous Hall effect) can be calculated by the Berry curvature, but we also know that $\sigma_{xy}$ is calculated by the properties of the body!

Why it can be explained as edge state to some extent? I know edge-boundary correspondence, but what is the physics in it? I hope that is a elegant explanation about that.

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  • $\begingroup$ Have you looked at the Landauer-Büttiker formalism? $\endgroup$
    – Massimo Ortolano
    Commented Nov 9, 2020 at 16:26
  • $\begingroup$ @MassimoOrtolano I know that. But I don not think it's a explanation that I hope. $\endgroup$
    – fbs147
    Commented Nov 9, 2020 at 16:27
  • $\begingroup$ I suggest you to clarify which kind of explanation your hoping for, because as is your question looks a bit unclear. $\endgroup$
    – Massimo Ortolano
    Commented Nov 9, 2020 at 16:31
  • $\begingroup$ @MassimoOrtolano why body conductivity correspond to a edge conductivity? $\endgroup$
    – fbs147
    Commented Nov 9, 2020 at 16:33
  • $\begingroup$ An edge state is not associated to an edge conductivity. $\endgroup$
    – Massimo Ortolano
    Commented Nov 9, 2020 at 16:35

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