Why average over fluxes when calculating Hall conductivity?
Answers
Hey !
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Here, the thermal conductivity C 1 = KA, where K is the heat conductivity of the material in W m-3 K-1 and A is the surface area in m 2, so for heat flow through a unit.
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Thanks !
As this question has not yet attracted an answer, I will post the answer that I have so far come up with here. Note that this is not yet as strong as I would like, so additions would be very welcome.
The thing to realize is that the derivation in the mentioned lecture notes holds for the lowest Landau level (LLL) only. If the system is not in the LLL, the Berry curvature may depend on momentum: Fxy=Fxy(k). In this case, the equation σxy=e2ℏFxy no longer holds without taking the average over the Brillouin zone.