I'm interested in the derivation of the classical Hall effect coefficient, given in cgs by $$R_{H}=-\frac{1}{nec},$$ where $n$ is the electron number density, $-e<0$ is the electron charge,and $c$ is the usual, ubiquitous velocity in Physics, from the fact that QHE provides the quantum of electrical conductance $$g=\frac{2e^{2}}{h},$$ where $h$ is Planck's constant, and the 2 comes from spin degeneracy.

Is there a convenient way to go from the quantum to the classical case for this problem?

  • $\begingroup$ I assume, if you consider 3d system instead of 2d, you would get it. $\endgroup$ – physshyp May 6 '19 at 10:24
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    $\begingroup$ @physshyp What an extremely unhelpful comment. $\endgroup$ – user1717828 May 6 '19 at 11:10

I think you cannot derive classical case from the quantum case. g=filling factor *2e_squared/h occurs at very high magnetic fields where Landau levels start filling and current is carried only by edge states. In classical regime, magnetic fields are low and Landau levels haven't started filling and there is no edge states

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