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Do I correctly understand the reason why the Hall resistivity in Quantum Hall Effect becomes larger as magnetic field increases?

Physics Asked by phys_gur on July 2, 2021

I’m wondering whether I correctly understand the increase of the Hall resistivity rho_xy in Quantum Hall effect.

As you can see the graph,

enter image description here

As magnetic field becomes much larger, the quantization of Landau level is also increase.

So, what I understand is, the density of states that passes the Fermi level(or Fermi surface) has lower states density than the density of states that passed the Fermi surface previously.

I mean, if we consider SHO, for each energy level, degeneracy becomes larger as the quantum number increases.

Like this, much more quantization makes the DOS with lower Landau level sits to the Fermi surface, making less states for electron, eventually makes much higher resistivity for the material. (in my opinion)

An I right? I know it’s really redundant question.

But I really want to know whether my understanding is correct or wrong.

Thanks.

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