Document Type

Article

Publication Date

8-1-2022

Abstract

We study discrete magnetic random Schrödinger operators on the square and honeycomb lattice. For the non-random magnetic operator on the hexagonal lattice with any rational magnetic flux, we show that the middle two dispersion surfaces exhibit Dirac cones. We then derive an asymptotic expansion for the density of states on the honeycomb lattice for oscillations of arbitrary rational magnetic flux. This allows us, as a corollary, to rigorously study the quantum Hall effect and conclude dynamical delocalization close to the conical point under disorder. We obtain similar results for the discrete random Schrödinger operator on the Z2-lattice with weak magnetic fields, close to the bottom and top of its spectrum.

Publication Source (Journal or Book title)

International Mathematics Research Notices

First Page

13447

Last Page

13504

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