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arXiv · 1304.7052

Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene

Yasumasa Hasegawa·Mahito Kohmoto
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Abstract

Energy versus magnetic field (Hofstadter butterfly diagram) in twisted bilayer graphene is studied theoretically. If we take the usual Landau gauge, we cannot take a finite periodicity even when the magnetic flux through a supercell is a rational number. We show that the \textit{periodic} Landau gauge, which has the periodicity in one direction, makes it possible to obtain the Hofstadter butterfly diagram. Since a supercell can be large, magnetic flux through a supercell normalized by the flux quantum can be a fractional number with a small denominator, even when a magnetic field is not extremely strong. As a result, quantized Hall conductance can be a solution of nontrivial Diophantine equation.

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Yasumasa Hasegawa, Mahito Kohmoto. 2013-10-02. Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene. https://doi.org/10.1103/physrevb.88.125426

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