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Honeycomb structures in magnetic fields

Published version
Peer-reviewed

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Authors

Han, Rui 
Jitomirskaya, Svetlana 
Zworski, Maciej 

Abstract

Abstract: We consider the nearest-neighbour tight binding model of the honeycomb lattice in magnetic fields and discover surprizing new analytical results that fully explain fractal spectra and experimentally observed asymmetries in the density of states of molecular graphene. We describe a fractal Cantor spectrum for irrational magnetic flux through a honeycomb, and establish the existence of zero energy Dirac cones for each rational flux with fully explicit estimates on the cone angle. Our results give a substantially more refined description of subtleties in the de Haas–van Alphen and quantum Hall effects, and provide the first quantitative bounds on transport coefficients for the tight-binding model under disorder.

Description

Funder: University of Cambridge Centre for Doctoral Training

Keywords

Paper, Mathematical physics, honeycomb, magnetic, Cantor spectrum, Anderson model, semiclassical analysis, quantum Hall effect, de Haas van Alphen effect

Journal Title

Journal of Physics A: Mathematical and Theoretical

Conference Name

Journal ISSN

1751-8113
1751-8121

Volume Title

54

Publisher

IOP Publishing
Sponsorship
National Science Foundation (1500852, 1901462, DMS-1800689)
UK Engineering and Physical Sciences Research Council (EPSRC) (EP/L016516/1)