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Cantor spectrum of graphene in magnetic fields

Spectral Theory 2020-01-08 v1 Mathematical Physics math.MP

Abstract

We consider a quantum graph as a model of graphene in magnetic fields and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the reduced magnetic flux Φ/2π\Phi/2\pi through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero.

Keywords

Cite

@article{arxiv.1803.00988,
  title  = {Cantor spectrum of graphene in magnetic fields},
  author = {Simon Becker and Rui Han and Svetlana Jitomirskaya},
  journal= {arXiv preprint arXiv:1803.00988},
  year   = {2020}
}

Comments

55 pages, 8 figures