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 / 2 π through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero.
Publication Source (Journal or Book title)
Becker, S., Han, R., & Jitomirskaya, S. (2019). Cantor spectrum of graphene in magnetic fields. Inventiones Mathematicae, 218 (3), 979-1041. https://doi.org/10.1007/s00222-019-00916-y