2020/08/14 by Simon Becker, Becker, Simon, Rui Han +5
Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph) #Quantum many-body systems #Spectral Theory (math.SP) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2008.06329
openalex publication_date 2020/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider reduced-dimensionality models of honeycomb lattices in magnetic fields and report results about the spectrum, the density of states, self-similarity, and metal/insulator transitions under disorder. We perform a spectral analysis by which we discover a fractal Cantor spectrum for irrational magnetic flux through a honeycomb, prove the existence of zero energy Dirac cones for each rational flux, obtain an explicit expansion of the density of states near the conical points, and show the existence of mobility edges under Anderson-type disorder. Our results give a precise description of de Haas-van Alphen and Quantum Hall effects, and provide quantitative estimates on transport properties. In particular, our findings explain experimentally observed asymmetry phenomena by going beyond the perfect cone approximation.