Cantor spectrum of graphene in magnetic fields

• 成果类型: Article
• 署名作者: Becker, Simon; Han, Rui; Jitomirskaya, Svetlana
• 署名单位: University of Cambridge; University System of Georgia; Georgia Institute of Technology; University of California System; University of California Irvine
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00916-y
• 发表日期: 2019
• 页码: 979-1041
• 关键词: schrodinger-operators; dirac fermions; quantum graphs

摘要

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 phi/2 pi\documentclass through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero.