• 文献标题:   LOCALIZATION FOR GAPPED DIRAC HAMILTONIANS WITH RANDOM PERTURBATIONS: APPLICATION TO GRAPHENE ANTIDOT LATTICES
  • 文献类型:   Article
  • 作  者:   BARBAROUX JM, CORNEAN HD, ZALCZER S
  • 作者关键词:   dirac operator, random potential, localization
  • 出版物名称:   DOCUMENTA MATHEMATICA
  • ISSN:   1431-0643
  • 通讯作者地址:   Univ Toulon Var
  • 被引频次:   0
  • DOI:  
  • 出版年:   2019

▎ 摘  要

In this paper we study random perturbations of firstorder elliptic operators with periodic potentials. We are mostly interested in Hamiltonians modeling graphene antidot lattices with impurities. The unperturbed operator H-0 := D-S + V-0 is the sum of a Dirac-like operator D-S plus a periodic matrix-valued potential V-0, and is assumed to have an open gap. The random potential V-omega is of Anderson-type with independent, identically distributed coupling constants and moving centers, with absolutely continuous probability distributions. We prove band edge localization, namely that there exists an interval of energies in the unperturbed gap where the almost sure spectrum of the family H-omega := H-0 + V-omega is dense pure point, with exponentially decaying eigenfunctions, that give rise to dynamical localization.