Geodesic
Localization for Gapped Dirac Hamiltonians with Random Perturbations: Application to Graphene Antidot Lattices
Documenta mathematica, Tome 24 (2019), pp. 65-93

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In this paper we study random perturbations of first order elliptic operators with periodic potentials. We are mostly interested in Hamiltonians modeling graphene antidot lattices with impurities. The unperturbed operator H0​:=DS​+V0​ is the sum of a Dirac-like operator DS​ plus a periodic matrix-valued potential V0​, and is assumed to have an open gap. The random potential Vω​ 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 Hω​:=H0​+Vω​ is dense pure point, with exponentially decaying eigenfunctions, that give rise to dynamical localization.
DOI : 10.4171/dm/675
Classification : 34L15, 46N50, 47A10, 81Q10, 82B20, 82D80
Mots-clés : localization, Dirac operators, random potentials 
Sylvain Zalczer; Jean-Marie Barbaroux; Horia D. Cornean. Localization for Gapped Dirac Hamiltonians with Random Perturbations: Application to Graphene Antidot Lattices. Documenta mathematica, Tome 24 (2019), pp. 65-93. doi: 10.4171/dm/675
@article{10_4171_dm_675,
     author = {Sylvain Zalczer and Jean-Marie Barbaroux and Horia D. Cornean},
     title = {Localization for {Gapped} {Dirac} {Hamiltonians} with {Random} {Perturbations:} {Application} to {Graphene} {Antidot} {Lattices}},
     journal = {Documenta mathematica},
     pages = {65--93},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/675},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/675/}
}
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