Localization for quasi-one-dimensional Dirac operators

We consider a random family of Dirac operators on \(N\) parallel real lines, modelling for example a graphene nanoribbon. We establish a localization criterion involving properties on the group generated by transfer matrices. In particular, we consider not only the case where this group is the sympl...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Boumaza, Hakim, Zalczer, Sylvain
Format: Article
Language:English
Subjects:
Graphene
Liapunov exponents
Localization
Nanoribbons
Operators (mathematics)
Subgroups
Transfer matrices
Online Access:Get full text
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Summary:We consider a random family of Dirac operators on \(N\) parallel real lines, modelling for example a graphene nanoribbon. We establish a localization criterion involving properties on the group generated by transfer matrices. In particular, we consider not only the case where this group is the symplectic group but also a strict subgroup of it. We establish under quite general hypotheses that the sum of the Lyapunov exponents and the integrated density of states are H\"older continuous. Moreover, for a set of concrete cases where the potentials are on Pauli matrices, we compute the transfer matrices and prove either localization or delocalization, depending on the potential and on the parity of \(N\).
ISSN:2331-8422