GAP OPENING IN THE SPECTRUM OF SOME DIRAC-LIKE PSEUDO-DIFFERENTIAL OPERATORS

J. M. Barbaroux; H. D. Cornean; S. Zalczer

GAP OPENING IN THE SPECTRUM OF SOME DIRAC-LIKE PSEUDO-DIFFERENTIAL OPERATORS

J. M. Barbaroux, H. D. Cornean, S. Zalczer

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Abstract

In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by σ·F (−i∇), where σ denotes the Pauli matrices and F is a sufficiently regular vector-valued function which equals 0 at the origin and grows at infinity. Its spectrum is the whole real line. We prove that a gap appears for perturbations in a certain class of periodic matrix-valued potentials depending on F, and we study how this gap depends on different parameters.

Original language	English
Journal	Revue Roumaine de Mathematiques Pures et Appliquees
Volume	66
Issue number	3-4
Pages (from-to)	597-616
Number of pages	20
ISSN	0035-3965
Publication status	Published - 2021

Bibliographical note

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© 2021, Publishing House of the Romanian Academy. All rights reserved.

Keywords

Dirac operators
Multilayer graphene
Pseudo-differential operators
Spectral gaps

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title = "GAP OPENING IN THE SPECTRUM OF SOME DIRAC-LIKE PSEUDO-DIFFERENTIAL OPERATORS",

abstract = "In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by σ·F (−i∇), where σ denotes the Pauli matrices and F is a sufficiently regular vector-valued function which equals 0 at the origin and grows at infinity. Its spectrum is the whole real line. We prove that a gap appears for perturbations in a certain class of periodic matrix-valued potentials depending on F, and we study how this gap depends on different parameters.",

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AU - Cornean, H. D.

AU - Zalczer, S.

PY - 2021

Y1 - 2021

N2 - In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by σ·F (−i∇), where σ denotes the Pauli matrices and F is a sufficiently regular vector-valued function which equals 0 at the origin and grows at infinity. Its spectrum is the whole real line. We prove that a gap appears for perturbations in a certain class of periodic matrix-valued potentials depending on F, and we study how this gap depends on different parameters.

AB - In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by σ·F (−i∇), where σ denotes the Pauli matrices and F is a sufficiently regular vector-valued function which equals 0 at the origin and grows at infinity. Its spectrum is the whole real line. We prove that a gap appears for perturbations in a certain class of periodic matrix-valued potentials depending on F, and we study how this gap depends on different parameters.

KW - Dirac operators

KW - Multilayer graphene

KW - Pseudo-differential operators

KW - Spectral gaps

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AN - SCOPUS:85123545682

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VL - 66

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JO - Revue Roumaine de Mathematiques Pures et Appliquees

JF - Revue Roumaine de Mathematiques Pures et Appliquees

IS - 3-4

ER -

GAP OPENING IN THE SPECTRUM OF SOME DIRAC-LIKE PSEUDO-DIFFERENTIAL OPERATORS

Abstract

Bibliographical note

Keywords

AUB Link

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