Localization of two-dimensional massless Dirac fermions in a magnetic quantum dot
type: Item
instance of: scholarly article
title: Localization of two-dimensional massless Dirac fermions in a magnetic quantum dot
zbMATH Open document ID: 1244.81023
DOI: 10.4171/JST/24
author: Martin Könenberg
author: E. Stockmeyer
published in: Journal of Spectral Theory
publication date: 2012-05-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1111.4549
review text: Summary: We consider a two-dimensional massless Dirac operator \(H\) in the presence of a perturbed homogeneous magnetic field \(B=B_0+b\) and a scalar electric potential \(V\). For \(V\in L_{\text{loc}}^p(\mathbb R^2), \;p\in(2,\infty]\), and \(b\in L_{loc}^q(\mathbb R^2), \;q\in(1,\infty]\), both decaying at infinity, we show that states in the discrete spectrum of \(H\) are superexponentially localized. We establish the existence of such states between the zeroth and the first Landau level assuming that \(V=0\). In addition, under the condition that \(b\) is rotationally symmetric and that \(V\) satisfies certain analyticity condition on the angular variable, we show that states belonging to the discrete spectrum of \(H\) are Gaussian-like localized.
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81Q37
zbMATH DE Number: 6035241
zbMATH Keywords: magnetic operator
zbMATH Keywords: localization
zbMATH Keywords: Dirac operator
MaRDI profile type: Publication
arXiv ID: 1111.4549
cites work: Q5558293
cites work: Schrödinger operators with magnetic fields. I: General interactions
cites work: Eigenvalues in spectral gaps of the two-dimensional Pauli operator
cites work: Schrödinger and Dirac operators with singular potentials and hyperbolic equations
cites work: On eigenfunction decay for two dimensional magnetic Schrödinger operators
cites work: Multiparticle equations for interacting Dirac fermions in magnetically confined graphene quantum dots
cites work: Gaussian decay of the magnetic eigenfunctions
cites work: Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value
cites work: Q5187597
cites work: The essential spectrum of two-dimensional Schrödinger operators with perturbed constant magnetic fields
cites work: Absence of eigenvalues of Dirac operators with potentials diverging at in-finity
cites work: Q3310242
cites work: Gaussian decay estimates for the eigenfunctions of magnetic schrödinger operators
cites work: Analytic vectors
cites work: Q4185363
cites work: Infiniteness of zero modes for the Pauli operator with singular magnetic field
cites work: On the Spectral Properties of the Landau Hamiltonian Perturbed by a moderately Decaying Magnetic Field
cites work: Q5640289
cites work: Q3891103
cites work: Q5694963
cites work: Gaussian decay for the eigenfunctions of a schrödinger operator with magnetic field constant at infinity
cites work: Q4000385
cites work: ABSENCE OF EMBEDDED EIGENVALUES OF THE DIRAC EQUATION FOR LONG RANGE POTENTIALS
description: scientific article; zbMATH DE number 6035241