Localization of two-dimensional massless Dirac fermions in a magnetic quantum dot

Autor(en)

Martin Könenberg, Edgardo Stockmeyer

Abstrakt

We consider a two-dimensional massless Dirac operator H in the presence of a perturbed homogeneous magnetic field B=B0+b and a scalar electric potential V. For V∈Lploc(R2), p∈(2,∞], and b∈Lqloc(R2), q∈(1,∞], 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.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Ludwig-Maximilians-Universität München

Journal

Journal of Spectral Theory

Band

2

Seiten

115-146

Anzahl der Seiten

32

ISSN

1664-039X

DOI

https://doi.org/10.4171/JST/24

Publikationsdatum

2012

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/80372845-0635-4b1b-85c2-534c6f1ba314