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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