JournalsjstVol. 2, No. 2pp. 115–146

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

  • Martin Könenberg

    Universität Wien, Austria
  • Edgardo Stockmeyer

    Ludwig-Maximilians-Universität, München, Germany
Localization of two-dimensional massless Dirac fermions in a magnetic quantum dot cover
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Abstract

We consider a two-dimensional massless Dirac operator HH in the presence of a perturbed homogeneous magnetic field B=B0+bB=B_0+b and a scalar electric potential VV. For VLlocp(R2)V\in L_{\rm loc}^p(\mathbb R^2), p(2,]p\in(2,\infty], and bLlocq(R2)b\in L_{\rm loc}^q(\mathbb R^2), q(1,]q\in(1,\infty], both decaying at infinity, we show that states in the discrete spectrum of HH are superexponentially localized. We establish the existence of such states between the zeroth and the first Landau level assuming that V=0V=0. In addition, under the condition that bb is rotationally symmetric and that VV satisfies certain analyticity condition on the angular variable, we show that states belonging to the discrete spectrum of HH are Gaussian-like localized.

Cite this article

Martin Könenberg, Edgardo Stockmeyer, Localization of two-dimensional massless Dirac fermions in a magnetic quantum dot. J. Spectr. Theory 2 (2012), no. 2, pp. 115–146

DOI 10.4171/JST/24