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

Könenberg, Martin; Stockmeyer, Edgardo (2012): Localization of two-dimensional massless Dirac fermions in a magnetic quantum dot. In: Journal of Spectral Theory, Vol. 2, No. 2: pp. 115-146

Abstract

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 is an element of L-loc(p) (R-2), p is an element of(2, infinity], and b is an element of L-loc(q)(R-2), q is an element of(1, infinity], 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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Keywords: Magnetic operator; localization; Dirac operator
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1664-039X
• Alliance/National Licence: This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
• Language: English