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

Könenberg, Martin und Stockmeyer, Edgardo (2012): Localization of two-dimensional massless Dirac fermions in a magnetic quantum dot. In: Journal of Spectral Theory, Bd. 2, Nr. 2: S. 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.

• Dokumententyp: Zeitschriftenartikel
• Publikationsform: Publisher's Version
• Keywords: Magnetic operator; localization; Dirac operator
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1664-039X
• Allianz-/Nationallizenz: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
• Sprache: Englisch