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