Localization of two-dimensional massless Dirac fermions in a magnetic quantum dot
Summary: 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 \(V\in L_{\text{loc}}^p(\mathbb R^2), \;p\in(2,\infty]\), and \(b\in L_{loc}^q(\mathbb R^2), \;q\in(1,\infty]\), 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.
scientific article; zbMATH DE number 6035241
scientific article