The Landau Hamiltonian with a delta-potential supported on curves

Jussi Behrndt, TU Graz, Austria

Abstract

We investigate the spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian $(i\nabla +A)^2 + \alpha\delta$ acting in the Hilbert space $L^2(\mathbb R^2)$ with a $\delta$-potential supported on a finite $C^{2,1}$-smooth curve $\Sigma$; here $\alpha\in L^\infty(\Sigma)$ is a position-dependent real coefficient modeling the strength of the singular interaction on $\Sigma$.

The talk is based on joint work with P. Exner, M. Holzmann, and V. Lotoreichik