Effect of a charged impurity on the fractional quantum Hall effect: Exact numerical treatment of finite systems

Abstract

We investigate the role of a single charged impurity on the fractional quantum Hall effect phenomenon by studying finite systems in spherical, toroidal, and disk geometries. Our qualitative results are independent of the geometry. We study the screening behavior systematically and find that screening charge accumulates at the impurity. The screening charge density shows an interesting oscillation with a characteristic scale of the magnetic length. We also find that the excitation gap is reduced significantly in the presence of the impurity.