Two-dimensional electron gas in a uniform magnetic field in the presence of a δ-impurity

The density of states and the Hall conductivity of a two-dimensional electron gas in a uniform magnetic field and in the presence of a δ-impurity are exactly calculated using elementary field theoretic techniques. The impurity creates one localized state per Landau level, but the Hall conductivity is unaffected. Our treatment is explicitly gauge-invariant, and can be easily adapted to other problems involving zero-range potentials. 03.65.-w, 05.30.Fk, 11.10.Gh, 73.40.Hm Typeset using REVTEX Present address: Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA. E-mail: [email protected] E-mail: [email protected] 1