Topological properties of the edge states scattered by a simply connected point contact

(Received 21 April 1994, accepted 18 July 1994)

Abstract
The singularities of the phase of an edge state scattered by a barrier interrupting a wire in a peipendicular magnetic field are discussed. The transmission properties of such a structure are expressed in terms of creation and annihilation of vortex-antivortex pairs that give rire to oscillations in the transmission coefficient. Vortices are trapped under the barrier causing oscillations in the transmission that are related to the resistance oscillations measured in quantum point contacts, whose period depends linearly on the magnetic field. We propose a theory of these oscillations which differs from other explanations based on the Aharonov-Bohm effect. An experiment is proposed in which oscillations in the transmission are monitored by the barrier voltage gate.