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

Abstract

The ~inguJanties of the pha~e of an edge ;taie scattered by a barrier interrupting a w ire ii a pei~pendicular magnetic field are di«ussed. The tran;mis,ion properiies Dl such a ~tructure are expres~ed in terms of creation and annihilation of vortex~antivoriex pairs that give n,e to o,cillation; in the tran~mi,Sion coefficient. Vortice, are trapped under the borner causing o,cillations in the tran,mi,,ion that are related to ihe re;i~tance o,cillation; mea,ured in quantum point contact;, who,e penod depend, linearly on the m;ignetic field. We propo,e a iheory of these oscillation, which differs from other explanation~ ba,ed on the Aharonov-Bohm ei'fect. An e~periment is propo~ed in which o,cillations in ihe tran,mis;ion are monitored by the barrier voltage gate.