Coupled edge-currents in a mesoscopic quantum Hall system

Abstract

A proposal of the author that a sufficiently narrow two-dimensional quantum Hall system of mseoscopic length should behave like a Josephson tunnel junction due to weak coupling of the edge-currents has been developed further here to study how the 'locked-in' phases of the two edge-currents slip with respect to each other in space as well as in time under the combined influence of the magnetic and the Hall fields. The spatio-temporal variation of the phase-difference, it is found, can be controlled by adjusting the system current. At a suitable velocity some of the current-carrying electrons, which also move back and forth between the edge-currents under the influence of the phase-slippage, form closed loops. As the electrons go around in a loop once the phase difference between the edge-currentschanges by 2π thus showing that the state of the system is a single-valued function of the phase-difference and that each loop encloses a flux quantum, hc/e. In this way our semiconducting mesoscopic quantum Hall system mimics a Josephson tunnel junction mainly due to the long-range phase coherence. The quantum interference effects are discussed as they show up in some experimental and numerical results. © 1995.