Electrostatic Aharonov-Bohm conductance oscillations in a mesoscopic ring: Effects of potential discontinuities.

Abstract

Quantum oscillations in a mesoscopic ring with two leads are studied where a magnetic flux and an electrostatic potential are applied simultaneously. Ballistic transport is investigated where electrons pass through the entire system without being scattered except at the junction of the ring and the lead. The effects of magnetic flux threading the ring can be considered as a phase shift in an Aharonov-Bohm (AB) sense. In the electrostatic AB effects, the effects of electrostatic potential applied to either of the two electron paths has so far been considered in terms of the electrostatic phase shift (model A). In a mesoscopic system (or in a rigorous theoretical treatment), we must consider the additional effects of scattering due to potential discontinuities at the edges of the electrode to which the electrostatic potential is applied (model B). In this paper, models A and B are considered on an equal footing. By comparing these two cases, we find that the conventional treatment of AB effects is possible at low electrostatic potential in a mesoscopic system. In model B, where the scattering effects at the gate edges are considered, the amplitudes of the quantum oscillation slowly decay as a function of increasing electrostatic potential. At higher electrostatic potential, we predict that conductance oscillations exhibit strong resonance structures at the maximum plateau regions. The relation between the transmission probability and electron energy is also calculated for fixed \ensuremath{\theta} and \ensuremath{\varphi}, and discussed.