Drift velocity of edge magnetoplasmons due to magnetic edge channels

Abstract

Edge magnetoplasmons arise on a boundary of conducting layer in perpendicular magnetic field due to an interplay of electron cyclotron motion and Coulomb repulsion. Lateral electric field, which confines electrons inside the sample, drives their spiraling motion in magnetic field along the edge with the average drift velocity contributing to the total magnetoplasmon velocity. We revisit this classical picture by developing fully quantum theory of drift velocity starting from analysis of magnetic edge channels and their electrodynamic response. We derive the quantum-mechanical expression for the drift velocity, which arises in our theory as a characteristic of such response and can be calculated as harmonic mean of group velocities of edge channels crossing the Fermi level. Using the Wiener-Hopf method to solve analytically the edge mode electrodynamic problem, we demonstrate that the edge channel response effectively enhances the bulk Hall response of the conducting layer and thus increases the edge magnetoplasmon velocity. In the long-wavelength limit of our model, the drift velocity is simply added to the total magnetoplasmon velocity, in agreement with the classical picture.