Bound states induced giant oscillations of the conductance in the quantum Hall regime

TL;DR

This paper theoretically investigates how bound states in a quantum Hall system with a lateral potential barrier cause giant oscillations in conductance, aligning well with experimental results.

Contribution

It introduces a theoretical model explaining giant conductance oscillations via bound states and tunneling in quantum Hall systems, matching experimental observations.

Findings

Bound states create a complex energy spectrum with peaks and gaps.

Giant conductance oscillations occur at spectrum gaps.

The model aligns with experimental data from Kang et al. (2000).

Abstract

We theoretically studied the quasiparticle transport in a 2D electron gas biased in the quantum Hall regime and in the presence of a lateral potential barrier. The lateral junction hosts the specific magnetic field dependent quasiparticle states highly localized in the transverse direction. The quantum tunnelling across the barrier provides a complex bands structure of a one-dimensional energy spectrum of these bound states, $\epsilon_n(p_y)$, where $p_y$ is the electron momentum in the longitudinal direction $y$. Such a spectrum manifests itself by a large number of peaks and drops in the dependence of the magnetic edge states transmission coefficient $D(E)$ on the electron energy $E$. E.g., the high value of $D$ occurs as soon as the electron energy $E$ reaches gaps in the spectrum. These peaks and drops of $D(E)$ result in giant oscillations of the transverse conductance $G_x$ with the magnetic field and/or the transport voltage. Our theoretical analysis based on the coherent macroscopic quantum superposition of the bound states and the magnetic edge states propagating along the system boundaries, is in a good accord with the experimental observations found in Ref. W. Kang et al., Letters to Nature, 403, 59 (2000).