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

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).