The Structure and Dispersion of a Sharp Quantum Hall Edge Probed by Momentum-Resolved Tunneling

Abstract

We present measurements of momentum-resolved magneto-tunneling from a perpendicular two-dimensional (2D) contact into integer quantum Hall (QH) edges at a sharp edge potential created by cleaved edge overgrowth. Resonances in the tunnel conductance correspond to coincidences of electronic states of the QH edge and the 2D contact in energy-momentum space. We directly probe the dispersion curves of individual integer QH edge modes, and find that an epitaxially overgrown cleaved edge realizes the sharp edge limit, where the Chklovskii picture relevant for soft etched or gated edges is no longer valid. The inter-channel distances turn out to be smaller than both the magnetic length and the Bohr radius. We provide a quantitative model for describing the lineshape of conductance peaks in quantum Hall edge tunneling. The zero bias tunnel conductance in our single edge tunnel experiment does not feature the persistent conductance previously reported for a double quantum Hall edge tunnel geometry, and we explain this as a consequence of using a probe contact with a non-fluctuating Fermi energy. Furthermore with the measured dispersion relation reflecting the potential distribution at the edge we directly deduce the band bending at our cleaved edge under the influence of an external voltage bias. At finite bias we observe significant deviations from the flat-band condition in agreement with self-consistent calculations of the edge potential.