Probing the Electrostatics of Integer Quantum Hall Edges with Momentum-Resolved Tunnel Spectroscopy

TL;DR

This study uses momentum-resolved tunneling to directly measure the electrostatic potential and band bending at integer quantum Hall edges, revealing deviations from flat-band conditions under bias.

Contribution

It introduces a novel momentum-resolved magneto-tunneling technique to probe the electrostatics of quantum Hall edges with high precision.

Findings

Resonances correspond to energy-momentum coincidences of edge and contact states.

Edge potential shows significant band bending under external bias.

Measurements agree with self-consistent electrostatic calculations.

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. With this dispersion relation reflecting the potential distribution at the edge we can directly measure 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.