Hartree simulations of coupled quantum Hall edge states in corner-overgrown heterostructures

TL;DR

This paper uses Hartree simulations to analyze the electronic states in corner-overgrown GaAs/AlGaAs quantum wells under magnetic fields, revealing complex hybrid quantum Hall edge states and their interactions.

Contribution

It introduces a subsystems model to explain hybrid dispersion and wavefunctions in bent quantum Hall systems, highlighting magnetic field-dependent coupling effects.

Findings

Hybrid system hosts coupled counter-propagating QH edges and an accumulation wire.

Coupling between subsystems increases with magnetic field, causing anticrossing gaps.

Model accurately estimates wavefunctions at low magnetic fields.

Abstract

The electronic states in a corner-overgrown bent GaAs/AlGaAs quantum well heterostructure are studied with numerical Hartree simulations. Transmission electron microscope pictures of the junction justify the sharp-corner assumption. In a tilted magnetic field both facets of the bent quantum well are brought to a quantum Hall (QH) state, and the corner hosts an unconventional hybrid system of two coupled counter-propagating quantum Hall edges and an additional one-dimensional accumulation wire. A subsystems model is introduced, whereby the total hybrid dispersion and wavefunctions are explained in terms of the constituent QH edge- and accumulation wire-subsystem dispersions and wavefunctions. At low magnetic fields, orthonormal basis wavefunctions of the hybrid system can be accurately estimated by projecting out the lowest bound state of the accumulation wire from the edge state wavefunctions. At high magnetic fields, the coupling between the three subsystems increases as a function of the applied magnetic field, in contrast to coplanar barrier-junctions of QH systems, leading to large anticrossing gaps between the subsystem dispersions. These results are discussed in terms of previously reported experimental data on bent quantum Hall systems.