Laterally coupled and field-induced quantum Hall systems

TL;DR

This paper investigates the complex Landau level dispersion in laterally coupled quantum Hall systems using magnetotunneling spectroscopy, revealing magnetic shifts in band gaps and quantum interference effects caused by disorder and tunneling centers.

Contribution

It introduces a novel algorithm to exactly solve the Schrödinger equation for complex potential landscapes in quantum Hall systems, combining experimental and theoretical insights.

Findings

Magnetic shift of band gaps on the scale of the cyclotron energy confirmed experimentally.

Disorder-induced quantum interferences create irregular conductance features.

Conductance fluctuations occur at small magnetic fields before Landau oscillations.

Abstract

A quantum Hall system which is divided into two laterally coupled subsystems by means of a tunneling barrier exhibits a complex Landau level dispersion. Magnetotunneling spectroscopy is employed to investigate the small energy gaps which separate subsequent Landau bands. The control on the Fermi level permits to trace the anticrossings for varying magnetic fields. The band structure calculation predicts a magnetic shift of the band gaps on the scale of the cyclotron energy. This effect is confirmed experimentally by a displacement of the conductance peaks on the axis of the filling factor. Tunneling centers within the barrier are responsible for quantum interferences between opposite edge channels. Due to the disorder potential, the corresponding Aharonov-Bohm interferometers generate additional long-period and irregular conductance features. In the regime of strong localization, conductance fluctuations occur at small magnetic fields before the onset of the regular Landau oscillations. The Landau dispersion is obtained by a dedicated algorithm which solves the Schroedinger equation exactly for a single electron residing in a quantum Hall system with an arbitrary unidirectional, threefold staircase potential.