Calculation and spectroscopy of the Landau band structure at a thin and atomically precise tunneling barrier

TL;DR

This study combines theoretical calculations and experimental measurements to analyze the Landau band structure at a thin tunneling barrier between quantum Hall systems, revealing energy gaps, anticrossings, and quantum interference effects.

Contribution

It provides a detailed quantum-mechanical calculation of Landau bands at a tunneling barrier and experimentally investigates gap shifts and interference signatures in a GaAs/AlGaAs heterostructure.

Findings

Reduced Landau level separation near the barrier

Displacement of conductance peaks with magnetic field

Observation of quantum interference effects

Abstract

Two laterally adjacent quantum Hall systems separated by an extended barrier of a thickness on the order of the magnetic length possess a complex Landau band structure in the vicinity of the line junction. The energy dispersion is obtained from an exact quantum-mechanical calculation of the single electron eigenstates for the coupled system by representing the wave functions as a superposition of parabolic cylinder functions. For orbit centers approaching the barrier, the separation of two subsequent Landau levels is reduced from the cyclotron energy to gaps which are much smaller. The position of the anticrossings increases on the scale of the cyclotron energy as the magnetic field is raised. In order to experimentally investigate a particular gap at different field strengths but under constant filling factor, a GaAs/AlGaAs heterostructure with a 52 Angstrom thick tunneling barrier and a gate electrode for inducing the two-dimensional electron systems was fabricated by the cleaved edge overgrowth method. The shift of the gaps is observed as a displacement of the conductance peaks on the scale of the filling factor. Besides this effect, which is explained within the picture of Landau level mixing for an ideal barrier, we report on signatures of quantum interferences at imperfections of the barrier which act as tunneling centers. The main features of the recent experiment of Yang, Kang et al. are reproduced and discussed for different gate voltages. Quasiperiodic oscillations, similar to the Aharonov Bohm effect at the quenched peak, are revealed for low magnetic fields before the onset of the regular conductance peaks.