Robust Nodal Structure of Landau Level Wave Functions Revealed by Fourier Transform Scanning Tunneling Spectroscopy

TL;DR

This study uses Fourier transform scanning tunneling spectroscopy to reveal the robust nodal structure of Landau level wave functions in a 2D electron system, highlighting fundamental properties of quantum Hall states.

Contribution

It demonstrates the real-space nodal structure of Landau level wave functions and its robustness, confirmed by experimental data, theory, and simulations.

Findings

Radial minima in Fourier-transformed LDOS at fixed momenta

Minima depend only on inverse magnetic length

Nodal structure decouples from disorder effects

Abstract

Scanning tunneling spectroscopy is used to study the real-space local density of states (LDOS) of a two-dimensional electron system in magnetic field, in particular within higher Landau levels (LL). By Fourier transforming the LDOS, we find a set of n radial minima at fixed momenta for the nth LL. The momenta of the minima depend only on the inverse magnetic length. By comparison with analytical theory and numerical simulations, we attribute the minima to the nodes of the quantum cyclotron orbits, which decouple in Fourier representation from the random guiding center motion due to the disorder. This robustness of the nodal structure of LL wave functions should be viewed as a key property of quantum Hall states.