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

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.

References in corpus (13)

• Landau Quantization of Massless Dirac Fermions in Topological Insulator
• Momentum-Resolved Landau-Level Spectroscopy of Dirac Surface State in Bi2Se3
• Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1-xMnxAs
• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Quantum Phase Extraction in Isospectral Electronic Nanostructures
• Single-Atom Gating of Quantum State Superpositions
• Localized Distributions of Quasi Two-Dimensional Electronic States near Defects Artificially Created at Graphite Surfaces in Magnetic Fields
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• Quantum transport properties of two-dimensional electron gases under high magnetic fields
• Scanning tunneling spectroscopy of a dilute two-dimensional electron system exhibiting Rashba spin splitting
• Compressibility stripes for mesoscopic quantum Hall samples
• Local density of states in disordered two-dimensional electron gases at high magnetic field
• Nonlocal correlations of the local density of states in disordered quantum Hall systems

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• Intra- and Interband Electron Scattering in the Complex Hybrid Topological Insulator Bismuth Bilayer on Bi${}_2$Se${}_3$
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