Microscopic verification of topological electron-vortex binding in the lowest-Landau-level crystal state

TL;DR

This paper provides microscopic evidence that the lowest-Landau-level crystal state in strong magnetic fields involves a quantum-mechanical binding of vortices to electrons, revealing a composite-fermion nature that impacts experimental observations.

Contribution

It demonstrates that the crystal phase is best described by a composite-fermion wave function, highlighting the quantum vortex-electron binding in the crystal state.

Findings

The crystal is well represented by a composite-fermion wave function.

Vortices are non-perturbatively bound to electrons in the crystal.

This binding leads to long-range quantum coherence.

Abstract

When two-dimensional electrons are subjected to a very strong magnetic field, they are believed to form a triangular Wigner crystal. We demonstrate that, in the entire crystal phase, this crystal is very well represented by a composite-fermion-crystal wave function, revealing that it is not a simple Hartree-Fock crystal of electrons but an inherently quantum mechanical crystal characterized by a non-perturbative binding of quantized vortices to electrons, which establishes a long range quantum coherence in it. It is suggested that this has qualitative consequences for experiment.