Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of lowest-Landau-level states in the neighborhood of nu=1/3

TL;DR

This paper introduces a unified microscopic approach combining RVEM theory and exact diagonalization to study the coexistence and transition between liquid FQHE states and Wigner-solid states near filling factor 1/3 in the lowest Landau level, revealing how weak disorder can induce crystalline patterns.

Contribution

The work develops a comprehensive microscopic framework that links liquid and solid quantum Hall states, incorporating disorder effects and finite-size analysis, extending understanding of Wigner crystallites and their relation to bulk states.

Findings

Intrinsic crystalline correlations are present even in symmetry-conserving states.

Weak pinning can induce pinned Wigner crystallites from symmetry-conserving states.

The approach explains experimental observations near nu=1, including Wigner-solid behavior.

Abstract

Motivated by recent experiments, and using the rotating-and-vibrating electron-molecule (RVEM) theory [Yannouleas and Landman, Phys. Rev. B 66, 115315 (2002); Phys. Rev. A 81, 023609 (2010)], in conjunction with exact diagonalization, we develop a unified microscopic approach for the interplay between liquid fractional-quantum-Hall-effect (FQHE) states and Wigner-solid states in the lowest Landau level (LLL) in the neighborhood of nu=1/3. Liquid characteristics of the FQHE states are associated with the symmetry-conserving rotations and vibrations of the electron molecule. Although the electron densities of the symmetry-conserving LLL states do not exhibit crystalline patterns, the intrinsic crystalline correlations are reflected in the conditional probability distributions and the emergence of cusp yrast states in the LLL spectra. It is shown that away from the exact fractional fillings, weak pinning perturbations (due to weak disorder) may overcome the energy gaps between adjacent global states and generate pinned broken symmetry ground states as a superposition of symmetry-conserving LLL states with different total angular momenta. The electron densities of such mixed states (without good angular momentum quantum numbers) exhibit oscillating patterns that correspond to molecular crystallites. These pinned Wigner crystallites represent finite-size precursors of the bulk Wigner-solid state. It is further shown that the emergence of these molecular crystallites is a consequence of the presence of RVEM components in the symmetry-conserving LLL states. In addition, it is shown that the RVEM approach accounts for the Wigner-solid state in the neighborhood of nu=1, which was also found in the experiments. We utilize results for sizes in a wide range from N=6 to N=29 electrons, and we address the extrapolation to the thermodynamic limit.