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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

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.