Unified microscopic approach to the interplay of pinned - Wigner - solid and liquid behavior of the lowest Landau - level states in the neighborhood of ν = 13

Recently observed microwave resonances in the spectrum of a two-dimensional electon gas under high magnetic fields in the neighborhood of the fractional filling ν = 1/3 were interpreted as signatures of a weakly pinned Wigner solid. 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, a unified microscopic approach is developed for the interplay between liquid fractional-quantum-Hall-effect (FQHE) and Wigner-solid states in the lowest Landau level (LLL) in the neighborhood of ν = 1/3. In contrast to more traditional treatments, the RVEM theory utilizes a single class of variational wave functions for the description of both the FQHE liquid and Wigner-solid states, and their coexistence. Liquid characteristics of the FQHE states are associated with the symmetry-conserving rotations and vibrations of the electron molecule. The liquid characteristics, however, coexist with intrinsic correlations that are crystalline in nature, as revealed by the conditional probability distributions. Although the electron densities of the symmetry-conserving LLL states do not exhibit crystalline patterns, the intrinsic crystalline correlations are reflected in the emergence of cusp yrast states in the LLL spectra. These cusp states correspond to fractional fillings in the thermodynamic limit and are the only ones to provide the global ground states of the system. 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 ν = 1, which was also found in the experiments. Utilizing results for sizes in a wide range from N = 6 to 29 electrons, we address the extrapolation to the thermodynamic limit of the energetics of pinned Wigner crystallites, showing development of a crystal of enhanced stability due to contributions of quantum correlations. Furthermore, we address the size evolution of the crystal motifs (culminating in a hexagonal bulk two-dimensional Wigner lattice).