| This thesis studies the solid phases of two-dimensional electrons subject to a perpendicular magnetic field (i.e., the "quantum Hall system"). Traditionally, such a solid, known as "Wigner crystal" (WC), is believed to be the ground state of a two dimensional electron system (2DES) when the Landau level (LL) filling factor nu = nh/eB ( n being the electron density and B the magnetic field) is sufficiently small (thus following the termination of quantum Hall states). Due to disorder in realistic samples, the solid is pinned, therefore insulating. Collective oscillation of crystalline domains of the solid around disorder gives rise to a "pinning mode" resonance in the frequency dependent conductivity, which we measure with rf/microwave spectroscopy.; The resonance has interesting behaviors in its dependence on samples, n, B and temperature (T) and contains valuable information about disorder. For example, we are able to show that the most relevant disorder that pins the solid comes from the interface that vertically confines the 2DES, with a (sample dependent) disorder correlation length that can become shorter than 10 nm.; Most importantly, the resonance is a characteristic signature of pinned electron solids, as well as a tool to study their physical properties. We show that many such solid phases can exist, in different regimes of nu; and their properties also depend largely on nu, which captures the quantum correlation between electrons.; Among the new solid phases that we have discovered in the state-of-the-art 2DES samples are the Wigner crystal phases formed in the partially filled top LL around integer Landau fillings. In high LLs, these "integer quantum Hall Wigner crystals" (IQHWC) join with other phases, such as the bubble and stripe phases, to form a rich array of charge density wave phases.; In the lowest Landau level (LLL), we have observed two distinct solid phases, which we name as solid "A" and "B" phases respectively. The "A" phase is observable for nu < 2/9 (but reentrant around the nu = 1/5 fractional quantum Hall liquid (FQHL)) and transitions to the "B" phase which dominates at sufficiently low nu. The two phases coexist in intermediate nu (0.18 ≳ nu ≳ 0.12). Moreover, the resonance of "A" phase is found to show dispersion with respect to the size of transmission line, indicating that "A" phase has a large correlation length. Many-body quantum correlations appear to play an important role in giving rise to the different solids. In particular, "A" phase appears to be a solid intimately related to FQHE. Possible interpretations involving a composite fermion crystal and/or a FQHL-WC mixed phase are discussed.; We have also studied the T-dependence of the pinning mode resonance of a Wigner crystal (in high magnetic fields) and in particular its melting behavior. In a given sample, the melting temperature ( Tm) is found to be mainly determined by nu, in contrast to the case for any other known solids (including, particularly, a classical 2D electron solid) whose Tm is determined by the solid density n. This not only attests to the quantum solid nature of the Wigner crystal in our samples; but also constitutes, to our best knowledge, the only example of a solid whose Tm has been shown to mainly depend on inter-particle quantum correlation (here through nu). (Abstract shortened by UMI.)... |
