The lattice dynamics of zinc-blende GaN and AlN were studied theoretically using a two-parameter Keating potential together with the long-range Coulomb interactions. Phonon frequencies transformed from those of the wurtzite counterparts were used to determine the two Keating parameters and the effective charge. We present for the first time the phonon dispersion curves for zinc-blende GaN and AlN. An interesting feature was found for the phonons propagating along the [110] direction, which does not exist in other III-V semiconductors.

The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges. We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite-size systems with disk geometry, and found numerical evidence of edge reconstruction under rather general conditions. In the present work we have taken into account effects such as layer thickness and Landau-level mixing, which are found to be of quantitative importance in edge physics. Due to edge reconstruction, additional nonchiral edge modes arise for both incompressible and compressible states. These additional modes couple to electromagnetic fields and thus can be detected in microwave conductivity measurements. They are also expected to affect the exponent of electron Green's function, which has been measured in tunneling experiments. We have studied in this work the electric dipole spectral function that is directly related to the microwave conductivity measurement. Our results are consistent with the enhanced microwave conductivity observed in experiments performed on samples with an array of antidots at low temperatures, and its suppression at higher temperatures. We also discuss the effects of the edge reconstruction on the single-electron spectral function at the edge.

We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern number calculation to many-body systems, we determine the mobility gaps of fractional quantum Hall states based on the distribution of Chern numbers in a microscopic model. We find excellent agreement between experimentally measured activation gaps and our calculated mobility gaps, when combining the effects of both disordered potential and layer thickness. We clarify the difference between mobility gap and spectral gap of fractional quantum Hall states and explain the disorder-driven collapse of the gap and the subsequent transitions from the fractional quantum Hall states to the insulator.

Motivated by the recent suggestion of anisotropic effective exchange interactions between Mn spins in Ga12xMnxAs (arising as a result of spin-orbit coupling), we study their effects in diluted Heisenberg spin systems. We perform Monte Carlo simulations on several phenomenological model spin Hamiltonians, and investigate the extent to which frustration induced by anisotropic exchanges can reduce the low-temperature magnetization in these models and the interplay of this effect with disorder in the exchange. In a model with low coordination number and purely ferromagnetic exchanges, we find that the low-temperature magnetization is gradually reduced as exchange anisotropy is turned on. As the connectivity of the model is increased, the effect of small-to-moderate anisotropy is suppressed, and the magnetization regains its maximum saturation value at low temperatures unless the distribution of exchanges is very wide. To obtain significant suppression of the low-temperature magnetization in a model with high connectivity, as is found for long-range interactions, we find it necessary to have both ferromagnetic and antiferromagnetic exchanges (e.g., as in the Ruderman-Kittel-Kasuya-Yosida interaction). This implies that disorder in the sign of the exchange interaction is much more effective in suppressing magnetization at low temperatures than exchange anisotropy.

We present the results of numerical studies of spin quantum Hall transitions in disordered superconductors, in which the pairing order parameter breaks time-reversal symmetry. We focus mainly on p-wave superconductors in which one of the spin components is conserved. The transport properties of the system are studied by numerically diagonalizing pairing Hamiltonians on a lattice, and by calculating the Chern and Thouless numbers of the quasiparticle states. We find that in the presence of disorder, (spin-) current carrying states exist only at discrete critical energies in the thermodynamic limit, and the spin quantum Hall transition driven by an external Zeeman field has the same critical behavior as the usual integer quantum Hall transition of noninteracting electrons. These critical energies merge and disappear as disorder strength increases, in a manner similar to those in lattice models for integer quantum Hall transition.