We present a numerical study of the spin Hall effect in a two-dimensional hole gas (2DHG) system in the presence of disorder. We find that the spin Hall conductance (SHC), extrapolated to the thermodynamic limit, remains finite in a wide range of dis
order strengths for a closed system on torus. But there is no intrinsic spin Hall accumulation as induced by an external electric field once the disorder is turned on. The latter is examined by performing a Laughlins Gedanken gauge experiment numerically with the adiabatical insertion of a flux quantum in a belt-shaped sample, in which the absence of level crossing is found under the disorder effect. Without disorder, on the other hand, energy levels do cross each other, which results in an oscillating spin-density-modulation at the sample boundary after the insertion of one flux quantum in the belt-shaped system. But the corresponding net spin transfer is only about one order of magnitude smaller than what is expected from the bulk SHC. These apparently contradictory results can be attributed to the violation of the spin conservation law in such a system. We also briefly address the dissipative Fermi surface contribution to spin polarization, which may be relevant to experimental measurements.
We present first numerical studies of the disorder effect on the recently proposed intrinsic spin Hall conductance in a three dimensional (3D) lattice Luttinger model. The results show that the spin Hall conductance remains finite in a wide range of
disorder strength, with large fluctuations. The disorder-configuration-averaged spin Hall conductance monotonically decreases with the increase of disorder strength and vanishes before the Anderson localization takes place. The finite-size effect is also discussed.
We present a systematic study of spin dynamics in a superconducting ground state, which itself is a doped-Mott-insulator and can correctly reduce to an antiferromagnetic (AF) state at half-filling with an AF long-range order (AFLRO). Such a doped Mot
t insulator is described by a mean-field theory based on the phase string formulation of the t-J model. We show that the spin wave excitation in the AFLRO state at half-filling evolves into a resonancelike peak at a finite energy in the superconducting state, which is located around the AF wave vectors. The width of such a resonancelike peak in momentum space decides a spin correlation length scale which is inversely proportional to the square root of doping concentration, while the energy of the resonancelike peak scales linearly with the doping concentration at low doping. An important prediction of the theory is that, while the total spin sum rule is satisfied at different doping concentrations, the weight of the resonancelike peak does not vanish, but is continuously saturated to the weight of the AFLRO at zero-doping limit. Besides the low-energy resonancelike peak, we also show that the high-energy excitations still track the spin wave dispersion in momentum space, contributing to a significant portion of the total spin sum rule. The fluctuational effect beyond the mean-field theory is also examined, which is related to the broadening of the resonancelike peak in energy space. In particular, we discuss the incommensurability of the spin dynamics by pointing out that its visibility is strongly tied to the low-energy fluctuations below the resonancelike peak. We finally investigate the interlayer coupling effect on the spin dynamics as a function of doping, by considering a bilayer system.
