Past Events

Abstract:

The talk mainly discusses both quantum-Hall effect (QHE) and spin-Hall effect (SHE) in two-dimensional square lattice model and graphene nanoribbons in the presence of disorders. In the SHE regime, two kinds of distinct universal spin-Hall conductance fluctuations (USCF) are discovered: (a) USCF₁ = 0.18e/4π for conventional (non-quantized) SHE induced by Rashba or/and Dresselhaus spin-orbit interactions (SOI); (b) USCF₂ = 0.285e/4π for quantum SHE induced by the fully spin polarized edge states. It's also found that the conventional spin-Hall conductance in the diffusive regime obeys the Gaussian distribution, while quantum spin-Hall conductance obeys a one-sided log-normal distribution. In QHE regime, the mechanism of how the edge states are destroyed in the presence of disorder is investigated. As the disorder strength W increases, edge states are destroyed one by one if transmission eigen-channels are used to characterize the edge states. And near the insulating regime, transmission eigen-channels are closed one by one in the same order as edges states are destroyed. When a mesoscopic four-terminal Hall-bar is placed in the presence of both SOI and perpendicular uniform magnetic field B, both QHE and mesoscopic SHE may exist simultaneously for weak disorder strength W. We have mapped out the entire low field “phase diagram” of mesoscopic SHE in the (B, W) plane, and clearly explained the physical picture on what is expected for SHE on the QHE plateaus as well as at large regions of the (B, W) plane.