Influence of dephasing process on the quantum Hall effect and the spin Hall effect

TL;DR

This study investigates how phase relaxation affects the quantum Hall and spin Hall effects in a 2D mesoscopic system, revealing the robustness of even-integer Hall plateaus and the fragility of odd-integer ones under dephasing.

Contribution

It provides new insights into the impact of phase relaxation on Hall effects and spin currents in systems with Rashba spin-orbit interaction under magnetic fields.

Findings

Even-integer Hall plateaus survive strong phase relaxation.

Odd-integer Hall plateaus are easily destroyed by weak phase relaxation.

Resonant behavior of spin Hall current is affected by phase relaxation.

Abstract

We study the influence of the phase relaxation process on Hall resistance and spin Hall current of a mesoscopic two-dimensional (2D) four-terminal Hall cross-bar with or without Rashba spin-orbit interaction (SOI) in a perpendicular uniform magnetic field. We find that the plateaus of the Hall resistance with even number of edge states can survive for very strong phase relaxation when the system size becomes much longer than the phase coherence length. On the other hand, the odd integer Hall resistance plateaus arising from the SOI are easily destroyed by the weak phase relaxation during the competition between the magnetic field and the SOI which delocalize the edge states. In addition, we have also studied the transverse spin Hall current and found that it exhibits resonant behavior whenever the Fermi level crosses the Landau band of the system. The phase relaxation process weakens the resonant spin Hall current and enhances the non-resonant spin Hall current.