Low field phase diagram of spin-Hall effect in the mesoscopic regime

TL;DR

This paper maps the low-field phase diagram of the mesoscopic spin-Hall effect in a disordered 2D Hall cross with spin-orbit interaction, revealing how conductance and fluctuations vary across different disorder regimes and quantum Hall plateaus.

Contribution

It provides the first detailed phase diagram of the mesoscopic spin-Hall effect in the presence of disorder and magnetic field, highlighting the behavior of conductance and fluctuations across regimes.

Findings

MSHE conductance vanishes on even IQHE plateaus

Finite MSHE conductance on odd IQHE plateaus induced by SOI

Disorder induces crossover to chaotic regime with zero average conductance

Abstract

When a mesoscopic two dimensional four-terminal Hall cross-bar with Rashba and/or Dresselhaus spin-orbit interaction (SOI) is subjected to a perpendicular uniform magnetic field $B$, both integer quantum Hall effect (IQHE) and mesoscopic spin-Hall effect (MSHE) may exist when disorder strength $W$ in the sample is weak. We have calculated the low field "phase diagram" of MSHE in the $(B,W)$ plane for disordered samples in the IQHE regime. For weak disorder, MSHE conductance $G_{sH}$ and its fluctuations $rms(G_{SH})$ vanish identically on even numbered IQHE plateaus, they have finite values on those odd numbered plateaus induced by SOI, and they have values $G_{SH}=1/2$ and $rms(G_{SH})=0$ on those odd numbered plateaus induced by Zeeman energy. For moderate disorder, the system crosses over into a regime where both $G_{sH}$ and $rms(G_{SH})$ are finite. A larger disorder drives the system into a chaotic regime where $G_{sH}=0$ while $rms(G_{SH})$ is finite. Finally at large disorder both $G_{sH}$ and $rms(G_{SH})$ vanish. We present the physics behind this ``phase diagram".