Quantum Hall effect in spin-degenerate Landau levels: Spin-orbit enhancement of the conductivity

TL;DR

This paper investigates how spin-orbit coupling influences the quantum Hall effect in spin-degenerate Landau levels, revealing a significant enhancement of dissipative conductivity and a distinctive box-like magnetic field dependence.

Contribution

It demonstrates that spin-orbit coupling drastically alters the percolation network, leading to a pronounced increase in conductivity in the quantum Hall regime with overlapping Zeeman levels.

Findings

Conductivity shows a box-like dependence on magnetic field.

Two asymmetric peaks of conductivity appear as temperature approaches zero.

Spin-orbit coupling enhances dissipative conductivity significantly.

Abstract

The quantum Hall regime in a smooth random potential is considered when two disorder-broadened Zeeman levels overlap strongly. Spin-orbit coupling is found to cause a drastic change in the percolation network which leads to a strong enhancement of the dissipative conductivity at finite temperature, provided the Fermi level $E_F$ lies between the energies of two delocalized states $E=\pm\Delta$, $2\Delta$ being the Zeeman splitting. The conductivity is shown to exhibit a box-like behavior with changing magnetic field: $\sigma_{xx}$ is $\sim e^2/h$ at $|E_F|<\Delta$ and exponentially small otherwise. Two peaks of $\sigma_{xx}$ arising as $T\to 0$ are found to be strongly asymmetric.