Quantum Hall Effect in Spin-Degenerate Landau Levels: Spin-Orbit Enhancement of the Conductivity

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 boxlike behavior with changing magnetic field: ${\sigma }_{\mathrm{xx}}$ is $\sim e^2/h$ at $|E_F|<\Delta$ and exponentially small otherwise. Two peaks of ${\sigma }_{\mathrm{xx}}$ arising as $T\to 0$ are found to be strongly asymmetric.