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 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.