Disorder effect of resonant spin Hall effect in a tilted magnetic field

We study the disorder effect of resonant spin Hall effect in a two-dimensional electron system with Rashba coupling in the presence of a tilted magnetic field. The competition between the Rashba coupling and the Zeeman coupling leads to the energy crossing of the Landau levels, which gives rise to the resonant spin Hall effect. Utilizing the Streda's formula within the self-consistent Born approximation, we find that the impurity scattering broadens the energy levels and the resonant spin Hall conductance exhibits a double peak around the resonant point, which is recovered in an applied tilted magnetic field.