Intrinsic Spin Hall Effect: Topological Transitions in Two-Dimensional Systems

The spin-Hall conductivity in spatially-homogeneous two-dimensional electron systems described by the spin-orbit Hamiltonian \hbar \Omega_p \sigma is presented as a sum of the universal part Me/8 \pi \hbar determined by the Berry phase \Phi=M \pi (M is an odd integer, the winding number of the vector \Omega_p) and a non-universal part which vanishes under certain conditions determined by the analytical properties of \Omega_p. The analysis reveals a rich and complicated behavior of the spin-Hall conductivity which is relevant to both electron and hole states in quantum wells and can be detected in experiments.