Intrinsic spin-Hall effect: topological transitions in two-dimensional systems

Topological transitions are the discontinuous changes of the Berry phase caused by continuous variation of parameters. These transitions can be detected by investigating the spin-Hall effect in two-dimensional electron and hole systems with a spin-obrit interaction when the density of carriers or the structural asymmetry are varied. The discontinuous behavior and the universality features of the spin-Hall conductivity are determined by the topological properties of the spin-orbit field.