Using $vec{k}$$cdot$$vec{p}$ theory, we derive an effective four band model describing the physics of the typical two-dimensional topological insulator (HgTe/CdTe quantum well) in the presence of out-of-plane in z-direction inversion breaking and in-
plane confining potentials. We find that up to third order in perturbation theory, only the inversion breaking potential generates new elements to the four band Hamiltonian that are off-diagonal in spin space. When this new effective Hamiltonian is folded into an effective two band model for the conduction (electron) or valence (heavy hole) bands, two competing terms appear: (1) a Rashba spin-orbit interaction originating from inversion breaking potential in z-direction and (2) an in-plane Pauli term as a consequence of the in-plane confining potential. Spin transport in the conduction band is further analysed within the Landauer-Buttiker formalism. We find that for asymmetrically doped HgTe quantum wells, the behaviour of the spin-Hall conductance is dominated by the Rashba term.
We present a unified theory of magnetic damping in itinerant electron ferromagnets at order $q^2$ including electron-electron interactions and disorder scattering. We show that the Gilbert damping coefficient can be expressed in terms of the spin con
ductivity, leading to a Matthiessen-type formula in which disorder and interaction contributions are additive. In a weak ferromagnet regime, electron-electron interactions lead to a strong enhancement of the Gilbert damping.
