1208.3755 (Tsung-Wei Chen)

Maximum intrinsic spin-Hall conductivity in two-dimensional systems with
k-linear spin-orbit interaction    [PDF]

Tsung-Wei Chen

We analytically calculate the spin-Hall conductivity (SHC) in two-dimensional systems with generic k-linear spin-orbit interaction. In the generic k-linear systems, we find that the SHC depend on the spin-orbit couplings and is not necessary a universal constant, as shown in previous results. In this study, we construct a spin-orbit matrix $\widetilde{\beta}$ and find that the determinant of spin-orbit matrix $\detbeta$ plays the role of effective coupling of spin $s_z$ and orbital motion $L_z$, and thus, explains the physical origin of the sign change of spin-Hall conductivity. This implies that $\detbeta$ exhibits a discriminant for the non-zero SHC. Furthermore, if the SHC is non-zero, we find that irrespective of the way in which the relative strength of these spin-orbit couplings is varied, there always exists a maximum value that the SHC can achieve. In particular, based on sign of the other discriminant $\Deltabeta$ obtained naturally from our result, two maximum values of SHC can be achieved. Interestingly, $\detbeta$ also appears in the expression of equilibrium spin current. We find that $\detbeta$ in this case plays the role of the field strength of SU(2) non-Abelian gauge field.

View original: http://arxiv.org/abs/1208.3755