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

Abstract

We analytically calculate the intrinsic spin-Hall conductivity (ISHC) (${\sigma }_{xy}^z$ and ${\sigma }_{yx}^z$) in a clean, two-dimensional system with generic k-linear spin-orbit interaction. The coefficients of the product of the momentum and spin components form a spin-orbit matrix $\tilde{\beta }$. We find that the determinant of the spin-orbit matrix $\detbeta$ describes the effective coupling of the spin $s_z$ and orbital motion $L_z$. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical (${\sigma }_{xy}^z\ne -{\sigma }_{yx}^z$), and it is governed by the asymmetric response function $\Deltabeta$, which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than $e/8\pi$, but has an upper bound value of $e/4\pi$. We will that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature at the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that $\detbeta$ determines the field strength of the SU(2) non-Abelian gauge field.

13 pages, 6 figures

References in corpus (19)

• Electric Field Effect in Atomically Thin Carbon Films
• Dissipationless Quantum Spin Current at Room Temperature
• Direct electronic measurement of the spin Hall effect
• Unconventional Integer Quantum Hall effect in graphene
• Spin current and polarization in impure 2D electron systems with spin-orbit coupling
• Current induced electron spin polarization in strained semiconductors
• On A Proper Definition of Spin Current
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Theory of Spin Hall conductivity in n-doped GaAs
• Current-Induced Polarization and the Spin Hall Effect at Room Temperature
• Dissipation effects in spin-Hall transport of electrons and holes
• Mesoscopic Spin Hall Effect in Multiprobe Ballistic Spin-Orbit Coupled Semiconductor Bridges
• Persistent spin current in nano-devices and definition of the spin current
• Spin-orbit interaction in a two-dimensional electron gas: a SU(2) formulation
• Spin Hall effect of conserved current: Conditions for a nonzero spin Hall current
• Equilibrium spin currents in the Rashba medium
• Mechanical measurement of equilibrium spin currents in the Rashba medium
• Equilibrium edge spin currents in two-dimensional electron systems with spin-orbit interaction

Cited by in corpus (1)

• Topological-Berry-phase-induced spin torque current in a two-dimensional system with generic $k$-linear spin-orbit interaction