Torque and conventional spin-Hall currents in two-dimensional spin-orbit coupled systems: Universal relation and hyper-selection rule

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dc.creatorChen, Tsung-Wei
dc.creatorGuo, Guang-Yu
dc.date2008-08-27
dc.date2009-02-01
dc.date.accessioned2026-07-07T12:49:44Z
dc.date.available2026-07-07T12:49:44Z
dc.descriptionWe investigate torque and also conventionally defined spin-Hall currents in two-dimensional (2D) spin-orbit coupled systems of spin-1/2 particles within the linear response Kubo formalism. We obtain some interesting relations between the conventional and torque spin-Hall conductivities for the generic effective Hamiltonian $H_0=ε_k^0+A(k)σ_x-B(k)σ_y$, where $A(k)=η^A_ik_i+η^A_{ij}k_ik_j+η^A_{ijl}k_ik_jk_l+...$, $B(k)=η^B_ik_i+η^B_{ij}k_ik_j+η^B_{ijl}k_ik_jk_l+...$, and $η$'s are the specific system-dependent coefficients. Specifically, we find that in the intrinsic case the magnitude of torque spin-Hall conductivity $σ^{τ_z}_{xy}(0)$ is always twice larger than the conventional spin-Hall conductivity $σ^{s_z}_{xy}(0)$, and the two conductivities have the opposite signs, i.e., $σ^{τ_z}_{xy}(0)=-2σ^{s_z}_{xy}(0)$. This universal relation also holds in the presence of an uniform in-plane magnetic field. We also find that if the energy dispersion is rotationally invariant, there exists a hyper-angular momentum $I_z = (k\times \partialθ/\partial k)_z s_z + L_z$ which is conserved. Furthermore, the hyper-angular momentum current $<{1/2}\{I_z,v_x\}>$ vanishes, and this leads to a hyper selection rule for the conventional spin-Hall current.
dc.description10 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0808.3625
dc.identifierhttp://arxiv.org/abs/0808.3625
dc.identifierPhysical Review B 79, 125301 (2009)
dc.identifierdoi:10.1103/PhysRevB.79.125301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222473
dc.subjectMesoscale and Nanoscale Physics
dc.titleTorque and conventional spin-Hall currents in two-dimensional spin-orbit coupled systems: Universal relation and hyper-selection rule
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