Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torque and conventional spin-Hall currents in two-dimensional spin-orbit
  coupled systems: Universal relation and hyper-selection rule   We 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 $H_0=\epsilon_k^0+A(k)\sigma_x-B(k)\sigma_y$, where
$A(k)=\eta^A_ik_i+\eta^A_{ij}k_ik_j+\eta^A_{ijl}k_ik_jk_l+...$,
$B(k)=\eta^B_ik_i+\eta^B_{ij}k_ik_j+\eta^B_{ijl}k_ik_jk_l+...$, and $\eta$'s
are the specific system-dependent coefficients. Specifically, we find that in
the intrinsic case the magnitude of torque spin-Hall conductivity
$\sigma^{\tau_z}_{xy}(0)$ is always twice larger than the conventional
spin-Hall conductivity $\sigma^{s_z}_{xy}(0)$, and the two conductivities have
the opposite signs, i.e., $\sigma^{\tau_z}_{xy}(0)=-2\sigma^{s_z}_{xy}(0)$.
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 $I_z = (k\times
\partial\theta/\partial k)_z s_z + L_z$ 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.

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The categories of this paper are: econ
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph