## Spin Hall and longitudinal conductivity of a conserved spin current in two dimensional heavy-hole gases

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Wong, Arturo

Mireles, Francisco

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The spin Hall and longitudinal conductivity of a 2D heavy-hole gas with {\it
k}-cubic Rashba and Dresselhaus spin-orbit interaction is studied in the ac
frequency domain. Using Kubo linear-response theory and a recently proposed
definition for the (conserved) spin current operator suitable for spin-3/2
holes, it is shown that the spin conductivity tensor exhibit very
distinguishable features from those obtained with the standard definition of
the spin current. This is due to a significant contribution of the spin-torque
term arisen from the alternative definition of spin current which strongly
affects the magnitude and the sign of the dynamic spin current. In the dc (free
of disorder) limit, the spin Hall conductivity for only (or dominant) {\it
k}-cubic Rashba coupling is $\sigma^{s,z}_{xy}(0)=-9e/8\pi$, whereas
$\sigma^{s,z}_{xy}(0)=-3e/8\pi$ for only (or dominant) {\it k}-cubic
Dresselhaus coupling. Such anisotropic response is understood in terms of the
absence of mapping the {\it k}-cubic Rashba $\leftrightarrow$ Dresselhaus
Hamiltonians. This asymmetry is also responsible for the non-vanishing dc spin
Hall conductivity ($\sigma^{s,z}_{xy}(0)=-6e/8\pi$) when the Rashba and
Dresselhaus parameters have the same strength, in contrast with its
corresponding case for electrons. These results are of relevance to validate
the alternative definition of spin-current through measurements in the
frequency domain of the spin accumulation and/or spin currents in 2D hole
gases.

Comment: 12 pages, 6 figures; typos added; Recommendations from referees added. Title changed

Comment: 12 pages, 6 figures; typos added; Recommendations from referees added. Title changed

##### Keywords

Condensed Matter - Mesoscale and Nanoscale Physics