Strain-induced nonlinear spin Hall effect in topological Dirac semimetal*

Topological Dirac seimetals (TDSMs) form a new class of three-dimensional topological semimetals, characterized by pair(s) of doubly-degenerate nodal points (Dirac points) in their momentum(k)-space band structures. They show the intrinsic spin Hall effect (SHE), which comes from the k-space topology around the Dirac points. This spin Hall conductivity is topologically protected, while it cannot be easily tuned or enhanced at linear response.
In order to overcome this problem, I theoretically propose that an electric field applied to a lattice-strained TDSM gives rise to an additional "nonlinear spin Hall current", namely the spin current perpendicular to and quadratic in the electric field [1]. The spin current response is obtained by the Boltzmann transport theory, regarding the strain as a pseudomagnetic field for the Dirac electrons. The nonlinear SHE arises as the hybrid of the regular Hall effect driven by the pseudomagnetic field (strain) and the anomalous Hall effect from the k-space topology. This behavior implies that one can obtain a rectified (dc) pure spin current out of an alternating (ac) electric field, which renders the TDSM an efficient spin-current injector.
[1] Y. Araki, Sci. Rep. 8, 15236 (2018).