Inertial spin Hall effect in noncommutative space

In the present paper the study of inertial spin current(that appears in an accelerated frame of reference) is extended to Non-Commutative (NC) space. The $θ$-dependence, ($θ$ being the NC parameter), of the inertial spin current is derived explicitly. We have provided yet another way of experimentally measuring $θ$. Our bound on $θ$ matches with previous results. In Hamiltonian framework, the Dirac Hamiltonian in an accelerating frame is computed in the low energy regime by exploiting the Foldy-Wouthuysen scheme. The NC $θ$-effect appears from the replacement of normal products and commutators by Moyal *-products and *-commutators. In particular, the commutator between the external magnetic vector potential and the potential induced by acceleration becomes non-trivial. Expressions for $θ$-corrected inertial spin current and conductivity are derived. The $θ$ bound is obtained from the out of plane spin polarization, which is experimentally observable.

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