Inertial spin Hall effect in non-commutative space

Abstract

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 $\theta$-dependence, ($\theta$ being the NC parameter), of the inertial spin current is derived explicitly. We have provided yet another way of experimentally measuring $\theta$. Our bound on $\theta$ 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 $\theta$-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 $\theta$-corrected inertial spin current and conductivity are derived. The $\theta$ bound is obtained from the out of plane spin polarization, which is experimentally observable.