Inertial spin Hall effect in noncommutative 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 $\hat{I}¸$-dependence, ($\hat{I}¸$ being the NC parameter), of the inertial spin current is derived explicitly. We have provided yet another way of experimentally measuring $\hat{I}¸$. Our bound on $\hat{I}¸$ 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 $\hat{I}¸$-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 $\hat{I}¸$-corrected inertial spin current and conductivity are derived. The $\hat{I}¸$ bound is obtained from the out of plane spin polarization, which is experimentally observable.

11 pages, no figures, Accepted in Phys. Lett. A