Inertial spin Hall effect in non-commutative space

• We have studied the inertial spin current in Non-Commutative (NC) space.
• Foldy–Wouthuysen scheme is used for considering the Dirac Hamiltonian in an accelerating frame in low energy regime.
• Non-trivial commutator between the external magnetic vector potential and the acceleration induced potential is effective.
• Expressions for the spin current and conductivity in NC space are derived
• A bound for theta is suggested from the expression of out of plane spin polarization.

In the present Letter the study of inertial spin current (that appears in an accelerated frame of reference) is extended to Non-Commutative (NC) space. In the 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 explicitly. We have provided yet another way of experimentally measuring θ. The θ bound is obtained from the out of plane spin polarization, which is experimentally observable.