Spin Hall effect on a noncommutative space

Details Spin Hall effect on a noncommutative space Spin Hall effect on a noncommutative space

2011-04-26

arxiv.org/abs/1104.4955v2

Phys.Rev.A84:012104,2011

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, references added, typos corrected

Scientific paper

10.1103/PhysRevA.84.012104

We study the spin-orbital interaction and the spin Hall effect(SHE) of an electron moving on a noncommutative space under the influence of a vector potential A. On a noncommutative space we find that the commutator between the vector potential A and the electric potential V_1(r) of lattice induces a new term which can be treated as an effective electric field, and the spin-Hall conductivity obtains some correction. In addition, the spin current as well as spin-Hall conductivity have distinct values in different direction. On a noncommutative space we derive the spin-depended electric current whose expectation value gives the spin Hall effect and spin Hall conductivity. We have defined a new parameter \varsigma=\rho\theta (\rho is electron concentration, \theta is noncommutative parameter) which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation which give a general Hamiltonian of a non-relativistic electron moving on a noncommutative space.

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