Spin Hall effect in noncommutative coordinates

Abstract

A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the constant noncommutativity parameter θ . The method is first illustrated by studying the Hall effect on the noncommutative plane in a gauge independent fashion. Then, the Drude model type and the Hall effect type formulations of spin Hall effect are considered in noncommuting coordinates and θ deformed spin Hall conductivities which they provide are acquired. It is shown that by adjusting θ different formulations of spin Hall conductivity are accomplished. Hence, the noncommutative theory can be envisaged as an effective theory which unifies different approaches to similar physical phenomena.

Spin Hall effect on a noncommutative space

“…The second term in (19) is the cross product of the electron magnetic moment and the effective electric field on a NCS.…”

“…Substitution of (19) and (20) into (18) yields the following form of Newton's second law for charge carriers on a NCS:…”

“…[16] found a lower limit of 1/ √ θ 10 GeV on the noncommutativity parameter. Reference [19] discussed the noncommutative spin Hall effect (SHE) through a semiclassical constrained Hamiltonian, and obtained interesting results. One can use the data on the spin Hall measurements [20] to impose some bounds on the value of the noncommutativity parameter 1/ √ θ , and we find that the limit on 1/ √ θ is weaker by thirteen orders of magnitude than the one imposed by the quantum Hall effect [16].…”

An alternative formulation of Hall effect and quantum phases in noncommutative space

“…We will show that θ-deformation of the Hall conductivity appears naturally in some realizations. Though in [15] a natural θ-deformed Hall conductivity was achieved, it was within the semiclassical approach of Section 2.…”

Aharonov-Bohm Phase for an Electric Dipole on a Noncommutative Space

“…The authors of Harms and Micu [23], Dayi and Jellal [24] and Chakraborty et al [25][26][27][28][29][30] have studied the noncommutative quantum Hall effect, and in Harms and Micu [23] a limit of 1/ √ θ ≥ 10GeV is given. The noncommutative spin Hall effect (SHE) is discussed through a semiclassical constrained Hamiltonian and interesting results are obtained in Dayi and Elbistan [31]. By studying the SHE in the framework of NCQM a lower limit for the noncommutative parameter is shown to be 1/ √ θ ≥ 10 −12 GeV in Ma and Dulat [32].…”