Spin Hall effect on a noncommutative space

Abstract

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 ς=ρθ(ρis electron concentration, θis 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.

5 pages, references added, typos corrected

References in corpus (13)

• Dissipationless Quantum Spin Current at Room Temperature
• Direct electronic measurement of the spin Hall effect
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• The topological AC effect on noncommutative phase space
• Theory of spin Hall effect
• Dirac Equation in Noncommutative Space for Hydrogen Atom
• Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
• Inverse Spin Hall Effect Driven by Spin Motive Force
• Aharonov-Casher effect for spin one particles in a noncommutative space
• The Aharonov-Casher effect for spin-1 particles in non-commutative quantum mechanics
• Quantum Electrodynamics on Noncommutative Spacetime
• Comment on "Theory of Spin Hall Effect: Extension of the Drude Model"
• Origin of Spin Hall Effect (Reply to Comment)

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• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
• Influences of Topological Defect on Spin Hall Effect
• Probing the noncommutative effects of phase space in the time-dependent Aharonov-Bohm effect
• Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry
• Hall conductivity in the cosmic defect and dislocation space-time
• Higgs Couplings in NonCommutative Standard Model
• Non-Commutativity effects in the Dirac equation in crossed electric and magnetic fields
• Noncommutative Brownian motion
• Influences of the coordinate dependent noncommutative space on charged and spin currents
• Chiral Spin Noncommutative Space and Anomalous Dipole Moments
• Noncommutative effects on the fluid dynamics and modifications of the Freidmann equation
• Thermodynamics Properties of Confined Particles on Noncommutative Plane