Frequency- and transverse wave-vector-dependent spin Hall conductivity in two-dimensional electron gas with disorder
Abstract
We determine wave number q and frequency ω dependent spin Hall conductivities σyxs(q,ω) for a disordered two-dimensional electron system with Rashba spin-orbit interaction when q is transverse to the electric field. Both the conventional definition of spin current and its new definition which takes care of the conservation of spins have been considered. The spin Hall conductivities for both of these definitions are qualitatively similar. σyxs(q,ω) is zero at q=0 , ω=0 and is maximum at q=0 and at small but finite ω whose value depends on different parameters of the system. Interestingly for ω→0 , σyxs(q) resonates when Λ≃Lso which are the wavelength (Λ=2π/q) of the electric field’s spatial variation and the length for one cycle of spin precession, respectively. The sign of the out-of-plane component of the electrons’ spin flips when the sign of electric field changes due to its spatial variation along transverse direction. It changes the mode of spin precession from clockwise to counterclockwise or vice versa, and consequently a finite spin Hall current flows in the bulk of the system.
- Publication:
-
Physical Review B
- Pub Date:
- November 2008
- DOI:
- 10.1103/PhysRevB.78.205313
- arXiv:
- arXiv:cond-mat/0702487
- Bibcode:
- 2008PhRvB..78t5313M
- Keywords:
-
- 72.25.-b;
- 71.70.Ej;
- Spin polarized transport;
- Spin-orbit coupling Zeeman and Stark splitting Jahn-Teller effect;
- Condensed Matter - Mesoscale and Nanoscale Physics
- E-Print:
- 6 pages