Understanding spin Hall effects from the motion in SU(2)XU(1) fields

Details Understanding spin Hall effects from the motion in SU(2)XU(1) fields Understanding spin Hall effects from the motion in SU(2)XU(1) fields

2006-08-14

arxiv.org/abs/cond-mat/0608303v1

Phys. Rev. B 77, 155304 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

RevTex, 4 pages, 2 figures

Scientific paper

10.1103/PhysRevB.77.155304

We derive the classical counterpart of a previously obtained quantum mechanical covariant ``continuitylike'' equation for the spin density, and present an intuitive picture for elucidating the non-conservation of the spin current. This reveals the equations of motion for a particle with spin under the Yang-Mills field (in certain semiconductors) as well as the Maxwell field, from which the condition for an infinite spin relaxation time is drawn out directly. As a concrete example, we discuss the procession of the spin orientation in spin Hall effect with the so called ReD field, which undergoes a circle with the frequency dependent on both the strength of the spin-orbit coupling and the initial velocity. The anti-commutation of the Pauli matrices is found to be crucial in simplifying the equations of motion in the view of quantum mechanism of the same topics.

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