Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2006-04-12
published in Phys. Rev. B 75, 085314(2007)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9 pages
Scientific paper
By generalizing the usual current density to a matrix with respect to spin variables, a general equation of continuity satisfied by the density matrix and current density matrix has been derived. This equation holds in arbitrary spin-orbit coupling systems as long as its Hamiltonian can be expressed in terms of a power series in momentum. Thereby, the expressions of the current density matrix and a torque density matrix are obtained. The current density matrix completely describes both the usual current and spin current as well; while the torque density matrix describes the spin precession caused by a total effective magnetic field, which may include a realistic and an effective one due to the spin-orbit coupling. In contrast to the conventional definition of spin current, this expression contains an additional term if the Hamiltonian includes nonlinear spin-orbit couplings. Moreover, if the degree of the full Hamiltonian $\geq3$, then the particle current must also be modified in order to satisfy the local conservation law of number.
Liu Cheng-shi
Yang Hua-Tong
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