Description of spin transport and precession in spin-orbit coupling systems and a general equation of continuity

Abstract

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 $\ge 3$, then the particle current must also be modified in order to satisfy the local conservation law of number.

9 pages

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Cited by in corpus (5)

• Torque and conventional spin-Hall currents in two-dimensional spin-orbit coupled systems: Universal relation and hyper-selection rule
• Conservation and persistence of spin currents and their relation to the Lieb-Schulz-Mattis twist operators
• Spin torque contribution to the a.c. spin Hall conductivity
• Deformation induced pseudo-magnetic fields in complex carbon architectures
• Some exact identities connecting one- and two-particle Green's functions in spin-orbit coupling systems