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We study theoretically some symmetry properties of spin currents and spin polarizations in multi-terminal mesoscopic spin-orbit coupled systems. Based on a scattering wave function approach, we show rigorously that in the equilibrium state no finite spin polarizations can exist in a multi-terminal mesoscopic spin-orbit coupled system (both in the leads and in the spin-orbit coupled region) and also no finite equilibrium terminal spin currents can exist. By use of a typical two-terminal mesoscopic spin-orbit coupled system as the example, we show explicitly that the nonequilibrium terminal spin currents in a multi-terminal mesoscopic spin-orbit coupled system are non-conservative in general. This non-conservation of terminal spin currents is not caused by the use of an improper definition of spin current but is intrinsic to spin-dependent transports in mesoscopic spin-orbit coupled systems. We also show that the nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in a thin strip of textit{finite} length of a two-dimensional electronic system with intrinsic spin-orbit coupling may be non-antisymmetric in general, which implies that some cautions may need to be taken when attributing the occurrence of nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in such a system to an intrinsic spin Hall effect.
Using response theory, we calculate the charge-current vortex generated by spin pumping at a point-like contact in a system with Rashba spin-orbit coupling. We discuss the spatial profile of the current density for finite temperature and for the zero
We show that in the multi-terminal ballistic devices with intrinsic spin-orbit interaction connected to normal metal contacts there are no equilibrium spin currents present at any given electron energy. Obviously, this statement holds also after the
We propose a new type of the spin Seebeck effect (SSE) emerging from the Rashba spin-orbit coupling in asymmetric four-terminal electron systems. This system generates spin currents or spin voltages along the longitudinal direction parallel to the te
The existence of spin-currents in absence of any driving external fields is commonly considered an exotic phenomenon appearing only in quantum materials, such as topological insulators. We demonstrate instead that equilibrium spin currents are a rath
We study high-harmonic generation in two-dimensional electron systems with Rashba and Dresselhaus spin-orbit coupling and derive harmonic generation selection rules with the help of group theory. Based on the bandstructures of these minimal models an