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Current pumping by an external potential is studied on the basis of the Keldysh Green’s function method, and a pumping formula written in terms of retarded and advanced Green’s functions is obtained. The formula is used to study the spin pumping effect in the case of strong s-d exchange interaction, and the driving field is identified to be the spin gauge field. At the lowest order in the precession frequency of magnetization, the spin gauge field works as a constant potential, and the system is shown to reduce to a static problem of spin current generation by a time-independent potential with off-diagonal spin components.
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We theoretically explore the optical properties of a bulk Rashba conductor by calculating the transport coefficients at
finite frequencies. It is demonstrated that the combination of direct and inverse Edelstein effects leads to a softening of
the plasma frequency for the electric field perpendicular to the Rashba field, resulting in a hyperbolic electromagnetic
metamaterial. In the presence of magnetization, a significant enhancement of anisotropic propagation (directional
dichroism) is predicted because of the interband transition edge singularity. On the basis of an effective Hamiltonian
analysis, the dichroism is demonstrated to be driven by toroidal and quadratic moments of the magnetic Rashba system.
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