  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-temperature limit. The main observation is that
the Rashba spin precession leads to a charge current that oscillates as a
function of the distance from the spin-pumping source, which is confirmed by
numerical simulations. In our calculations, we consider a Rashba model on a
square lattice, for which we first review the basic properties related to
charge and spin transport. In particular, we define the charge- and
spin-current operators for the tight-binding Hamiltonian as the currents
coupled linearly with the U(1) and SU(2) gauge potentials, respectively. By
analogy to the continuum model, the spin-orbit-coupling Hamiltonian on the
lattice is then introduced as the generator of the spin current.
