  We study the texture of helical currents in metallic planar strips in the
presence of Rashba spin-orbit coupling (RSOC) on the lattice at zero
temperature. In the noninteracting case, and in the absence of external
electromagnetic sources, we determine by exact numerical diagonalization of the
single-particle Hamiltonian, the distribution across the strip section of these
Rashba helical currents (RHC) as well as their sign oscillation, as a function
of the RSOC strength, strip width, electron filling, and strip boundary
conditions. Then, we study the effects of charge currents introduced into the
system by an Aharonov-Bohm flux for the case of rings or by a voltage bias in
the case of open strips. The former setup is studied by variational Monte
Carlo, and the later, by the time-dependent density-matrix-renormalization
group technique. Particularly for strips formed by two, three and four coupled
chains, we show how these RHC vary in the presence of such induced charge
current, and how their differences between spin-up and spin-down electron
currents on each chain, help to explain the distribution across the strip of
charge currents, both of the spin conserving and the spin flipping types. We
also predict the appearance of polarized charge currents on each chain.
Finally, we show that these Rashba helical currents and their derived features
remain in the presence of an on-site Hubbard repulsion as long as the system
remains metallic, at quarter filling, and even at half-filling where a
Mott-Hubbard metal-insulator transition occurs for large Hubbard repulsion.
