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.
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