Highly spin-selective transport of electrons through a helically shaped electrostatic potential is demonstrated in the frame of a minimal model approach. The effect is significant even for weak spin-orbit coupling. Two main factors determine the selectivity: an unconventional Rashba-like spin-orbit interaction, reflecting the helical symmetry of the system, and a weakly dispersive electronic band of the helical system. The weak electronic coupling, associated with the small dispersion, leads to a low mobility of the charges in the system and allows even weak spin-orbit interactions to be effective. The results are expected to be generic for chiral molecular systems displaying low spin-orbit coupling and low conductivity.

This study is devoted to a consistent derivation of an effective model Hamiltonian to describe spin transport along a helical pathway and in presence of spin-orbit interaction, the latter being induced by an external field with helical symmetry. It is found that a sizeable spin polarization of an unpolarized incoming state can be obtained without introducing phase breaking processes. For this, at least two energy levels per lattice site in the tight-binding representation are needed. Additionally, asymmetries in the effective electronic-coupling parameters as well as in the spin-orbit interaction strength must be present to achieve net polarization. For a fully symmetric system -in terms of electronic and spin-orbit couplings-no spin polarization is found. The model presented is quite general and is expected to be of interest for the treatment of spindependent effects in molecular scale systems with helical symmetry.

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We investigate Bloch oscillations of interacting cold atoms in a mean-field framework. In general, atom-atom interaction causes dephasing and destroys Bloch oscillations. Here, we show that Bloch oscillations are persistent if the interaction is modulated harmonically with suitable frequency and phase. For other modulations, Bloch oscillations are rapidly damped. We explain this behavior in terms of collective coordinates whose Hamiltonian dynamics permits to predict a whole family of stable solutions. In order to describe also the unstable cases, we carry out a stability analysis for Bogoliubov excitations. Using Floquet theory, we are able to predict the unstable modes as well as their growth rate, found to be in excellent agreement with numerical simulations.