Spin polarization in a chiral ladder: elastic and inelastic environments
We study how the transport window and environmental reinjection determine the spin polarization transmitted through a minimal two-leg chiral ladder. The model contains time-reversal-invariant helical spin--orbit coupling, spin-independent interchain hopping, and nonmagnetic contacts with two orbital modes per lead. Sublattice symmetry makes the coherent spin-transmission kernel exactly odd in energy. A window centered on the symmetry point therefore gives zero integrated spin current, whereas a displaced window selects an uncanceled spectral interval. The resulting polarization reverses between enantiomers and vanishes in the decoupled-chain, zero-spin--orbit, and equivalent-strand limits of this model. We compare uniform absorption, energy-resolved elastic probes, and thermalized voltage probes at the same finite bias, including reinjection whenever probes are present. Charge conservation alone does not prohibit enhancement of the integrated spin signal: the elastic-probe response can increase at finite bias even where its linear-response counterpart decreases. Thermalized probes can also lift the centered-window zero that elastic probes preserve. Absorption and reinjection also change the transmitted charge, so enhancement of spin current and enhancement of normalized polarization must be distinguished. Static onsite disorder produces sample-dependent fluctuations; its signed ensemble mean is reported with uncertainty and is not forced to vanish in a displaced window. These results identify the energy interval and reservoir prescription that must be controlled when interpreting dephasing trends in minimal models relevant to chirality-induced spin selectivity.