Lattice tuning of charge and spin transport in $β_{12}$-borophene nanoribbons

$β_{12}$-borophene nanoribbons (BNRs) exhibit magnetic zigzag edges, while other edge configurations are nonmagnetic. However, when the source, central, and drain regions of a logic device are all composed of zigzag BNRs (ZBNRs), the resulting spin polarization remains weak, unless a high voltage is applied. In this work, we demonstrate that lattice vibrations-introduced for example, via a thermal bath coupled to the central BNR-can enhance spin polarization in ZBNRs. This enhancement manifests as marked changes in the current-voltage characteristics, enabling direct experimental probing. In contrast, nonmagnetic edge configurations exhibit phonon-enhanced charge transport. We employ a tight-binding approach augmented with local electron-phonon interactions described by the Holstein model, and compute the phonon-renormalized Green's functions and transport currents using the Landauer-Büttiker formalism. The mechanism is supported by analyzing both spinless and spinful electronic dispersions and the corresponding density of states. Compared to the phonon-free edges, structural distortions lead to anisotropic electron-phonon couplings, which significantly modify both charge and spin transport. These results position phonon as an effective tuning parameter for optimizing borophene-based logic devices via engineered edge configurations.