Dielectric Function, Screening, and Plasmons in a Spin‐Split Dimerized 1D Dirac Model

We investigate the dielectric response, screening properties, and collective excitations in a 1D dimerized Dirac system with spin‐dependent bandgaps, described by the Su–Schrieffer–Heeger model extended to include spin‐resolved dimerization. Within the random phase approximation, we derive closed‐form analytic expressions for both the intrinsic interband and extrinsic intraband contributions to the dynamical polarization function, accounting for distinct effective masses in the two spin channels. We find that the particle‐hole continuum separates into two distinct spin‐resolved regions with different interband absorption thresholds. The static polarization function develops a characteristic double‐cusp structure at the two spin‐dependent Fermi wavevectors, contrasting sharply with the single cusp in conventional systems. This momentum space structure manifests in real space as Friedel oscillations with a robust beating pattern. The plasmon dispersion is renormalized by combined contributions from both spin channels, leading to modified collective mode frequencies that remain undamped outside the spin‐resolved continua.