Plasmon modes in tilted three-dimensional nodal-ring semimetals. II. Vortex nodal ring

Abstract

We investigate collective charge excitations in three-dimensional vortex nodal-ring semimetals (VNRs), whose pseudospin texture winds around the nodal ring and differs qualitatively from that of the conventional $\mathcal{PT}$-symmetric nodal-ring semimetal (PTNR). While plasmon modes in PTNRs have been studied in a companion work, arXiv:2609.35373. Here, we focus on how a VNR's pseudospin texture changes the response compared with the former. Within a low-energy two-band description and the random-phase approximation, we analyse the density response, density-of-states, Drude weights, dielectric function, and plasmon modes at low doping. We consider the untilted system together with in-plane and axial band-tilts. Although the VNR and PTNR have distinct Hamiltonians, pseudospin textures, and Berry-curvature distributions, their linearised energy dispersions coincide. The vortex texture, however, introduces a toroidal-angle dependence in the band-overlap factor and quantum metric, thereby modifying the charge response. We examine how these effects enter the dielectric screening and collective modes for different wavevector orientations. Our results clarify how pseudospin texture, beyond the band dispersion alone, influences collective charge dynamics in three-dimensional nodal-ring semimetals.