Plasmon modes in tilted three-dimensional nodal-ring semimetals. I. $\mathcal{P}\mathcal{T}$-symmetric nodal ring and its gapped cousin

Abstract

We study collective charge excitations in three-dimensional $\mathcal{P}\mathcal{T}$-symmetric nodal-ring semimetals (PTNRs) and their gapped counterparts (GNRs) in the presence of band tilt, together with Weyl semimetals (WSMs). Within a low-energy two-band description, we consider untilted systems as well as in-plane and axial tilts. Using the random-phase approximation, we obtain the density of states, Drude weights, dielectric functions, and plasmon dispersions at low doping and in the intrinsic limit. The mass gap and the two inequivalent tilt directions generate distinct Fermi-surface topologies and thereby control the formation and damping of plasmons. By comparing the collective modes with the particle-hole continuum, we identify the regimes in which plasmons remain well defined. We also calculate the response of untilted and tilted WSMs and contrast it with that of PTNRs and GNRs. The two classes of semimetals differ in the carrier-density dependence and isotropy of the plasmon frequency as well as in interband screening and their response to tilt. These differences reflect their distinct Fermi-surface geometries and interband structures. Our results establish how mass and tilt govern collective charge dynamics through their interplay with intraband spectral weight and interband particle-hole excitations.

arXiv commentcompanion paper of arXiv:2610.03188; substantially revised and expanded