Toroidal Fermi-surface geometry and phonon-limited transport in nodal-line semimetals

Nodal-line semimetals (NLSs) can display unconventional quasiparticle dynamics and charge transport properties due to their extended band degeneracy and the peculiar geometry of their Fermi surface. We consider electron–acoustic phonon scattering as the dominant relaxation mechanism and compute the quasiparticle decay rate and dc conductivity by solving the linearized semiclassical Boltzmann equation in a minimal model of a doped circular NLS. We find that the toroidal geometry of the Fermi surface gives rise to two parametrically distinct Bloch--Grüneisen temperatures, associated with momentum transfers along the poloidal and toroidal directions, respectively. As a result, an intermediate temperature window opens between these two scales, in which the decay rate follows $\Gamma\propto T^2$, while the conductivity follows $\sigma\propto T^{-2}$. We also obtain the low- and high-temperature asymptotic behaviors, and discuss implications for ARPES and transport measurements in candidate NLS materials. This is the dataset of our work (arxiv: arxiv:2602.18303).