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-Gr\"uneisen 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.