Many-Body Effects In Nodal-Line Semimetals: Correction To The Optical Conductivity

Coulomb interaction might have important effects on the physical observables in topological semimetals with vanishing density of states at the band touching due to the weak screening. In this work, we show that Kohn's theorem is not fulfilled in nodal-line semimetals (NLSMs), which implies nonvanishing interaction corrections to the conductivity. Using renormalized perturbation theory, we determine the first-order optical conductivity in a clean NLSM to be sigma perpendicular to perpendicular to(Omega) = 2 sigma(parallel to parallel to)(Omega) = sigma(0)[1 +C-2 alpha(R)(Omega)], where perpendicular to and parallel to denote the perpendicular and parallel components with respect to the nodal loop, sigma(0) = (2 pi k(0))e(2)/(16h) is the conductivity in the noninteracting limit, 2 pi k(0) is the nodal-loop perimeter, C-2 = (19 - 6 pi)/12 similar or equal to 0.013 is a numerical constant, and alpha(R)(Omega) is the renormalized fine-structure constant in the NLSM. The analogies between three-dimensional NLSMs and two-dimensional Dirac fermions are reflected in the parallelism between their respective optical conductivities, both in the noninteracting limit and in the correction, as pointed out by the equality of the universal coefficient C-2 in both systems. Finally, we analyze some experiments that have determined the optical conductivity in NLSMs, discussing the possibility of experimentally measuring our result.