Conductivity in nodal line semimetals with short-ranged impurity potentials

We study the transport properties in nodal line semimetals with short-ranged impurity potentials at zero temperature. By computing the Drude conductivity and the corrections from the interference of particle and hole trajectories, we find that the electrons are localized in directions both parallel and perpendicular to the plane of nodal ring. We further calculate the conductivity in a weak magnetic field, and find that the perpendicular magnetic field totally destroys the weak localization gives a positive quantum interference correction, which is similar to the result in Weyl semimetals. But for a parallel magnetic field, because of the $\pi$ Berry phase of the electron orbit around the nodal line, the magnetoconductivity is negatively proportional to $B$. The difference between the perpendicular and the parallel magnetic field may be verified by experiments. Nodal line semimetals which break inversion and time-reversal symmetry and have spin-orbit coupling are also considered and produce qualitatively the same results.