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The peculiar shape of the Fermi surface of topological nodal line semimetalsat low carrier concentrations results in their unusual optical and transportproperties. We analytically investigate the linear optical responses of threeand two-dimensional nodal line semimetals using the Kubo formula. The opticalconductivity of a three-dimensional nodal line semimetal is anisotropic. Alongthe axial direction (\textit{i.e.}, the direction perpendicular to thenodal-ring plane), the Drude weight has a linear dependence on the chemicalpotential at both low and high carrier dopings. For the radial direction(\textit{i.e.}, the direction parallel to the nodal-ring plane), thisdependence changes from linear into quadratic in the transition from low intohigh carrier concentration. The interband contribution into opticalconductivity is also anisotropic. In particular, at large frequencies, itsaturates to a constant value for the axial direction and linearly increaseswith frequency along the radial direction. In two-dimensional nodal linesemimetals, no interband optical transition could be induced and the onlycontribution to the optical conductivity arises from the intraband excitations.The corresponding Drude weight is independent of the carrier density at lowcarrier concentrations and linearly increases with chemical potential at highcarrier doping.

Optical conductivity of three and two dimensional topological nodal line semimetals