Optical response of a line node semimetal

We calculate the AC optical response of a line node semimetal with emphasis on characteristic behaviours which can be used to distinguish them from point node materials such as Dirac and Weyl semimetals. The interband optical background at zero temperature displays a flat region at small photon energies ([Formula: see text]) analogue to the universal background seen in graphene. However, in contrast to graphene, the height of the constant region is not universal but depends inversely on the Fermi velocity of the charge carriers and directly on the radius (b) in momentum space of the nodal circle. The parameter b is a defining energy scale and determines the range of photon energy over which the flat response persists. At high energies [Formula: see text], the interband response becomes linear in [Formula: see text] in agreement with the case for 3D-Dirac fermions with point node. The optical spectral weight contained in the interband or Drude conductivity shows the same two distinct regimes. At low temperature (T) (chemical potential (μ)), it rises linearly with [Formula: see text] and is proportional to b. At high temperature, [Formula: see text], a [Formula: see text] law is obtained, which is independent of b. At T  =  0, the Lorentz number takes on the conventional value [Formula: see text] for all values of μ. It increases with increasing temperature to reach a first plateau of 2.4L _o provided [Formula: see text] but [Formula: see text]. At high temperature, T  >  b, a second plateau of height 4.2L _o emerges. The first plateau is characteristic of 2D-Dirac while the second corresponds to 3D-Dirac. The thermopower as a function of temperature also shows an evolution from a 2D to 3D behaviour.