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Optical conductivity of triple point fermions

As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian which is parameterized by an angular parameter $λ$. We find strong $λ$ dependence in both Drude and interband optical absorption of these systems. The deviation of the $T^2$ coefficient of the Drude weight from Dirac/Weyl fermions can be used as a quick way to optically distinguish the triple point degeneracies from the Dirac/Weyl degeneracies. At the particular $λ=π/6$ point, we find that the "helicity" reversal optical transition matrix element is identically zero. But deviating from this point, the helicity reversal emerges as an absorption channel.