Linear-in-Frequency Optical Conductivity in GdPtBi due to Transitions near the Triple Points.

The complex optical conductivity of the half-Heusler compound GdPtBi is measured in a frequency range from 20 to 22 000 cm^{-1} (2.5 meV-2.73 eV) at temperatures down to 10 K in zero magnetic field. We find the real part of the conductivity, σ_{1}(ω), to be almost perfectly linear in frequency over a broad range from 50 to 800 cm^{-1} (∼6-100 meV) for T≤50 K. This linearity strongly suggests the presence of three-dimensional linear electronic bands with band crossings (nodes) near the chemical potential. Band-structure calculations show the presence of triple points, where one doubly degenerate and one nondegenerate band cross each other in close vicinity of the chemical potential. From a comparison of our data with the optical conductivity computed from the band structure, we conclude that the observed nearly linear σ_{1}(ω) originates as a cumulative effect from all the transitions near the triple points.

Flat Optical Conductivity in ZrSiS due to Two-Dimensional Dirac Bands.

ZrSiS exhibits a frequency-independent interband conductivity σ(ω)=const(ω)≡σ_{flat} in a broad range from 250 to 2500 cm^{-1} (30-300 meV). This makes ZrSiS similar to (quasi-)two-dimensional Dirac electron systems, such as graphite and graphene. We assign the flat optical conductivity to the transitions between quasi-two-dimensional Dirac bands near the Fermi level. In contrast to graphene, σ_{flat} is not universal but related to the length of the nodal line in the reciprocal space, k_{0}. Because of spin-orbit coupling, the discussed Dirac bands in ZrSiS possess a small gap Δ, for which we determine an upper bound max(Δ)=30 meV from our optical measurements. At low temperatures the momentum-relaxation rate collapses, and the characteristic length scale of momentum relaxation is of the order of microns below 50 K.