Optical study of Dirac fermions and related phonon anomalies in antiferromagnetic compound CaFeAsF

We performed optical studies on CaFeAsF single crystals, a parent compound of the 1111-type iron-based superconductors that undergoes a structural phase transition from tetragonal to orthorhombic at $T_s$ = 121 K and a magnetic one to a spin density wave (SDW) state at $T_N$ = 110 K. In the low temperature optical conductivity spectrum, after the subtraction of a narrow Drude peak, we observe a pronounced singularity around 300 cm$^{-1}$ that separates two regions of quasilinear conductivity. We outline that these characteristic absorption features are signatures of Dirac fermions, similar to what was previously reported for the BaFe$_2$As$_2$ system [1]. In support of this interpretation, we show that for the latter system this singular feature disappears rapidly upon electron and hole doping, as expected if it arises from a van Hove singularity in-between two Dirac cones. Finally, we show that one of the infrared-active phonon modes (the Fe-As mode at 250 cm$^{-1}$) develops a strongly asymmetric line shape in the SDW state and note that this behaviour can be explained in terms of a strong coupling with the Dirac fermions.