Electronic structure of Na$_3$Bi near the Dirac point: Optical measurements*

The first optical characterization of Na$_3$Bi is reported. Reflection measurements on c-plane oriented single-crystals, over the spectral range from 3 mev to 2.5 eV and temperature ranging from 8 to 250K, show a low frequency response consistent with the low doping level $n\sim10^{17} \text{ cm}^{-1}$. The number of observed phonons in the optical spectra is $>$5, which eliminates the P6$_{3}$/mmc symmetry since point group analysis indicates only 2 IR active phonons. A striking, strongly temperature dependent plasma edge reverses direction at $T\sim100$K. The behavior is consistent with thermal population effects in a Dirac cone permitting an estimation of the Fermi level. The Lifshitz gap energy is reported.