Three-dimensional Dirac cone carrier dynamics inNa3BiandCd3As2

Abstract

Optical measurements and band structure calculations are reported on three-dimensional Dirac materials. The electronic properties associated with the Dirac cone are identified in the reflectivity spectra of ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$ and ${\mathrm{Na}}_{3}\mathrm{Bi}$ single crystals. In ${\mathrm{Na}}_{3}\mathrm{Bi}$, the plasma edge is found to be strongly temperature dependent due to thermally excited free carriers in the Dirac cone. The thermal behavior provides an estimate of the Fermi level ${E}_{F}=25$ meV and the $z$-axis Fermi velocity ${v}_{z}=0.3$ eV \AA{} associated with the heavy bismuth Dirac band. At high energies above the $\mathrm{\ensuremath{\Gamma}}$-point Lifshitz gap energy, a frequency- and temperature-independent ${\ensuremath{\epsilon}}_{2}$ indicative of Dirac cone interband transitions translates into an ab-plane Fermi velocity of 3 eV \AA{}. The observed number of IR phonons rules out the $P{6}_{3}/mmc$ space-group symmetry but is consistent with the $P\overline{3}c1$ candidate symmetry. A plasmaron excitation is discovered near the plasmon energy that persists over a broad range of temperature. The optical signature of the large joint density of states arising from saddle points at $\mathrm{\ensuremath{\Gamma}}$ is strongly suppressed in ${\mathrm{Na}}_{3}\mathrm{Bi}$, consistent with band structure calculations that show the dipole transition-matrix elements to be weak due to the very small $s$-orbital character of the Dirac bands. In ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$, a distinctive peak in reflectivity due to the logarithmic divergence in ${\ensuremath{\epsilon}}_{1}$ expected at the onset of Dirac cone interband transitions is identified. The center frequency of the peak shifts with temperature quantitatively consistent with a linear dispersion and a carrier density of $n=1.3\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{4.pt}{0ex}}{\text{cm}}^{\ensuremath{-}3}$. The peak width gives a measure of the Fermi-velocity anisotropy of $10%$, indicating a nearly spherical Fermi surface. The line shape gives an upper bound estimate of 7 meV for the potential fluctuation energy scale.