3D Dirac cone carrier dynamics in Na3Bi and Cd3As2

Abstract

Optical measurements and band structure calculations are reported on 3D Dirac materials. The electronic properties associated with the Dirac cone are identified in the reflectivity spectra of Cd${}_3$As${}_2$ and Na${}_3$Bi single crystals. In Na${}_3$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 $v_z=0.3\text{ eV}\mathring{A}$ associated with the heavy bismuth Dirac band. At high energies above the $\Gamma$-point Lifshitz gap energy, a frequency and temperature independent ${\epsilon }_2$ indicative of Dirac cone interband transitions translates into an ab-plane Fermi velocity of $3\text{ eV}\mathring{A}$. The observed number of IR phonons rules out the $\text{P}{6}_3\text{/mmc}$ space group symmetry but is consistent with the $\text{P}\bar{3}\text{c}1$ 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 $\Gamma$ is strongly suppressed in Na${}_3$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 Cd${}_3$As${}_2$, a distinctive peak in reflectivity due to the logarithmic divergence in ${\epsilon }_1$ 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 $n=1.3\times 10^{17}{\text{ cm}}^{-3}$. The peak width gives a measure of the Fermi velocity anisotropy of $10\%$, indicating a nearly spherical Fermi surface. The lineshape gives an upper bound estimate of 7 meV for the potential fluctuation energy scale.

arXiv comment15 pages, 6 figures, 3 tables

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