Tiny Fermi surface with an extremely light mass of ternary chalcopyrite ${\mathrm{CdSnAs}}_2$ revealed by angle-resolved photoemission spectroscopy

We report the electronic structure of the ternary chalcopyrite ${\mathrm{CdSnAs}}_2$ using angle-resolved photoemission spectroscopy (ARPES) combined with the band-structure calculation. The tiny Fermi surface (FS) with the Fermi wave number $k_F=0.012 {\AA }^{-1}$ was observed, and the carrier density $n=1.2\times {10}^{17}{\mathrm{cm}}^{-3}$ was estimated. The deduced carrier density $n$ indicates the electron density parameter $r_s=240$, which corresponds to the extremely low density limit of the three-dimensional (3D) electron gas. On the other hand, the calculated band structure of ${\mathrm{CdSnAs}}_2$ well reproduced the band gap and the effective mass reported by the Hall measurement, the Shubnikov–de Haas (SdH) oscillation, and the optical measurement, quantitatively. Therefore, the ARPES results indicate that the carrier density $n$ decreases and there is a large deviation between the band calculation and the ARPES band structure. These results reveal that the extremely low electron density can be realized near the surface due to the bulk band-bending effect. Moreover, we found the high Fermi velocity of $v_F=2.55\times {10}^6$ m/s and the extremely light mass of $m^{*}/m_0\sim 0.005$ comparable to the Dirac materials. This suggests that the effective mass $m^{*}/m_0$ is reduced due to the effect of the long-range Coulomb interaction in the extremely low-density limit. Our findings provide a venue to investigate the physics of the electron correlation in the extremely low-density electron gas as well as the Wigner crystallization or Anderson localization.