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 $k_{\mathrm{F}}=0.012 {\AA }^{-1}$ 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 $r_{\mathrm{s}}=240$, 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 $v_{\mathrm{F}}=2.55\times {10}^6$ 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.

Figure 1

(a) Crystal structure and (b) Brillouin zone (BZ) of ${\mathrm{CdSnAs}}_2$. The crystal structure of ${\mathrm{CdSnAs}}_2$ is visualized using the software package vesta [20]. (c), (d) FSs of the $\mathrm{\Gamma }{XZPY}_1$ plane and the $\mathrm{\Gamma }XY\mathrm{\Sigma }$ plane. The ARPES measurements were performed for the ${\mathrm{CdSnAs}}_2$ (110) plane at $h\nu$ = 26 eV and the (001) plane at $h\nu$ = 21.5 eV, respectively. (e) ARPES constant energy contours of the blue box area in Fig. 1 extracted at different binding energies from $E_{\mathrm{F}}$ to 350 meV. (f) Band dispersion along the $\mathrm{\Gamma }\text{−}Z$ direction, which corresponds to the blue arrow in Fig. 1. The data were collected at $T=20$ K.

Figure 2

(a) Band-structure calculation with SO+mBJ of ${\mathrm{CdSnAs}}_2$ along the $\mathrm{\Gamma }\text{−}X$ and $\mathrm{\Gamma }\text{−}Z$ directions. (b) Band dispersions along the $\mathrm{\Gamma }\text{−}X$ and $\mathrm{\Gamma }\text{−}Z$ directions compared with the band-structure calculations. The valence bands are shifted down by 180 meV. (c) ARPES spectrum near $E_{\mathrm{F}}$ compared with the band-structure calculations and energy distribution curve (EDC) at the $\mathrm{\Gamma }$ point ($k=0\pm 0.025$ Å${}^{-1}$). The arrow indicates the shoulder structure around $-110$ meV. The ARPES data were obtained from the (110) plane at $h\nu =26$ eV and the (001) plane at $h\nu =21.5$ eV, respectively.

Figure 3

(a) Near-$E_{\mathrm{F}}$ band dispersion along $\mathrm{\Gamma }$-Z direction taken at $T$ = 8 K and $h\nu$ = 26 eV. The dots and the solid line indicate the peak position of the momentum distribution curve (MDC) deduced from the Voigt fitting and its fitted parabolic band dispersion. The fitted result is compared with the band calculation including mBJ $+$ SO. The error bars represent the uncertainty of the peak position. (b) The MDCs of ARPES spectrum of (a). The top panel is the fitted result of MDC at $E$ = $E_{\mathrm{F}}\pm 5$ meV. The bottom panel is the energy dependence of MDC.

Figure 4

(a) Temperature dependence of ARPES spectra along $\mathrm{\Gamma }$-Z direction (top panel). The ARPES spectra divided by FD functions for each temperature convoluted with the energy resolution (bottom panel). (b) Temperature dependence of angle-integrated spectra along $\mathrm{\Gamma }$-Z direction.