Two types of Dirac-cone surface states on the (111) surface of the topological crystalline insulator SnTe

We have performed angle-resolved photoemission spectroscopy (ARPES) on the (111) surface of the topological crystalline insulator SnTe. Distinct from a pair of Dirac-cone surface states across the $\overline{X}$ point of the surface Brillouin zone on the (001) surface, we revealed two types of Dirac-cone surface states each centered at the $\overline{\Gamma }$ and $\overline{M}$ points, which originate from the bulk-band inversion at the $L$ points. We also found that the energy location of the Dirac point and the Dirac velocity are different from each other. This ARPES experiment demonstrates the surface states on different crystal faces of a topological material, and it elucidates how mirror-symmetry-protected Dirac cones of a topological crystalline insulator show up on surfaces with different symmetries.

Figure 1

(a) Bulk fcc Brillouin zone (BZ) and corresponding hexagonal (111) surface BZ of SnTe. Green shaded area represents the (110) mirror plane of the rocksalt structure. (b) ARPES intensity mapping at $E_{\mathrm{F}}$ at $T=30$ K on the (111) surface plotted as a function of in-plane wave vector; this intensity is obtained by integrating the spectra within $\pm$10 meV of $E_{\mathrm{F}}$. (c) Bulk BZ in the $k_x$-$k_z$ plane, together with measured cuts for $h\nu =13$–27 eV. The inner potential value is estimated to be 6.9 eV from the normal-emission ARPES measurements. (d) EDCs in the VB region along the $\overline{\Gamma }\overline{M}$ line at $h\nu =23$ eV. (e) ARPES intensity in the VB region along the $\overline{\Gamma }\overline{M}$ line plotted as a function of wave vector and binding energy.

Figure 2

(a)–(e) Near-$E_{\mathrm{F}}$ ARPES intensity of SnTe plotted as a function of the wave vector and binding energy at $h\nu =$ 23 eV measured along several cuts (A–E) around the $\overline{\Gamma }$ point shown by red lines in the surface BZ in (f). Blue arrow indicates the top of the band. (g) ARPES intensity maps around the $\overline{\Gamma }$ point as a function of two-dimensional wave vector at various binding energies, measured at $h\nu =$ 23 eV. (h) Photon-energy dependence of normal-emission EDCs. Red arrow indicates the peak position. (i)–(k) Intensity plots of the second derivatives of the momentum distribution curves (MDCs) across the cut crossing the $\overline{\Gamma }$ point for $h\nu =19$, 23, and 27 eV. Red arrow denotes the top of the bulk VB which is determined in (h). (l) Comparison of the band dispersions for different photon energies extracted by fitting the MDCs for (i)–(k) with two Lorentzians (Ref. [23]); error bars reflect the uncertainties originating from the momentum resolution and the standard deviation in the peak positions of MDCs. Dotted lines represent the linear extrapolations of the band. $E_{\mathrm{D}}$ denotes the energy position of the Dirac point.

Figure 3

(a)–(c) Intensity plots of the second derivatives of the MDCs across the cut crossing the $\overline{M}$ point [blue line in Fig. 2] for $h\nu =15$, 19, and 23 eV. (d) Comparison of the band dispersions for different photon energies extracted by tracking the peak position of MDCs by numerical fittings (Ref. [23]). (e) Schematic picture of the Dirac cones located at the $\overline{\Gamma }$ and $\overline{M}$ points. The estimated difference of the $E_{\mathrm{D}}$ value between the $\overline{\Gamma }$ and $\overline{M}$ points is $\sim$170 meV.

Figure 4

Schematic picture of the Dirac-cone SS on two different surface planes of (001) (Refs. [11, 13]) and (111). Green shaded area and green line represent the (110) mirror plane and the mirror-symmetric line on the surface BZ, respectively.