Topological surface states on the nonpolar (110) and (111) surfaces of SmB 6

In order to clarify the controversial issue of the topological nature in a mixed-valent Kondo system, ${\mathrm{SmB}}_{6}$, we have explored the surface states on the nonpolar (110) surface of ${\mathrm{SmB}}_{6}$, employing both angle-resolved photoemission spectroscopy (ARPES) experiment and ab initio density-functional theory (DFT) band calculations. Based on ARPES spectroscopic fingerprints and the DFT surface band structures, we ascribe the observed spectral weights at $\overline{X}$ and $\overline{Y}$ on the (110) surface Brillouin zone to topological surface states (TSSs) of ``topological insulator (TI)'' nature and of ``topological crystalline insulator (TCI)'' nature, respectively. With varying the chemical potential, the double Dirac cones of the TCI nature exhibit a Lifshitz transition of Fermi surfaces with intriguing spin textures. We have also examined the TSSs on the nearly nonpolar (111) surface of ${\mathrm{SmB}}_{6}$ in connection with a recently reported ARPES result and proposed a way to probe the Dirac points that are buried in the bulk-projected bands.