Topological surface states on the nonpolar (110) and (111) surfaces of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>SmB</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>

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