$\beta -$Ag$_{2}$Te: A topological insulator with strong anisotropy*

We present evidence of topological surface states in $\beta $-Ag$_{2}$Te through first-principles calculations, periodic quantum interference effect and ambipolar electric field effect in single crystalline nanoribbon. Our first-principles calculations show that $\beta $-Ag$_{2}$Te is a topological insulator with a gapless Dirac cone with strong anisotropy. To experimentally probe the topological surface state, we synthesized high quality $\beta $-Ag$_{2}$Te nanoribbons and performed electron transport measurements. The coexistence of pronounced Aharonov-Bohm oscillations and weak Altshuler-Aronov-Spivak oscillations clearly demonstrates coherent electron transport around the perimeter of $\beta $-Ag$_{2}$Te nanoribbon and therefore the existence of topological surface states, which is further supported by the ambipolar electric field effect for devices fabricated by $\beta $-Ag$_{2}$Te nanoribbons. The experimentally confirmed topological surface states and the theoretically predicted isotropic Dirac cone of $\beta $-Ag$_{2}$Te suggest that the material may be a promising material for fundamental study and future spintronic devices.