Experimental demonstration of the topological surface states protected by the time-reversal symmetry

We report direct imaging of standing waves of the nontrivial surface states of topological insulator Bi$_2$Te$_3$ by using a low temperature scanning tunneling microscope. The interference fringes are caused by the scattering of the topological states off Ag impurities and step edges on the Bi$_2$Te$_3$(111) surface. By studying the voltage-dependent standing wave patterns, we determine the energy dispersion $E(k)$, which confirms the Dirac cone structure of the topological states. We further show that, very different from the conventional surface states, the backscattering of the topological states by nonmagnetic impurities is completely suppressed. The absence of backscattering is a spectacular manifestation of the time-reversal symmetry, which offers a direct proof of the topological nature of the surface states.