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

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