  Topological insulators are attracting considerable interest due to their
potential for technological applications and as platforms for exploring
wide-ranging fundamental science questions. In order to exploit, fine-tune,
control and manipulate the topological surface states, spectroscopic tools
which can effectively probe their properties are of key importance. Here, we
demonstrate that positrons provide a sensitive probe for topological states,
and that the associated annihilation spectrum provides a new technique for
characterizing these states. Firm experimental evidence for the existence of a
positron surface state near Bi$_2$Te$_2$Se with a binding energy of $E_b = 2.7
\pm 0.2 \, \text{eV}$ is presented, and is confirmed by first-principles
calculations. Additionally, the simulations predict a significant signal
originating from annihilation with the topological surface states and shows the
feasibility to detect their spin-texture through the use of spin-polarized
positron beams.
