  Bi$_2$Te$_3$ is a topological insulator whose unique properties result from
topological surface states in the band gap. The neutralization of scattered low
energy Na$^+$, which is sensitive to dipoles that induce inhomogeneities in the
local surface potential, is larger when scattered from Te than from Bi,
indicating an upwards dipole at the Te sites and a downwards dipole above Bi.
These dipoles are caused by the spatial distribution of the conductive
electrons in the topological surface states. This result demonstrates how this
alkali ion scattering method can be applied to provide direct experimental
evidence of the spatial distribution of electrons in filled surface states.
