  Bi$_2$Te$_3$ is a material with high efficiency of thermoelectric energy
conversion. Recently, it was also recognized as a topological insulator, and is
often used as the basis for creation of other types of topological matter.
Pulsed laser deposition (PLD) is widely considered as a simple method for
growing of multicomponent films, but not as a tool for van der Waals epitaxy.
We demonstrate here that the van der Waals epitaxy of Bi$_2$Te$_3$ is indeed
impossible in vacuum PLD, but is possible in the presence of a background gas,
which is confirmed by the results of scanning tunneling microscopy and
spectroscopy studies. Results of {\it ab initio} calculations reproduce
tunneling spectra of the first three terraces of epitaxial films of
Bi$_2$Te$_3$. In addition, an unusual hexagonal superstructure resembling a
charge-density wave is observed in overheated films.
