  Topological insulators in the Bi$_2$Se$_3$ family manifest helical Dirac
surface states that span the topologically ordered bulk band gap. Recent
scanning tunneling microscopy measurements have discovered additional states in
the bulk band gap of Bi$_2$Se$_3$ and Bi$_2$Te$_3$, localized at one
dimensional step edges. Here numerical simulations of a topological insulator
surface are used to explore the phenomenology of edge state formation at the
single-quintuple-layer step defects found ubiquitously on these materials. The
modeled one dimensional edge states are found to exhibit a stable topological
connection to the two dimensional surface state Dirac point.
