  It is well known that the 3D electronic topological insulator (TI) with
charge-conservation and time-reversal symmetry cannot have a trivial insulating
surface that preserves symmetry. It is often implicitly assumed that if the TI
surface preserves both symmetries then it must be gapless. Here we show that it
is possible for the TI surface to be both gapped and symmetry-preserving, at
the expense of having surface-topological order. In contrast to analogous
bosonic topological insulators, this symmetric surface topological order is
intrinsically non-Abelian. We show that the surface-topological order provides
a complete non-perturbative definition of the electron TI that transcends a
free-particle band-structure picture, and could provide a useful perspective
for studying strongly correlated topological Mott insulators.
