  We prove theoretically that certain strongly correlated Kondo insulators are
topological crystalline insulators with nontrivial topology protected by
crystal symmetries. In particular, we find that SmB$_6$ is such a material. In
addition to a nontrivial Z$_2$ topological index protected by time reversal
symmetry, SmB$_6$ also has nontrival mirror Chern numbers protected by mirror
symmetries. On the $(100)$ surface of SmB$_6$, the nontrivial mirror Chern
numbers do not generate additional surface states beyond those predicted by the
Z$_2$ topological index. However, on the $(110)$ surface, two more surface
Dirac points are predicted. Remarkably, we find that for SmB$_6$ both the Z$_2$
topological index and the mirror Chern numbers are independent of microscopic
details, which enables us to obtain surface state properties that are
universal.

Strongly Correlated Electrons