  We consider an interface between two strong time-reversal invariant
topological insulators having surface states with opposite spin chirality, or
equivalently, opposite mirror Chern number. We show that such an interface
supports gapless modes that are protected by mirror symmetry. The interface
states are investigated with a continuum model for the Bi2Se3 class of
topological insulators that takes into account terms up to third order in the
crystal momentum, which ensures that the model has the correct symmetry. The
model parameters are obtained from ab initio calculations. Finally, we consider
the effect of rotational mismatch at the interface, which breaks the mirror
symmetry and opens a gap in the interface spectrum.
