  Topological crystalline insulators (TCIs) are insulating materials whose
topological property relies on generic crystalline symmetries. Based on
first-principles calculations, we study a three-dimensional (3D) crystal
constructed by stacking two-dimensional TCI layers. Depending on the
inter-layer interaction, the layered crystal can realize diverse 3D topological
phases characterized by two mirror Chern numbers (MCNs) ($\mu_1,\mu_2$) defined
on inequivalent mirror-invariant planes in the Brillouin zone. As an example,
we demonstrate that new TCI phases can be realized in layered materials such as
a PbSe (001) monolayer/h-BN heterostructure and can be tuned by mechanical
strain. Our results shed light on the role of the MCNs on inequivalent
mirror-symmetric planes in reciprocal space and open new possibilities for
finding new topological materials.
