  Topological crystalline insulator (TCI) is one of the symmetry-protected
topological states. Any TCI can be deformed into a simple product state of
several decoupled two-dimensional (2D) topologically nontrivial layers in its
lattice respecting its crystalline symmetries called the layer construction
(LC) limit. In this work, based on first-principles calculations we have
revealed that both tetragonal LaSbTe (t-LaSbTe) and orthorhombic LaSbTe
(o-LaSbTe) can be interpreted as stacking of 2D topological insulators in each
lattice space. The structural phase transition from t-LaSbTe to o-LaSbTe due to
soft phonon modes demonstrates how the real space change can lead to the
modification of topological states. Their symmetry-based indicators and
topological invariants have been analyzed based on LC. We propose that LaSbTe
is an ideal example demonstrating the LC paradigm, which bridges the crystal
structures in real space to the band topology in momentum space.
