  The effect of the octahedral tilting of ASnO3 (A = Ca, Sr, Ba) parent
compound and bi-color ASnO3/BSnO3 superlattice (A, B = Ca, Sr, Ba) was
predicted from density-functional theory. In the ASnO3 parent compound, the
structural phase transition as a function of the A-site cation size was
correlated with the magnitude of the two octahedral tilting modes (a-a-c0
tilting and a0a0c+ tilting). The magnitude of the octahedral tilting modes in
the superlattices was analyzed quantitatively and found to be associated with
that of the constituent parent materials. The ASnO3/BSnO3 superlattices showed
hybrid improper ferroelectricity resulting from the coupling of two octahedral
tilting modes (a-a-c0 tilting and a0a0c+ tilting), which are also responsible
for the structural phase transition from a tetragonal to orthorhombic phase.
The ferroelectricity due to A-site mirror symmetry breaking is a secondary
order parameter for an orthorhombic phase transition in the bi-color
superlattice and is related to the {\Gamma}5- symmetry mode. The coupling
between the tilting modes and ferroelectric mode in the bi-color superlattice
of ASnO3/BSnO3 was analyzed by group theory and symmetry mode analysis.
