  Ruddlesden-Popper (RP) oxides (A$_{n+1}$B$_n$O$_{3n+1}$) comprised of
perovskite (ABO$_3$)$_n$ slabs can host a wider variety of structural
distortions than their perovskite counterparts. This makes accurate structural
determination of RP oxides more challenging. In this study, we investigate the
structural phase diagram of $n=1$ RP Sr$_2$SnO$_4$, one of alkaline earth
stannates that are promising for opto-electronic applications by using group
theory-based symmetry analysis and first-principles calculations. We explore
the symmetry breaking effects of different dynamical instabilities, predict the
energies of phases they lead to, and take into account different (biaxial
strain and hydrostatic pressure) boundary conditions. We also address the
effect of structural changes on the electronic structure and find that
compressive biaxial strain drives Sr$_2$SnO$_4$ into a regime with wider
bandgap and lower electron effective mass.
