  Driving quantum phase transitions in the 3D topological insulators offers
pathways to tuning the topological states and their properties. We use
DFT-based calculations to systematically investigate topological phase
transitions in Bi$_2$Se$_3$, Sb$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$ by
varying the $c/a$ ratio of lattice constants. This ensures no net hydrostatic
pressure under anisotropic stress and strain and allows a clear identification
of the physics leading to the transition. As a function of $c/a$, all of these
materials exhibit structural and electronic stability of the quintuple layers
(QLs), and quasi-linear behavior of both the inter-quintuple layer distance and
the energy gap near the topological transition. Our results show that the
transition is predominantly controlled by the inter-QL physics, namely by
competing Coulomb and van der Waals interactions between the outer atomic
sheets in neighboring quintuple layers. We discuss the implications of our
results for topological tuning by alloying.
