  Low-buckled silicene is a prototypical quantum spin Hall insulator with the
topological quantum phase transition controlled by an out-of-plane electric
field. We show that this field-induced electronic transition can be further
tuned by an in-plane hydrostatic biaxial strain $\varepsilon$, owing to the
curvature-dependent spin-orbit coupling (SOC): There is a $Z_2$ = 1 topological
insulator phase for biaxial strain $|\varepsilon|$ smaller than 0.07, and the
band gap can be tuned from 0.7 meV for $\varepsilon = +0.07$ up to a fourfold
3.0 meV for $\varepsilon = -0.07$. First-principles calculations also show that
the critical field strength $E_c$ can be tuned by more than 113\%, with the
absolute values nearly 10 times stronger than the theoretical predictions based
on a tight-binding model. The buckling structure of the honeycomb lattice thus
enhances the tunability of both the quantum phase transition and the
SOC-induced band gap, which are crucial for the design of topological
field-effect transistors based on two-dimensional materials.
