  For controlling the critical electric fields of the topological phase
transition in single bilayer Bi(111), we investigated topological phases in a
strained system through first-principles calculations. We found a quadratic
band touching semimetallic state at tensile strain $\epsilon=0.5$%. Around this
strain, the topological phase can be switched to a trivial insulator by an
infinitesimal electric field. The positions at which Dirac cones appear in the
electric-field-induced topological phase transition changed for the strain
$\epsilon>0.5$% and $\epsilon<0.5$%. Our results indicate that this topological
phase transition could be applied to novel spintronic devices.
