  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. 
Electric-field-induced Z2 topological phase transition in strained   single bilayer Bi(111)