  We investigate the effects of the in-plane biaxial strain and charge doping
on the charge density wave (CDW) order of monolayer $1T$-TiSe$_2$ by using the
first-principles calculations. Our results show that the tensile strain can
significantly enhance the CDW order, while both compressive strain and charge
doping (electrons and holes) suppress the CDW instability. The tensile strain
may provide an effective method for obtaining higher CDW transition temperature
on the basis of monolayer $1T$-TiSe$_2$. We also discuss the potential
superconductivity in charge-doped monolayer $1T$-TiSe$_2$. Controllable
electronic phase transition from CDW state to metallic state or even
superconducting state can be realized in monolayer $1T$-TiSe$_2$, which makes
$1T$-TiSe$_2$ possess a promising application in controllable switching
electronic devices based on CDW.
