Charged Higgs discovery potential in the single top mode in 2HDMs

We discuss the discovery potential of a charged Higgs boson in the single top mode. The models discussed include a CP-conserving and a CP-violating version of the softly broken $Z_2$ symmetric 2HDM potential. We conclude that the single top mode could help to constrain the ($m_{H^{\pm }}$, $\tan \beta$) plane in several versions of 2HDMs.