  We perform a detailed analysis of the Two-Higgs Doublet Model (2HDM)
potential. At the tree-level, the potential may accommodate more than one
minima, one of them being the electroweak (EW) minimum where the universe
lives. The parameter space allowed after the data from the Large Hadron
Collider (LHC) came in almost excludes those cases where the EW vacuum is
shallower than the second minimum. We extend the analysis by including terms in
the 2HDM potential that break the $Z_2$ symmetry of the potential by
dimension-4 operators and show that the conclusions remain unchanged.
Furthermore, a one-loop analysis of the potential is performed for both cases,
namely, where the $Z_2$ symmetry of the potential is broken by dimension-2 or
dimension-4 operators. For quantitative analysis, we show our results for the
Type-II 2HDM, qualitative results remaining the same for other 2HDMs. We find
that the nature of the vacua from the tree-level analysis does not change; the
EW vacuum still remains deeper.
