  Using the cluster Gutzwiller mean-field method, we numerically study the
ground-state phase diagram of the non-hard-core two-component interacting
bosons trapped in a two-leg ladder with and without an artificial magnetic
field. There are three quantum phases namely Mott insulator (MI),
supercounterfluid (SCF), and superfluid (SF) are found in the phase diagram.
Interestingly, several loophole SCF phases are observed at a sufficiently small
intra- to inter-leg hopping ratio when the magnetic flux is absent. While if
the ratio is not so small, the loophole SCF phase would disappear, but it can
still be induced by applying a sufficiently large magnetic flux. Additionally,
we also find that the presence of the magnetic flux leads to an enlargement of
the MI lobe and the conventional SCF lobe. Moreover, the SF-MI phase boundary
is quantitatively consistent with the strong-couping expansion at a weak
hopping amplitude.
