  We consider a square optical lattice in two dimensions and study the effects
of both the strength and symmetry of spin-orbit-coupling (SOC) and Zeeman field
on the ground-state, i.e., Mott insulator (MI) and superfluid (SF), phases and
phase diagram, i.e., MI-SF phase transition boundary, of the two-component
Bose-Hubbard model. In particular, based on a variational Gutzwiller ansatz,
our numerical calculations show that the spin-orbit coupled SF phase is a
nonuniform (twisted) one with its phase (but not the magnitude) of the order
parameter modulating from site to site. Fully analytical insights into the
numerical results are also given.
