  Flat bands and dynamical localization of binary mixtures of Bose-Einstein
condensates, with spin-orbit coupling subjected to a deep optical lattice which
is shaking in time and to a periodic time modulation of the Zeeman field, are
investigated. In contrast with usual dynamical localization in the absence of
spin-orbit coupling, we find that to fully suppress the tunneling in the system
the optical lattice shaking is not enough, and a proper tuning of the
spin-orbit term, achievable via the Zeeman field modulation, is also required.
This leads to a sequence of Zeeman parameter values where energy bands become
flat, the tunneling in the system is suppressed, and the dynamical localization
phenomenon occurs. Exact wave functions at the dynamical localization points
show that the binary mixture localizes on a dimer with the two components
occupying different sites. This type of localization occurs in exact form also
for the ground state of the system at the dynamical localization points in the
presence of nonlinearity and remains valid, although in approximate form, for a
wide range of the Zeeman parameter around these points. The possibility of
observing the above phenomena in real experiments is also briefly discussed.
