  The flat band localization, as an important phenomenon in solid state
physics, is fundamentally interesting in the exploration of exotic ground
property of many-body system. Here we demonstrate the appearance of a flat band
in a general bipartite optomechanical lattice, which could have one or two
dimensional framework. Physically, it is induced by the hybrid interference
between the photon and phonon modes in optomechanical lattice, which is quite
different from the destructive interference resulted from the special geometry
structure in the normal lattice (e.g., Lieb lattice). Moreover, this novel flat
band is controllable and features a special local density of states (LDOS)
pattern, which makes it is detectable in experiments. This work offers an
alternative approach to control the flat band localization with optomechanical
interaction, which may substantially advance the fields of cavity optomechanics
and solid state physics.
