The nonlinear feedback between the gauge field and the material field can yield novel quantum
phenomena. Here, the interplay of a density-dependent artificial gauge field and Bose-Einstein con densates (BECs) trapped in optical lattice are studied. The energy spectrum and superfluidity
represented by energetic and dynamical stabilities of the system are systematically discussed. The
density-dependent artificial gauge field with a back-action between the BECs dynamics and the
gauge field induces an effective atomic interaction that depends on the quasi-momentum and den sity of the condensates, resulting in symmetry-broken energy spectrum and exotic stability phase
diagram, i.e., the system is stable only in a certain range of atoms density and under a limited lattice
strength. The density-dependent artificial gauge field changes the sequence for the emergence of
energetic and dynamical instability and the regimes of the energetic and dynamical instabilities are
significantly separated, offering an efficient way to study the energetic and dynamical instabilities
of superfluid separately. Particularly, the density-dependent artificial gauge field, as a mechanism
for transferring momentum to the fluid, results in dynamic instability of the condensates even in
free space. Our results provide a deep insight into the dynamical response of superfluid system to
the gauge field and have potential application for coherent control of exotic superfluid states.