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Nonlinear feedback between the gauge field and the material field can yield novel quantum phenomena. Here, the interplay between a density-dependent artificial gauge field and Bose–Einstein condensates (BECs) trapped in an optical lattice is studied. The energy spectrum and superfluidity represented by energetic and dynamical stabilities of the system are systematically discussed. A 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 density of the condensates, resulting in a symmetry-broken energy spectrum and exotic stability phase diagram, that is, the system is only stable 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 examine the energetic and dynamical instabilities of superfluids separately. In particular, 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 deep insights into the dynamical response of superfluid systems to gauge fields and have potential applications for the coherent control of exotic superfluid states. [ABSTRACT FROM AUTHOR]