Shaping the dynamics of aharonov-bohm caged localized modes by nonlinearity

Two-dimensional dice lattice can be dressed by artificial flux to host the Aharonov-Bohm (AB) caging effect resulting in the occurrence of a fully flatband spectrum. Here, we focus on the dynamics of flatband compact localized eigenmodes shared by a few unit cells in two snowflake configurations. We numerically show the possibility of dynamically stable propagation of two types of compact localized complexes by tuning the nonlinearity. The caging is imprinted in complexes dynamics regardless of the type and strength of nonlinearity. On the other hand, nonlinearity can only affect the appearance of the caged complex. These findings open a new route for the manipulation of structured light in photonic systems.