Barriers to macroscopic superfluidity and insulation in a 2D Aubry-André model

We study the ground state phases of interacting bosons in the presence of a 2D Aubry-André (AA) potential. By using a mean-field percolation analysis, we focus on several superlattice and quasicrystalline regimes of the 2D AA model, including generalisations that account for a tilting or skewing of the potential. We show that barriers to the onset of macroscopic phases naturally arise from weakly modulated domains in the 2D AA model. This leads to the formation of extended crossover domains, in which the macroscopic properties are dominated by a minority of the system. The phase diagrams then exhibit substantially different features when compared against crystalline systems, including a lobe-like or wave-like appearance of the Bose glass, sharp extrusions and thin, percolating clusters. By studying the 2D AA model across multiple regimes, we have shown that these extended crossover domains are not distinct to a small set of parameters.