Moire localization in two-dimensional quasiperiodic systems

We discuss a two-dimensional system under the perturbation of a moire potential, which takes the same geometry and lattice constant as the underlying lattices but mismatches up to relative rotation. Such a self-dual model belongs to the orthogonal class of a quasiperiodic system whose features have been evasive in previous studies. We find that such systems enjoy the same scaling exponent as the one-dimensional Aubry-Andre model nu approximate to 1, which saturates the Harris bound nu > 2/d = 1 in two dimensions. Meanwhile, there exists a continuous and rapid change for the inverse participation ratio in the eigenstate-disorder plane, different from the typical one-dimensional situation where only a few or no steplike contours show up. An experimental scheme based on optical lattices is discussed. It allows for using lasers of arbitrary wavelengths and therefore is more applicable than the one-dimensional situations requiring laser wavelengths close to certain incommensurate ratios.