Numerical investigation of localization in two-dimensional quasiperiodic mosaic lattice

A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g. clear mobility edges (Wang et al 2020 Phys. Rev. Lett. 125 196604). We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class. For example, the sharp peak at g similar to 0 g limit of the universal scaling function beta resemble those behaviors of three-dimensional disordered systems.