# Moire Localization in Two Dimensional Quasi-Periodic Systems

## TL;DR

This paper investigates a two-dimensional quasi-periodic system with Moire potential, revealing critical scaling behavior and multiple mobility edges, and proposes an optical lattice experimental scheme for realization.

## Contribution

It demonstrates that 2D Moire systems share the same scaling exponent as the Aubry-Andre model and exhibit numerous mobility edges, expanding understanding of quasi-periodic localization phenomena.

## Key findings

- Scaling exponent $
u \,\approx\, 1$ in 2D Moire systems
- Presence of infinitely many mobility edges
- Experimental scheme using arbitrary wavelength lasers

## Abstract

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 quasi-periodic 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\approx 1 $, which saturates the Harris bound $ \nu>2/d=1 $ in two-dimensions. Meanwhile, there exist an infinite number of mobility edges different from the typical one-dimensional situation where only a few or no mobility edges 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.