Three-dimensional Moir\'e Crystal

TL;DR

This paper explores the extension of moiré physics into three dimensions using ultracold atomic gases, revealing new possibilities for tunable crystal structures and band properties.

Contribution

It introduces the concept of three-dimensional moiré patterns in ultracold gases and analyzes their unique symmetry and structural properties, expanding moiré physics beyond two dimensions.

Findings

Conditions for three-dimensional moiré periodicity identified

Twist operation does not commute with lattice symmetry in 3D

Twisting can generate diverse crystal structures

Abstract

The work intends to extend the moir\'e physics to three dimensions. Three-dimensional moir\'e patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a structure currently unachievable in solid-state materials. We give the commensurate conditions under which the three-dimensional moir\'e pattern features a periodic structure, termed a three-dimensional moir\'e crystal. We emphasize a key distinction of three-dimensional moir\'e physics: in three dimensions, the twist operation generically does not commute with the rotational symmetry of the original lattice, unlike in two dimensions, where these two always commute. Consequently, the moir\'e crystal can exhibit a crystalline structure that differs from the original underlying lattice. We demonstrate that twisting a simple cubic lattice can generate various crystal structures. This capability of altering crystal structures by twisting offers a broad range of tunability for three-dimensional band structures.