Low-dimensional compact states in 3D moiré lattices.

Area of Science:

• Physics
• Materials Science
• Condensed Matter Physics

Background:

• Two-dimensional (2D) moiré lattices exhibit unique properties due to superposition of rotated sublattices.
• The physics of three-dimensional (3D) moiré lattices remains largely unexplored despite their potential for novel phenomena.

Purpose of the Study:

• To investigate the physics of 3D moiré potentials formed by superimposing rotated 3D periodic sublattices.
• To explore the different phases and compact quantum states supported by these 3D moiré systems.

Main Methods:

• Theoretical investigation of moiré potentials formed by two cubic sublattices with varying rotation angles.
• Analysis of the resulting potentials' dimensionality (fully 3D incommensurate, partially incommensurate, or fully periodic).
• Demonstration of compact state localization (fully, linear, or planar) within these potentials for non-interacting atom condensates using laser beams.

Main Results:

• Three distinct phases of 3D moiré potentials were identified based on rotation angles: fully 3D incommensurate, 1D incommensurate with 2D periodicity, and fully periodic.
• Incommensurate potentials were shown to support three types of compact states: fully localized, line-localized, and plane-localized.
• The creation of these potentials is feasible for condensates of non-interacting atoms using laser manipulation.

Conclusions:

• The study establishes a foundational understanding of wave localization control in 3D incommensurate moiré systems.
• Findings pave the way for novel applications in cold atom systems, optics, and other fields leveraging engineered 3D potentials.