Unfolding method for periodic twisted systems with commensurate Moiré patterns

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Chemistry

Background:

• Understanding electronic band structures is crucial for designing novel materials.
• Stacked two-dimensional (2D) materials exhibit complex electronic properties due to interlayer interactions.
• Existing methods struggle to accurately describe systems with multiple periodicities.

Purpose of the Study:

• To present a general unfolding method for electronic band structures of systems with double-periodicity.
• To enable the study of physical effects arising from interactions between periodically arranged systems.
• To investigate the electronic properties of vertically stacked 2D heterostructures.

Main Methods:

• Developed a general unfolding method within density functional theory (DFT).
• Incorporated standard expansion and single rotation symmetry operations of the primitive cell.
• Applied the method to twisted single-layer graphene and graphene-tungsten disulfide heterostructures.

Main Results:

• Successfully studied the electronic properties of stacked 2D materials.
• Observed characteristic mini-gaps in heterostructures, crucial for device applications.
• Identified electronic deviations from pristine structures, previously indistinguishable.

Conclusions:

• The developed unfolding method accurately captures electronic properties of complex stacked 2D systems.
• Interlayer angle is a significant parameter influencing electronic properties in heterostructures.
• The method provides a valuable tool for experimental comparison and future material design.