A Deterministic Method to Construct a Common Supercell Between Two Similar Crystalline Surfaces

Area of Science:

• Materials Science
• Computational Materials Science
• Crystallography

Background:

• Constructing common supercells for similar crystalline surfaces is crucial for designing 2D heterostructures.
• Conventional methods often involve computationally expensive brute-force approaches, limiting efficiency.

Purpose of the Study:

• To develop a deterministic algorithm for efficiently constructing common supercells between two similar crystalline surfaces.
• To accelerate the design and discovery of novel 2D heterostructures and their associated moiré patterns.

Main Methods:

• Representing 2D lattices as complex vectors in the complex plane.
• Defining the relationship between surfaces as an eigenvector-eigenvalue problem.
• Directly determining the transformation matrix from lattice parameters and rotation angles with O(log Nmax) time complexity.

Main Results:

• A deterministic algorithm was developed and implemented in Python, significantly outperforming brute-force methods.
• The algorithm successfully generated experimental 2D heterostructures and their moiré patterns.
• New, potentially stable moiré patterns were discovered and predicted using density functional theory (DFT) calculations.

Conclusions:

• The proposed algorithm offers a computationally efficient tool for constructing common supercells.
• This method facilitates the design of new 2D heterostructures with unique properties.
• The approach is expected to be widely applicable in materials design and discovery.