Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns

Area of Science:

• Condensed Matter Physics
• Materials Science
• Crystallography

Background:

• Hyperuniformity describes materials with suppressed large-scale density fluctuations.
• Understanding hyperuniformity is crucial for designing materials with specific physical properties.
• Point patterns, both periodic and quasiperiodic, exhibit varying degrees of hyperuniformity.

Purpose of the Study:

• To develop an efficient method for calculating the hyperuniformity order metric.
• To investigate the relationship between lattice symmetry and hyperuniformity order.
• To compare a novel calculation method with conventional approaches.

Main Methods:

• Utilized the histogram of two-point distances for efficient hyperuniformity order metric calculation.
• Analyzed 2D periodic lattices (trellis, Shastry-Sutherland) and quasiperiodic tilings (Stampfli hexagonal, dodecagonal).
• Maintained identical point densities across different lattice structures for direct comparison.

Main Results:

• The novel method efficiently quantifies hyperuniformity order in point patterns.
• Identified a strong correlation between lattice symmetry and the hyperuniformity order metric.
• The Shastry-Sutherland lattice and Stampfli dodecagonal tilings exhibited smaller order metrics, indicating higher regularity for their symmetry.

Conclusions:

• The developed method provides an efficient way to assess hyperuniformity.
• Higher lattice symmetry in point patterns leads to a smaller hyperuniformity order metric at equal densities.
• This finding deepens the understanding of structure-property relationships in materials.