Designing a minimal Landau theory to stabilize desired quasicrystals

TL;DR

This paper introduces an intelligent screening method to design minimal Landau theories with essential length scales, enabling the stabilization and prediction of various quasicrystals with specific symmetries.

Contribution

The paper presents a novel ISM approach to efficiently identify minimal Landau models that stabilize targeted quasicrystals, including new predictions for less-studied symmetries.

Findings

Confirmed known behaviors of 10- and 12-fold quasicrystals.

Predicted stability of 8-, 14-, 16-, and 18-fold quasicrystals.

Demonstrated the effectiveness of ISM in designing minimal Landau theories.

Abstract

Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a given quasicrystal is a challenging problem. To address this challenge, we propose an intelligent screening method (ISM) to design a Landau theory with a minimal number of length scales -- referred to as the minimal Landau theory -- that includes only the essential length scales necessary to stabilize quasicrystals. Based on a generalized multiple-length-scale Landau theory, ISM first evaluates various spectral configurations of candidate structures under a hard constraint. It then identifies the configuration with the lowest free energy. Using this optimal configuration, ISM calculates phase diagrams to explore the thermodynamic stability of desired quasicrystals. ISM can design a minimal Landau theory capable of stabilizing the desired quasicrystals by incrementally increasing the number of length scales. Our application of ISM has not only confirmed known behaviors in 10- and 12-fold quasicrystals but also led to a significant prediction that quasicrystals with 8-, 14-, 16-, and 18-fold symmetry could be stable within three-length-scale Landau models.