Designing a minimal Landau model to stabilize desired quasicrystals

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 a symmetry-preserving screening method (SPSM) 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, SPSM 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, SPSM calculates phase diagrams to explore the thermodynamic stability of desired quasicrystals. SPSM can design a minimal Landau theory capable of stabilizing the desired quasicrystals by incrementally increasing the number of length scales. Our application of SPSM 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.