# Which wavenumbers determine the thermodynamic stability of soft matter quasicrystals?

## TL;DR

This paper investigates how specific wavenumbers in interparticle interactions influence the thermodynamic stability of soft matter quasicrystals, highlighting the importance of certain length scales and reciprocal lattice vectors.

## Contribution

It identifies key features in particle pair potentials that can promote or inhibit quasicrystal formation by affecting density modes at specific wavenumbers.

## Key findings

- Two characteristic wavenumbers are crucial for stable quasicrystals.
- Higher reciprocal lattice vectors influence the competition with crystalline order.
- Interaction potential features can control the emergence of quasicrystals.

## Abstract

For soft matter to form quasicrystals an important ingredient is to have two characteristic lengthscales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wavenumbers should be favored, and the ratio of these wavenumbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed. However, for more realistic models, where in principle all wavenumbers can be involved, other wavenumbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials which can suppress or encourage density modes with wavenumbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems.