Designing isotropic interactions for self-assembly of complex lattices

TL;DR

This paper introduces a direct method for designing isotropic potentials that enable the self-assembly of complex target lattices, including structures like the kagome lattice, by matching energy spectra to ensure ground state stability.

Contribution

The authors develop a novel inverse design approach for isotropic interactions that reliably produce complex lattices, expanding the possibilities for self-assembly in materials science.

Findings

Successfully self-assembled complex lattices like the snub square tiling and kagome lattice.

Demonstrated the method's ability to produce structures with geometric frustration.

Provided a new tool for designing materials with specific lattice properties.

Abstract

We present a direct method for solving the inverse problem of designing isotropic potentials that cause self-assembly into target lattices. Each potential is constructed by matching its energy spectrum to the reciprocal representation of the lattice to guarantee that the desired structure is a ground state. We use the method to self-assemble complex lattices not previously achieved with isotropic potentials, such as a snub square tiling and the kagome lattice. The latter is especially interesting because it provides the crucial geometric frustration in several proposed spin liquids.