Continuous Chiral Distances on 2D Lattices

17^th August 2023, 14:20
Matthew Bright
MIF

Abstract

Useful properties of many periodic materials can arise from asymmetry - that is, how far deformed those structures are from one with higher symmetry. We are therefore interested in developing some numerical quantifier of this deformation for periodic structures, beginning with two dimensional lattices and rigorously developing this simple but non-trivial case in a way that is applicable to higher dimensional structures. In previous publications (and in a talk at A023) we have developed complete invariants of two dimensional lattices which have the crucial property of changing continuously - that is, a small perturbation of the lattice leads to a small perturbation of the invariant. We use this invariant to develop a true metric between any pair of lattices and show how this can be used to define an easily computable family of chiral distances that measure how close any given lattice is to having a particular Bravais system. We apply this measure initially to a very large database of 2D lattices generated from 3D crystal structures, and more practically to public databases of actual and theoretical 2D monolayer structures to observe their asymmetry when part of and separate from their parent material, and also to isolate candidate materials from which we might synthesise monolayers with highly asymmetric lattice geometries.