Optimized Monotonic Convex Pair Potentials Stabilize Low-Coordinated Crystals

TL;DR

This paper demonstrates that simple, monotonic convex pair potentials can be optimized to stabilize low-coordinated crystal structures like square and honeycomb lattices in two dimensions, challenging previous assumptions about the need for multiple extrema.

Contribution

It introduces a novel approach showing that low-coordinated crystals can be stabilized with monotonic convex potentials, simplifying design strategies.

Findings

Monotonic convex potentials can stabilize square and honeycomb crystals in 2D.

No extrema are necessary in the potential to achieve these low-coordinated ground states.

Potentially feasible experimental realization using colloids and polymers.

Abstract

We have previously used inverse statistical-mechanical methods to optimize isotropic pair interactions with multiple extrema to yield low-coordinated crystal classical ground states (e.g., honeycomb and diamond structures) in d-dimensional Euclidean space R^d. Here we demonstrate the counterintuitive result that no extrema are required to produce such low-coordinated classical ground states. Specifically, we show that monotonic convex pair potentials can be optimized to yield classical ground states that are the square and honeycomb crystals in R^2 over a non-zero number density range. Such interactions may be feasible to achieve experimentally using colloids and polymers.