Penrose Matching Rules from Realistic Potentials in a Model System

TL;DR

This paper presents a toy model of a binary decagonal Al-Co quasicrystal where realistic pair potentials produce a ground state that implements Penrose's matching rules, highlighting the importance of the second potential minimum.

Contribution

It demonstrates that realistic pair potentials can lead to quasicrystal ground states obeying Penrose matching rules in a simplified model.

Findings

Realistic pair potentials can produce Penrose matching rules in a model system.

The second minimum of the potentials is crucial for the matching rules.

The ground state closely resembles actual quasicrystal structures.

Abstract

We exhibit a toy model of a binary decagonal Al-Co quasicrystal -- closely related to actual structures -- in which realistic pair potentials yield a ground state which appears to perfectly implement Penrose's matching rules, for Hexagon-Boat-Star (HBS) tiles of edge 2.45 A. The second minimum of the potentials is crucial for this result.