Breaking of symmetry in graphene growth on metal substrates

TL;DR

This paper investigates how symmetry breaking occurs during graphene growth on metal substrates, revealing how energy variations influence shape distortions and lead to diverse island geometries.

Contribution

It combines first-principles calculations and Monte Carlo modeling to explain experimental observations of symmetry breaking in graphene islands on metals.

Findings

Edge energy variations cause distorted hexagon shapes.

Energy exponential dependence amplifies symmetry breaking.

Shapes can change to triangular, ribbon-like, or rhombic.

Abstract

In graphene growth, island symmetry can become lower than the intrinsic symmetries of both graphene and the substrate. First-principles calculations and Monte Carlo modeling explain the shapes observed in our experiments and earlier studies for various metal surface symmetries. For equilibrium shape, edge energy variations $\delta E$ manifest in distorted hexagons with different ground-state edge structures. In growth or nucleation, energy variation enters exponentially as $\sim e^{\delta E / k_{B} T}$, strongly amplifying the symmetry breaking, up to completely changing the shapes to triangular, ribbon-like, or rhombic.