Breaking of symmetry in graphene growth on metal substrates

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 δE manifest in distorted hexagons with different ground-state edge structures. In growth or nucleation, energy variation enters exponentially as ∼eδE/kBT, strongly amplifying the symmetry breaking, up to completely changing the shapes to triangular, ribbonlike, or rhombic. © 2015 American Physical Society