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 delta E manifest in distorted hexagons with different ground-state edge structures. In growth or nucleation, energy variation enters exponentially as similar to e(delta E/kBT), strongly amplifying the symmetry breaking, up to completely changing the shapes to triangular, ribbonlike, or rhombic