Breaking of Symmetry in Graphene Growth on Metal Substrates
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TLDR
First-principles calculations and Monte Carlo modeling explain the shapes observed in experiments and earlier studies for various metal surface symmetries.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 $\ensuremath{\delta}E$ manifest in distorted hexagons with different ground-state edge structures. In growth or nucleation, energy variation enters exponentially as $\ensuremath{\sim}{e}^{\ensuremath{\delta}E/{k}_{B}T}$, strongly amplifying the symmetry breaking, up to completely changing the shapes to triangular, ribbonlike, or rhombic.read more
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