From the 2D graphene honeycomb lattice to 1D nanoribbons: dimensional crossover signals in the structural thermal fluctuations

Abstract

We study the dimensional crossover from 2D to 1D type behavior, which takes place in the thermal excited rippling of a graphene honeycomb lattice, when one of the dimensions of the layer is reduced. Through a joint study, by Monte Carlo (MC) atomistic simulations using a quasi-harmonic potential and analytical calculations, we find that the normal-normal correlation function does not change its power law behavior in the long wavelength limit. However the system size dependency of the square of out of plane displacement $<h^2>$ changes its scaling behavior when going from a layer to a nanoribbon. We show that a new scaling law appears which corresponds to a truly 1D behavior and we estimate the ratio of the sample dimensions where the crossover takes place as $R_{2D\leftrightarrow 1D}\approx 1.609$. Having explored a wide number of realistic systems sizes, we conclude that narrow ribbons present stronger corrugations than the square graphene sheets and we discuss the implications for the electronic properties of freestanding graphene systems.

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
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• The structure of suspended graphene sheets
• Limits on electron quality in suspended graphene due to flexural phonons
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Cited by in corpus (7)

• Thermal properties of fluorinated graphene
• Thermomechanical properties of a single hexagonal boron nitride sheet
• Thermal rippling behavior of graphane
• Rippling, buckling and melting of single- and multi-layer MoS${}_2$
• Thermodynamics of quantum crystalline membranes
• Bending mode fluctuations and structural stability of graphene nanoribbons
• Melting of Partially Fluorinated Graphene: From Detachment of Fluorine Atoms to Large Defects and Random Coils