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

TL;DR

This study investigates how reducing the width of graphene sheets to nanoribbons induces a transition from 2D to 1D thermal fluctuation behavior, revealing a new scaling law and implications for electronic properties.

Contribution

It provides a combined analytical and simulation analysis of the dimensional crossover in graphene, identifying a specific size ratio where 1D behavior emerges and characterizing the scaling laws involved.

Findings

Normal-normal correlation function retains power law behavior.

Square of out-of-plane displacement scales differently in 1D.

Crossover occurs at a width-to-length ratio of approximately 1.609.

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.