Year: 2010
Type: article
Abstract: Crystalline membranes at finite temperatures have an anomalous behavior of the bending rigidity that makes them more rigid in the long-wavelength limit. This issue is particularly relevant for applications of graphene in nanoelectromechanical and microelectromechanical systems. We calculate numerically the height-height correlation function $G(q)$ of crystalline two-dimensional membranes, determining the renormalized bending rigidity, in the range of wave vectors $q$ from ${10}^{\ensuremath{-}7}\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$ till $10\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$ in the self-consistent screening approximation (SCSA). For parameters appropriate to graphene, the calculated correlation function agrees reasonably with the results of atomistic Monte Carlo simulations for this material within the range of $q$ from ${10}^{\ensuremath{-}2}\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$ till $1\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$. In the limit $q\ensuremath{\rightarrow}0$ our data for the exponent $\ensuremath{\eta}$ of the renormalized bending rigidity ${\ensuremath{\kappa}}_{R}(q)\ensuremath{\propto}{q}^{\ensuremath{-}\ensuremath{\eta}}$ is compatible with the previously known analytical results for the SCSA $\ensuremath{\eta}\ensuremath{\simeq}0.82$. However, this limit appears to be reached only for $q<{10}^{\ensuremath{-}5}\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$ whereas at intermediate $q$ the behavior of $G(q)$ cannot be described by a single exponent.
Source: Physical Review B
Institution: Radboud University Nijmegen
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1995267038