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Anomalous Hooke's law in disordered graphene | | I. V. Gornyi
; V. Yu. Kachorovskii
; A. D. Mirlin
; | | Date: |
1 Mar 2016 | | Abstract: | The discovery of graphene, a single monolayer of graphite, closed the
discussion on stability of 2D crystals. Although thermal fluctuations of such
crystals tend to destroy the long-range order in the system, they can be
stabilized by strong anharmonicity effects, which preserve thermodynamic
stability. This competition is the central issue of crumpling transition, i.e.
transition between flat and crumpled phases governed by the ratio of the
bending rigidity $varkappa$ of the crystal to the temperature $T$. The
graphene is deeply in the flat phase because $varkappa/Tsimeq 30$ (at room
temperature and at the atomic scales) and renormalizes in a power-law way with
increasing the system size: $varkappa/Tpropto L^{eta},$ where $eta approx
0.7$ is the critical index of the crumpling transition. Critical fluctuations
of graphene membrane around flat equilibrium phase lead to unusual elastic
properties. In particular, we demonstrate that stretching $xi$ of a flake of
graphene turns out to be nonlinear function of the applied tension at small
tension: $xiproptosigma^{eta/(2-eta)}$ and
$xiproptosigma^{eta/(8-eta)}$ for clean and strongly disordered graphene,
respectively. Conventional linear Hooke’s law, $ xiproptosigma$ is realized
at sufficiently large tensions: $sigmaggsigma_*,$ where $sigma_*$ depends
both on temperature and on the disorder strength. We also study the effect of
tension on the crumpling transition as well as properties of dynamical and
static correlation functions of disordered suspended graphene under tension.
Two different phases within the flat phase are identified that are
characterized by different scaling behavior of the singular part of
fluctuations. | | Source: | arXiv, 1603.0398 | | Services: | Forum | Review | PDF | Favorites | |
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