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Rippling and crumpling in disordered free-standing graphene | | I. V. Gornyi
; V. Yu. Kachorovskii
; A. D. Mirlin
; | | Date: |
18 May 2015 | | Abstract: | Graphene is a famous realization of elastic crystalline two-dimensional (2D)
membrane. Thermal fluctuations of a 2D membrane tend to destroy the long-range
order in the system. Such fluctuations are stabilized by strong anharmonicity
effects, which preserve thermodynamic stability. The anharmonic effects
demonstrate critical behaviour on scales larger than the Ginzburg scale. In
particular, clean suspended flake of graphene shows a power-law increase of the
bending rigidity with the system size, $varkappapropto L^{eta},$ due to
anharmonic interaction between in-plane and out-of-plane (flexural) phonon
modes. We demonstrate that random fluctuations of membrane curvature caused by
static disorder may change dramatically the scaling of the bending rigidity and
lead to a non-monotonous dependence of $varkappa$ on $L.$ We derive coupled
renormalization-group equations describing combined flow of $varkappa$ and
effective disorder strength $b$, find a critical curve $b(varkappa)$
separating flat and crumpled phases, and explore the behavior of disorder in
the flat phase. Deep in the flat phase, disorder decays in a power-law way at
scales larger than the Ginzburg length which therefore sets a characteristic
size for the ripples---static out-of-plane deformations observed experimentally
in suspended graphene. We find that in the limit $L o infty $ ripples are
characterized by anomalous exponent $2eta$ in contrast to dynamical
fluctuations governed by $eta$. In the near-critical regime, disorder first
increase with $L$, then reaches a maximum and starts to decrease. In this case,
the membrane shows fractal properties implying a multiple folding starting form
a certain length scale $L_1$ and finally flattens at a much larger scale $L_2$
(which diverges at criticality). We conclude the paper by a comparison of our
results with available experimental data on graphene ripples. | | Source: | arXiv, 1505.4483 | | Services: | Forum | Review | PDF | Favorites | |
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