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Fluctuations dans la phase plate des membranes cristallines

Abstract : This works deals with the mechanical properties of crystalline membranes, which are two-dimensional materials with an underlying periodic lattice at the microscopic scale which provides them with elastic properties. It is one of the scarce examples of two-dimensional systems possessing a stable ordered phase at large distance in the presence of thermal fluctuations. In that phase, the vectors normal to the surface generated by the membrane are strongly correlated; it is thus called the flat phase. This manuscript presents a study of the properties of the flat phase with help of renormalisation group tools, and in particular the effective average action formalism. First, by studying the perturbation theory beyond lowest order, we confirm the stability of our effective average action ansatz used in the following, and unveil some pathologies of the perturbative development. Then we show how the non-perturbative renormalisation group flow can be used to compute various thermodynamic properties of crystalline membranes and draw their complete phase diagram in the space (volume, applied stress, temperature). Afterwards, we improve our model to account for the effect of quantum fluctuations, which allows to describe the low temperature regime. Finally, we examine the consequences of the presence of various defects in the material. In particular, we describe a new disorder driven phase transition which seems to be in good qualitative agreement with experimental observations.
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  • HAL Id : tel-02555243, version 1

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Olivier Coquand. Fluctuations dans la phase plate des membranes cristallines. Matière Condensée [cond-mat]. Sorbonne Université, 2018. Français. ⟨NNT : 2018SORUS096⟩. ⟨tel-02555243⟩

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