# Anomalous elasticity of 2D materials beyond self–consistent approximation

**Date:**

We study elastic properties of two–dimensional crystalline materials, such as graphene. It is known that in 2D membranes strong thermal fluctuations of flexural phonons lead to dramatic change of phonon spectrum and, as a result, in anomalous material–independent elastic properties, such as non-linear Hooke’s law under the low stress and auxetic behavior. We compute elastic moduli η and Poisson ratio ν of 2D membrane in the approximation of high embedded dimensionality. We go beyond one-loop approximation and find that famous self-consistent screening approximation is only as good as first-order approximation. Most remarkably, we analyze a case of disordered membrane and find new disorder–dominant phase, where all the critical exponents are different from the clean case. We find that phase transition happens at finite temperature in contrast to the prediction given by self–consistent screening approximation, that transition is only possible at absolute zero.

Presented work is a continuation of the results reported in papers PhysRevB.97.125402, PhysRevB.92.155428.

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