Quantum and classical elasticity of graphene
In this talk, I present an review of recent results [1,2,3] for the elastic properties of 2D crystalline membranes, including graphene. I discuss how an interplay between quantum and classical anharmonicity-controlled fluctuations leads to unusual elastic properties of the crystalline membrane. In particular, I discuss how anomalous Hooke’s law leads to the negative and almost constant thermal expansion coefficient in a wide temperature range and how the third law of the thermodynamics is restored at extremely low temperatures. Also, I discuss why the anomalous Hooke’s law is responsible for negative absolute and differential Poisson ratios of the crystalline membrane. I present the overall dependence of the Poisson ratio on the stress and the membrane size. I explain a possible reason of discrepancy in the results for the Poisson ratio between the self-consistent screening theory of membrane and numerical simulations.
 I.S. Burmistrov, I.V. Gornyi, V.Yu. Kachorovskii, M.I. Katsnelson, A.D. Mirlin, Phys. Rev. B 94, 195430 (2016).
 I.S. Burmistrov, I.V. Gornyi, V.Yu. Kachorovskii, M.I. Katsnelson, J.H. Los, A.D. Mirlin, Phys. Rev. B 97, 125402 (2018).
 I.S. Burmistrov, I.V. Gornyi, V.Yu. Kachorovskii, A.D. Mirlin, Annals of Physics 396, 119 (2018).