Speaker
Description
Discovery of graphene and thermally induced ripples in graphene created a new playground for statistical mechanics of two-dimensional membranes embedded into three-dimensional Euclidean space [1,2]. I will give a general review of the problem including main experimental observations and computer simulation results. After that, I will focus on recent works [3-5] based on the use of the methods of quantum field theory, especially renormalization group. It turns out that the membranes provide a nontrivial example of strongly interacting field theory with scaling invariance but without conformal invariance. At low temperatures the membranes are in quantum regime which is characterized by unusual thermal properties. In particular, thermal expansion coefficient α remains constant till very low temperatures and, instead of vanishing by power-law in temperature T, α ~ Ta as in any “normal” crystals it behaves like α ~ 1/(ln|T|)4/7. At the end I will discuss briefly some open questions such as statistical mechanics of compressed membranes.
[1] M. I. Katsnelson and A. Fasolino, Graphene as a prototype crystalline membrane, Acc. Chem. Research 46, 97 (2013)
[2] M. I. Katsnelson, The Physics of Graphene (Cambridge Univ. Press, 2020), Chapter 9.
[3] A. Mauri and M. I. Katsnelson, Scaling behavior of crystalline membranes: An ε-expansion approach, Nucl. Phys. B 956, 115040 (2020)
[4] A. Mauri and M. I. Katsnelson, Scale without conformal invariance in membrane theory, Nucl. Phys. B 969, 115482 (2021)
[5] A. Mauri and M. I. Katsnelson, Perturbative renormalization and thermodynamics of quantum crystalline membranes, Phys. Rev. B 105, 195434 (2022)
