The understanding of the structural and thermal properties of membranes, low-dimensional flexible systems in a space of higher dimension, is pursued in many fields from string theory to chemistry and biology. The case of a two-dimensional (2D) membrane in three dimensions is the relevant one for dealing with real materials. Traditionally, membranes are primarily discussed in the context of biological membranes and soft matter in general. The complexity of these systems hindered a realistic description of their interatomic structures based on a truly microscopic approach. Therefore, theories of membranes were developed mostly within phenomenological models. From the point of view of statistical mechanics, membranes at finite temperature are systems governed by interacting long-range fluctuations. Graphene, the first truly two-dimensional system consisting of just one layer of carbon atoms, provides a model system for the development of a microscopic description of membranes. In this Account, we review key results in the microscopic theory of structural and thermal properties of graphene and compare them with the predictions of phenomenological theories. The two approaches are in good agreement for the various scaling properties of correlation functions of atomic displacements. However, some other properties, such as the temperature dependence of the bending rigidity, cannot be understood based on phenomenological approaches. We also consider graphene at very high temperature and compare the results with existing models for two-dimensional melting. The melting of graphene presents a different scenario, and we describe that process as the decomposition of the graphene layer into entangled carbon chains.
High-$Q$ membrane resonators using ultra-high-stress crystalline TiN films
Komaba Institute for Science (KIS), The University of Tokyo（东京大学绪方理工学研究所）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；IBM Quantum, IBM Research - Tokyo（IBM量子，IBM研究-东京）；Advanced ICT Research Institute, National Institute of Information and Communications Technology（信息通信技术研究所高级ICT研究所）；Inamori Research Institute for Science (InaRIS)（稻盛理工学研究所）
Reply to 'Comment on "Thermodynamics of quantum crystalline membranes"'
在这篇文章中，我们回复了E.I.Kats和V.V.Lebedev [arXiv：1407.4298]对我们最近的工作“量子结晶膜的热力学”[Phys. Rev. B 89，224307（2014）]的评论。Kats和Lebedev质疑我们工作中提出的计算的有效性，特别是使用德拜动量作为理论的紫外调节器。我们处理和反驳Kats和Lebedev对我们工作的批评。
Curvature-Controlled Infrared Regularization of Crystalline Membranes
Research Division, Araya Inc.（Araya公司研究部）；Centre for Complexity Science, Imperial College London（伦敦帝国理工学院复杂性科学中心）；Facultad de Ciencias en Física y Matemáticas, Benemérita Universidad Autónoma de Chiapas（恰帕斯自治优秀大学物理与数学科学学院）
