Anomalous elasticity: from phase transitions to flexible electronics

该项目的主要目标是从理论上研究二维（2D）材料的独立膜的异常弹性，电子和磁性。由于其动态（弯曲声子）和静态（波纹，皱纹）的平面外变形，二维膜表现出特殊的性能，如非线性虎克定律，负的热膨胀系数，保持恒定的超低温，负泊松比（auxeticity），和异常软化的体积和剪切模量。开发2D材料的可能应用，例如，在柔性纳米电子学的新兴领域，需要更深入地了解异常弹性和电子结构之间的相互作用，包括电子相关性对膜的纳米力学的反馈。二维材料的弹性和电子性质的相互影响是该项目的重点。主要的研究目标是：（一）发展一个理论描述的现实膜托管相关电子，重点是可能的相互作用引起的相变以及膜电阻率的异常应力依赖性;（二）调查的机械，电子和磁性能的膜的相互作用，超越微扰理论和占赝隙的形成和极化效应;以及（iii）研究相关莫尔超晶格（如扭曲双层石墨烯）中弹性性质对电子自由度的反馈。该项目的预期成果是一个新的知识库，量化可用于电子学，等离子体和光子学的2D材料的异常弹性和传输特性。潜在的应用包括基于扭曲石墨烯的超导设备，基于通过外部应变控制弯曲声子的振幅的电阻和热开关，基于传导电子和平面外动态弹性模式（弯曲声子）和静态波纹（波纹）之间的相互耦合的宽带红外辐射检测器，以及新型的纳米机电设备。该联盟由俄罗斯和德国的理论小组组成，他们都拥有该领域的重要专业知识和国际知名度。俄罗斯和德国的研究小组在石墨烯、无序和强相关系统以及临界现象领域建立了合作。这种新的研究趋势的共同发展构成了持久合作的基础。德国团队在强关联现象和超导性研究方面的专业知识将得到俄罗斯团队在结晶膜异常弹性特性领域的专业知识的补充，为该项目的成功实施提供额外的保障。

The primary goal of the project is to study theoretically anomalous elastic, electronic, and magnetic properties of free-standing membranes of two-dimensional (2D) materials. Owing to their dynamic (flexural phonons) and static (ripples, wrinkles) out-of-plane deformations, 2D membranes exhibit peculiar properties such as nonlinear Hooke’s law, negative thermal expansion coefficient which remains constant down to ultralow temperatures, negative Poisson ratio (auxeticity), and anomalous softening of the bulk and shear moduli. Development of possible applications of 2D materials, e.g., in the emerging field of flexible nano-electronics, requires a deeper understanding of the interplay between the anomalous elasticity and electronic structure, including the feedback of electronic correlations on the nano-mechanics of membranes. The mutual influence of elastic and electronic properties of 2D materials is the focus of the project. The key research objectives are (i) to develop a theoretical description of realistic membranes hosting correlated electrons, with the emphasis on possible interaction-induced phase transitions as well as anomalous stress-dependence of membrane resistivity; (ii) to investigate the interplay of mechanical, electronic, and magnetic properties of membranes, going beyond the perturbation theory and accounting for pseudogap formation and polaronic effects; and (iii) to study the feedback of elastic properties on electronic degrees of freedom in correlated Moiré superlattices, such as twisted bilayer graphene. The envisioned outcome of the project is a new knowledge base, quantifying the anomalous elastic and transport properties of 2D materials that could be used in electronics, plasmonics, and photonics. Potential applications include superconduciting devices based on twisted graphene, resistive and thermal switches based on controlling the amplitude of flexural phonons via external strain, broadband infrared radiation detectors based on mutual coupling between conduction electrons and out-of-plane dynamical elastic modes (flexural phonons) and static corrugations (ripples), and new types of nanoelectromechanical devices. The consortium consists of theoretical groups in Russia and Germany that all possess significant expertise and international visibility in the field. The Russian and German groups have established cooperation in the fields of graphene, disordered and strongly-correlated systems, and critical phenomena. Joint development of this novel research trend forms a basis for lasting collaboration. The expertise of the German group in the study of strongly correlated phenomena and superconductivity will be complemented by the expertise of the Russian team in the field of anomalous elastic properties of crystalline membranes, providing additional guarantee for the successful implementation of the project.