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)材料的自立膜的反常弹性、电子和磁性。由于其动态(弯曲声子)和静态(波纹、褶皱)的离面变形，二维膜表现出特殊的性质，如非线性胡克定律、负热膨胀系数(在超低温度下保持不变)、负泊松比(伸长率)以及体积和剪切模数的反常软化。发展2D材料的可能应用，例如在新兴的柔性纳米电子学领域，需要更深入地了解反常弹性和电子结构之间的相互作用，包括电子关联对膜纳米力学的反馈。二维材料的弹性和电学性质的相互影响是该项目的重点。主要的研究目标是：(I)发展含有相关电子的现实薄膜的理论描述，重点是可能的相互作用诱导的相变以及薄膜电阻率的反常应力依赖；(Ii)研究薄膜的机械、电子和磁性的相互作用，超越微扰理论，解释赝隙形成和极化子效应；以及(Iii)研究弹性性质对相关莫尔超晶格中电子自由度的反馈，例如扭曲的双层石墨烯。该项目的预期成果是一个新的知识库，量化了可用于电子学、等离子激元和光子学的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器件，基于通过外部应变控制弯曲声子幅度的电阻和热开关，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)之间相互耦合的宽带红外辐射探测器，以及新型纳米机电设备。该联盟由俄罗斯和德国的理论小组组成，这些小组都在该领域拥有重要的专业知识和国际知名度。俄罗斯和德国的小组已经在石墨烯、无序和强关联系统以及临界现象等领域建立了合作。这一新的研究趋势的共同发展形成了持久合作的基础。德国小组在研究强关联现象和超导方面的专业知识将得到俄罗斯团队在结晶膜异常弹性性质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.