Modeling, Analysis, and Computation of 2D Layered Materials

二维层状材料的建模、分析和计算

• 批准号: 1906129
• 负责人: Mitchell Luskin
• 金额: $ 25.94万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1906129&HistoricalAwards=false
• 关键词: Modeling; Analysis; Computation; 2D; Layered

Experimental methods for interleaving layers of 2D materials have been developed with endless possibilities for creating stable structures with desired electronic, optical, magnetic and thermal properties. This project will develop mathematical models and computational methods to guide the search and design of 2D materials with optimal properties. This approach makes possible the long-sought goal of atomic-level control of nanostructures as building blocks for creating devices of desirable properties and performance characteristics. The mathematical modeling, analysis, and computation from the atomic to macroscopic scale developed by the project will contribute to the design of new materials leading to applications in incommensurate 2D materials. This effort will impact the development of materials and devices with desired characteristics and performance for a wide range of applications of interest including ultra-fast electronic, opto-electronic, and magnetic devices; nonconventional optical and photonics devices; and communication devices. The challenge of modeling layered incommensurate heterostructures will also promote the development of multiscale models for many other aperiodic materials systems such as composites, atomically engineered structures, and bio-materials. 2D materials research is an ideal platform to motivate new mathematics training and curricula in the analysis, modeling, and computation of quantum electronic structure and transport, and mechanical and topological properties of materials. The project's graduate student training and outreach to underrepresented student populations will broaden the diversity of the mathematical research community.The main issue encountered in the mathematical modeling of layered 2D materials is that the lattice periodicities of different layers do not match and thus lead to incommensurate structures. New theory and computational methods that do not use Bloch-Fourier methods will be developed to accurately predict material properties in currently inaccessible regimes. This project will utilize the notions of local configuration space and locality to give new formulations and computational methods for the electronic density of states and for transport properties such as conductivity. New momentum space formulations and corresponding fast computational methods will be developed that exploit the structure of the momentum space Hamiltonian. Novel models and computational methods will also be developed and analyzed that extend our model for electronic density of states and conductivity to include mechanical relaxation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

已经开发出交错二维材料层的实验方法，为创建具有所需电子、光学、磁和热性能的稳定结构提供了无限的可能性。该项目将开发数学模型和计算方法来指导具有最佳性能的二维材料的搜索和设计。这种方法使得纳米结构的原子级控制作为构建块来创建具有所需特性和性能特征的设备的长期追求的目标成为可能。该项目开发的从原子到宏观尺度的数学建模、分析和计算将有助于新材料的设计，从而在不相称的二维材料中得到应用。这项工作将影响具有所需特性和性能的材料和器件的开发，适用于各种感兴趣的应用，包括超快电子、光电和磁性器件；非传统光学和光子器件；和通讯设备。分层不相称异质结构建模的挑战也将促进许多其他非周期性材料系统（例如复合材料、原子工程结构和生物材料）的多尺度模型的发展。二维材料研究是在量子电子结构和输运以及材料的机械和拓扑特性的分析、建模和计算方面激发新的数学培训和课程的理想平台。该项目的研究生培训和对代表性不足的学生群体的推广将扩大数学研究界的多样性。层状二维材料的数学建模遇到的主要问题是不同层的晶格周期不匹配，从而导致结构不相称。将开发不使用布洛赫-傅立叶方法的新理论和计算方法，以准确预测当前无法访问的区域中的材料特性。该项目将利用局域构型空间和局域性的概念，为电子态密度和电导率等输运特性提供新的公式和计算方法。将开发新的动量空间公式和相应的快速计算方法，以利用动量空间哈密顿量的结构。还将开发和分析新的模型和计算方法，以扩展我们的电子态密度和电导率模型，以包括机械弛豫。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优势和更广泛的影响进行评估，被认为值得支持审查标准。

项目成果

Finite-size effects in wave transmission through plasmonic crystals: A tale of two scales

通过等离子体晶体的波传输的有限尺寸效应：两个尺度的故事

• DOI: 10.1103/physrevb.102.075308
• 发表时间: 2020-05-26
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: M. Maier;M. Luskin;D. Margetis
• 通讯作者: D. Margetis

Efficient computation of Kubo conductivity for incommensurate 2D heterostructures

有效计算不相称二维异质结构的 Kubo 电导率

• DOI: 10.1140/epjb/e2020-100518-7
• 发表时间: 2020-04
• 期刊: The European Physical Journal B
• 作者: Massatt, Daniel;Carr, Stephen;Luskin, Mitchell
• 通讯作者: Luskin, Mitchell

Homogenization of hydrodynamic transport in Dirac fluids

狄拉克流体中流体动力传递的均匀化

• DOI: 10.1063/5.0021961
• 发表时间: 2021-01
• 期刊: Journal of Mathematical Physics
• 影响因子: 1.3
• 作者: Bal, Guillaume;Lucas, Andrew;Luskin, Mitchell
• 通讯作者: Luskin, Mitchell

Electronic Observables for Relaxed Bilayer Two-Dimensional Heterostructures in Momentum Space

动量空间中松弛双层二维异质结构的电子可观测量

• DOI: 10.1137/21m1451208
• 发表时间: 2023-12
• 期刊: Multiscale Modeling & Simulation
• 影响因子: 1.6
• 作者: Massatt, Daniel;Carr, Stephen;Luskin, Mitchell
• 通讯作者: Luskin, Mitchell

Relaxation and Domain Wall Structure of Bilayer Moiré Systems

双层莫尔系统的弛豫和畴壁结构

• DOI: 10.1007/s10659-023-10013-0
• 发表时间: 2023-04
• 期刊: Journal of Elasticity
• 影响因子: 2
• 作者: Cazeaux, Paul;Clark, Drake;Engelke, Rebecca;Kim, Philip;Luskin, Mitchell
• 通讯作者: Luskin, Mitchell