The deep understanding of the physical properties of 2D materials requires the study crossing over from microscopic to macroscopic. New quantum phenomena emerge at the mesoscopic and macroscopic level, such as interference effects, quantum confinement effects, and charging effects. For structures with scales larger than 100 nanometers, the ab initio calculations are unfeasible. Tight-binding propagation methods (TBPMs) are developed for the modeling of systems range from mesoscopic to macroscopic level, and applied for the calculations of electronic, transport and optical properties. We will give a brief introduction of the methods, and show their applications together with our recent progresses in the study of 2D materials, heterostructures and superstructures, such as the many-body enhancement of insulating states at the additional Dirac points in graphene-hBN heterostructures, the modification of optical gap in fluorographene due to (super)structure disorders, effects of disorder in the electronic and optical properties of semiconducting black phosphorus and transition metal dichalcogenides, a new tight-binding model parametrization for black phosphorus with an arbitrary number of layers, transition from semiconductor to Dirac semimetal in biased black phosphorus, and fractional dimension appeared in the electronic transport in 2D fractals. We will also show how to combine the TBPMs with other well-known numerical methods such as DFT-GW and molecular dynamics, and discuss briefly the extension to many-body problem.

袁声军, 武汉大学物理科学与技术学院教授、博士生导师, 现任武汉大学量子物质能量转换协同创新中心理论部主任, 武汉大学理论物理中心副主任, 荷兰奈梅亨大学材料与分子学院客座教授, 北京计算科学中心客座教授。主要的研究领域为计算物理学、凝聚态理论和高性能科学计算, 包括发展针对复杂量子体系的多尺度模拟方法, 发展针对量子多体问题的计算方法, 低维量子体系的电学、光学、输运和等离基元性质, 强关联自旋系统的弛豫和退相干等等。