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.

Dr. Shengjun Yuan is a tenure-track assistant professor at Radboud University of Nijmegen, the Netherlands. He graduated from the Department of Physics at Zhejiang University in 2001, received his MSc. degree in theoretical physics from University of Siegen (Germany) in 2003, and received his PhD degree in computational physics from University of Groningen (The Netherlands) in 2008, for work on relaxation and decoherence in quantum spin systems. From 2009, he joined Theory of Condensed Matter group headed by Prof. M. I. Katsnelson at Radboud University of Nijmegen as a postdoc, and become an assistant professor since 2014. He developed a series of new numerical methods in the modeling of large-scale quantum systems, and applied on the study of the electronic, optical and transport properties of various 2D materials.