Relation between topology and electronic structure of 2D polymers

New 2D materials open access to a whole new world of compounds and properties. Graphene monolayer is such a material, since it has special electron transport features due to its honeycomb topology. Apart from the honeycomb net, there are many more topologies, which promise a manifold of new properties, e.g. the kagomé or the Lieb lattice. As recently shown in the case of the kagomé net, 2D polymers (covalent organic frameworks) can be designed in a way, that their geometric and electronic structures match the desired topology.[1] Other nets, e.g. the Lieb lattice, can at the moment only be realized as optical lattices or via adsorption of molecules on a surface.[2]
In this project, we want to work out the relation between topology and electronic properties. For this purpose, we employ a tight-binding model. In Fig. 1, exemplary results for the aforementioned kagomé and Lieb lattices are shown. Based on these findings, we want to propose new 2D polymers with the desired structures and new properties using density- functional theory.
[1] Y. Jing, T. Heine, J. Am. Chem. Soc. 141, 2, 743 (2019)
[2] S. Mukherjee et al., Phys. Rev. Lett. 114, 245504 (2015); S. Taie et al., Sci. Adv. 1, e1500854 (2015); M. R. Slot et al., Nat. Phys. 13, 672 (2017)