Topological two-dimensional polymers.

There are more than 200 two-dimensional (2D) networks with different topologies. The structural topology of a 2D network defines its electronic structure. Including the electronic topological properties, it gives rise to Dirac cones, topological flat bands and topological insulators. In this Tutorial Review, we show how electronic properties of 2D networks can be calculated by means of a tight-binding approach, and how these properties change when 2nd-neighbour interactions and spin-orbit coupling are included. We explain how to determine whether or not the resulting electronic features have topological signatures by calculation of Chern numbers, Z2 invariants, and by the nanoribbon approach. This tutorial gives suggestions how such topological properties could be realized in explicit atomistic chemical 2D systems made of molecular frameworks, in particular in 2D polymers, where the edges and vertices of a given 2D net are substituted by properly selected molecular building blocks and stitched together in such a way that long-range π-conjugation is retained.