Event

We describe a powerful theoretical approach to studying electronic band structures, which associates them with elements of a vector space. The set of consistent band structures in a space group can then be expanded in terms of a small set of basis vectors. We calculate the dimension of this vector space, and the necessary electron fillings to obtain band insulators in all magnetic space groups. Furthermore, by contrasting with atomic insulators, we find the full set of symmetry eigenvalues that enforce stable band topology, and show how this aids in the search for topological semimetals and insulators.