Automatic generation and topological classification of low-energy Hamiltonians at multi-fold degeneracies

In this talk, we show a method of generating general high-symmetry Hamiltonian with the goal of topologically classifying all possible multi-fold crossings in bandstructures of condensed matter systems. To do so, we found all higher-dimensional irreducible representations at all high-symmetry points in all space groups. The topological phase diagrams of the automatically generated low-energy Hamiltonian at these k-points were mapped out. During this process, we identified a prevalent topological phase with an unusually high Chern number of 5 in point crossings of space groups larger than 195. A material was found featuring this topological phase. Further ab-initio calculations of this materials surface density of states showed a high number of Fermi arcs.