Topology of contact points in Lieb–kagomé model

We analyse Lieb–kagomé model, a three-band model with contact points showing particular examples of the merging Dirac points. prove that eigenstates can be parametrized in classification surface, which is hypersurface 4-dimension space. This surface powerful device giving topological properties energy band structure; analysis its fundamental group proves all singularities structure characterized by four independent winding (integer) numbers. Lieb case separates: differs and there only one number.