Flat bands with band crossings enforced by symmetry representation

Flat bands have band crossing points with other dispersive bands in many systems including the canonical flat band models in the Lieb and kagome lattices. Here we show that some of such band degeneracy points are unavoidable because of the symmetry representation (SR) of the flat band under unitary symmetry. We refer to such a band degeneracy point of flat bands as a SR-enforced band crossing. SR-enforced band crossing is distinct from the...