Diverging dc conductivity due to a flat band in disordered pseudospin-1 Dirac-Weyl fermions
Several lattices, such as the dice or the Lieb lattice, possess Dirac cones and a flat band crossing the Dirac point, whose effective model is the pseudospin-1 Dirac-Weyl equation. We investigate the fate of the flat band in the presence of disorder by focusing on the density of states (DOS) and dc conductivity. While the central hub site does not reveal the presence of the flat band, the sublattice resolved DOS on the noncentral sites exhibits a narrow peak with height similar to 1/root g with g the dimensionless disorder variance. Although the group velocity is zero on the flat band, the dc conductivity diverges as 1n(1/g) with decreasing disorder due to interband transitions around the band touching point between the propagating and the flat band. Generalizations to higher pseudospin are given.