Diverging dc conductivity due to a flat band in disordered pseudospin-1 Dirac-Weyl fermions

TL;DR

This paper studies how disorder affects the flat band in pseudospin-1 Dirac-Weyl fermions, revealing diverging dc conductivity due to interband transitions despite zero group velocity.

Contribution

It demonstrates that disorder induces a diverging dc conductivity in flat bands of pseudospin-1 systems, highlighting the role of interband transitions and providing generalizations to higher pseudospin.

Findings

Flat band DOS exhibits a narrow peak on non-central sites.

Dc conductivity diverges logarithmically as disorder decreases.

Interband transitions cause conductivity divergence despite zero group velocity.

Abstract

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 non-central sites exhibits a narrow peak with height ~ 1/\sqrt{g} with g the dimensionless disorder variance. Although the group velocity is zero on the flat band, the dc conductivity diverges as ln(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.