On the origin of minimal conductivity at a band crossing

Abstract

Several materials with energy bands crossing giving rise to relativisticlike electronic excitations have recently been discovered beyond the seminal example of graphene. These relativistic phases exhibit remarkable properties, among which is a finite minimal conductivity. While the density of propagating wave states vanishes at the band crossing, the conductivity may remain finite due to evanescent modes in a confined geometry. Studying the generalizations of graphene to three-band models we find that this property is intimately related to the existence of topological Berry phases. We show that the topological robustness of the latter originates from geometrical properties of the underlying lattice, which are encoded into duality properties of the Hamiltonian.