Minimal conductivity, topological Berry winding and duality in three-band semimetals

TL;DR

This paper explores the relationship between topological Berry winding and minimal conductivity in three-band semimetals, revealing that only topologically nontrivial semimetals exhibit finite minimal conductivity, linked through a lattice duality.

Contribution

It demonstrates that topological Berry phases and minimal conductivity are closely related in three-band semimetals, highlighting the role of lattice duality in their electronic properties.

Findings

Topologically nontrivial semimetals support finite minimal conductivity.

Berry phase and minimal conductivity are intimately connected.

Lattice duality underpins the robustness of these properties.

Abstract

The physics of massless relativistic quantum particles has recently arisen in the electronic properties of solids following the discovery of graphene. Around the accidental crossing of two energy bands, the electronic excitations are described by a Weyl equation initially derived for ultra-relativistic particles. Similar three and four band semimetals have recently been discovered in two and three dimensions. Among the remarkable features of graphene are the characterization of the band crossings by a topological Berry winding, leading to an anomalous quantum Hall effect, and a finite minimal conductivity at the band crossing while the electronic density vanishes. Here we show that these two properties are intimately related: this result paves the way to a direct measure of the topological nature of a semi-metal. By considering three band semimetals with a flat band in two dimensions, we find that only few of them support a topological Berry phase. The same semimetals are the only ones displaying a non vanishing minimal conductivity at the band crossing. The existence of both a minimal conductivity and a topological robustness originates from properties of the underlying lattice, which are encoded not by a symmetry of their Bloch Hamiltonian, but by a duality.