Flat bands and long range Coulomb interactions: conducting or insulating?

TL;DR

This paper explores how long-range Coulomb interactions influence the conductance of flat electronic bands, revealing complex behavior including multiple zeros in conductivity and phase transitions.

Contribution

It introduces a detailed analysis of Coulomb effects on flat bands using the $ ext{T}_3$-lattice, uncovering novel conductivity patterns and phase transition phenomena.

Findings

Conductivity exhibits an infinite number of zeros at specific fillings.

Near zeros, conductivity increases linearly with carrier density.

Enhanced conductivity occurs at half-integer fillings, indicating phase transitions.

Abstract

Dispersionless (flat) electronic bands are investigated regarding their conductance properties. Due to "caging" of carriers these bands are usually insulating at partial filling, at least on the non-interacting level. Considering the specific example of a $\mathcal{T}_3$--lattice we study long-range Coulomb interactions. A non-trivial dependence of the conductivity on flat band filling is obtained, exhibiting an infinite number of zeros. Near these zeros, the conductivity rises linearly with carrier density. At densities half way in between adjacent conductivity-zeros, strongly enhanced conductivity is predicted, accompanying a solid-solid phase transition.