Interacting nodal semimetals with non-linear bands

TL;DR

This paper studies how non-linear energy bands affect the electronic and transport properties of interacting Dirac and Weyl semimetals, revealing a crossover from non-Fermi-liquid to Fermi-liquid behavior influenced by an energy scale and proximity to a Mott transition.

Contribution

It introduces a model incorporating non-linear dispersion in interacting semimetals and analyzes how this affects spectral weight, scattering rates, and resistivity near the Mott transition.

Findings

Spectral weight renormalization weakly depends on the non-linear scale  but is sensitive to Mott proximity.

High-temperature scattering rates and resistivity exponents depend on the non-linear energy scale  leading to a Fermi-liquid crossover.

Identifies a density crossover related to chemical potential using the Nernst-Einstein relation.

Abstract

We investigate the quasi-particle and transport properties of a model describing interacting Dirac and Weyl semimetals in the presence of local Hubbard repulsion $U$, where we explicitly include a deviation from the linearity of the energy-momentum dispersion through an intermediate-energy scale $\Lambda$. Our focus lies on the correlated phase of the semimetal. At the nodal point, the renormalization of spectral weight at a fixed temperature $T$ exhibits a weak dependence on $\Lambda$ but is sensitive to the proximity to the Mott transition. Conversely, the scattering rate of quasi-particles and the resistivity display high-temperature exponents that crucially rely on $\Lambda$, leading to a crossover towards a conventional Fermi-liquid behaviour at finite T. Finally, by employing the Nernst-Einstein relation for conductivity, we identify a corresponding density crossover as a function of the chemical potential.