Nernst effect in Dirac and inversion-asymmetric Weyl semimetals

TL;DR

This paper investigates the Nernst effect in Dirac and Weyl semimetals, revealing the dominance of anomalous Nernst response in Dirac semimetals near Dirac points and conventional response in inversion asymmetric Weyl semimetals, with implications for experiments.

Contribution

It provides a theoretical analysis of the Nernst response in Dirac and Weyl semimetals, highlighting the role of Berry curvature and crystalline symmetries, and compares the responses in different topological phases.

Findings

Anomalous Nernst effect dominates in Dirac semimetals near Dirac points.

Conventional Nernst response dominates in inversion asymmetric Weyl semimetals.

The Nernst response serves as an experimental probe for topological features.

Abstract

Dirac semimetals are three dimensional analog of graphene with massless Dirac fermions as low energy electronic excitations. In contrast to Weyl semimetals, the point nodes in the bulk spectrum of topological Dirac semimetals have a vanishing Chern number, but can yet be stable due to the existence of crystalline symmetries such as uniaxial (discrete) rotation symmetry. We consider a model low-energy Hamiltonian appropriate for the recently discovered topological Dirac semimetal Cd$_3$As$_2$, and calculate the Nernst response within semiclassical Boltzmann dynamics in the relaxation time approximation. We show that, for small chemical potentials near the Dirac points, the low temperature, low magnetic field, Nernst response is dominated by \textit{anomalous} Nernst effect, arising from a non-trivial profile of Berry curvature on the Fermi surface. Although the Nernst coefficient (both anomalous as well as conventional) vanish in the limit of zero magnetic field, the low temperature, low magnetic field, Nernst response, which has an almost step like profile near $\mathbf{B}=0$, serves as an effective experimental probe of anomalous Nernst effect in topological Dirac semimetals protected by crystalline symmetries. Additionally, we also calculate the Nernst response for a lattice model of an inversion asymmetric Weyl semimetal for which, in contrast to the case of Dirac semimetal, we find that the conventional Nernst response dominates over the anomalous. Our calculations in this paper on Nernst response of Dirac semimetal and inversion broken Weyl semimetal are directly relevant to recent experiments on Cd$_3$As$_2$ (Dirac semimetal) and NbP (inversion broken Weyl semimetal) respectively.