Thermoelectric properties of Weyl and Dirac semimetals

Abstract

We study the electronic contribution to the thermal conductivity and the thermopower of Weyl and Dirac semimetals using a semiclassical Boltzmann approach. We investigate the effect of various relaxation processes including disorder and interactions on the thermoelectric properties, and also consider doping away from the Weyl or Dirac point. We find that the thermal conductivity and thermopower have an interesting dependence on the chemical potential that is characteristic of the linear electronic dispersion, and that the electron-electron interactions modify the Lorenz number. For the interacting system, we also use the Kubo formalism to obtain the transport coefficients. We find exact agreement between the Kubo and Boltzmann approaches at high temperatures. We also consider the effect of electric and magnetic fields on the thermal conductivity in various orientations with respect to the temperature gradient. Notably, when the temperature gradient and magnetic field are parallel, we find a large contribution to the longitudinal thermal conductivity that is quadratic in the magnetic field strength, similar to the magnetic field dependence of the longitudinal electrical conductivity due to the presence of the chiral anomaly when no thermal gradient is present.Comment: 17 pages, 2 Figure

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

“…It has been shown recently that negative magnetoresistance can be derived using the semi-classical equations of motion employing Boltzmann transport 60 . Other recent works have also developed a modified Boltzmann equation, taking into account Berry curvature and chiral anomaly effects 45,46,[78][79][80] . In these works a linearized model of the WSM has been examined, i.e.…”

“…In turn, a non-zero α xy implies an anomalous (zero field) Nernst coefficient given by α xy /σ xx . In recent work 45 , however, based on a linearized model of a TR-broken Weyl semimetal, the anomalous Nernst response has been argued to be zero, because a linearized Weyl Hamiltonian with unbounded (or very high) ultraviolet cut-off of the Dirac spectrum produces ∂σ xy /∂µ = 0. Here we show, from a lattice model of a WSM (with the lattice regularization providing a physical ultra-violet cut-off to the low energy Dirac spectrum) that the anomalous Peltier coefficient, and in turn the anomalous Nernst coefficient is finite and measurable in a physical time reversal breaking Weyl semimetal such as Bi 1−x Sb x .…”

“…In the SI broken Weyl semimetal, because of TR symmetry there is no Berry curvature induced anomalous charge or thermal Hall effect in the absence of an external magnetic field. However, in the TR broken WSM, because of a finite Berry curvature flux through any plane intermediate between the Weyl nodes in the momentum space, the anomalous charge and thermal Hall conductivities are nonzero 13,[44][45][46] .…”

“…Unlike earlier works which were based on a linearized WSM model, 45,46 we employ a lattice Bloch Hamiltonian. With the Nernst experimental setup i.e.…”

“…For k 0 = 0, the two Weyl points collapse onto each other giving rise to a topologically trivial (i.e with a zero Berry curvature flux) massless degenerate Dirac fermion. The topological nature of a WSM leads to a host of interesting physics, for example Berry curvature induced anomalous transport, namely charge and thermal Hall conductivities [43][44][45][46][47][48] and open Fermi arcs on surfaces 11,[49][50][51][52][53][54][55] . Anomalous transport phenomena, however, have been already known to exist in a variety of systems which possess a non-trivial distribution of the Berry curvature flux 56,57 .…”