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Dirac semimetals (DSM) and Weyl semimetal (WSM) fall under the generic classof three-dimensional solids, which follow relativistic energy-momentum relation$\epsilon_\mathbf{k}= \hbar v_F |\mathbf{k}|$ at low energies. Such a lineardispersion when regularized on a lattice can lead to remarkable properties suchas the anomalous Hall effect, presence of Fermi surface arcs, positivelongitudinal magnetoconductance, and dynamic chiral magnetic effect. The lasttwo properties arise due to the manifestation of chiral anomaly in thesesemimetals, which refers to the non-conservation of chiral charge in thepresence of electromagnetic gauge fields. Here, we propose the planar Nernsteffect, or transverse thermopower, as another consequence of chiral anomaly,which should occur in both Dirac and Weyl semimetals. We analytically calculatethe planar Nernst coefficient for DSMs (type-I and type-II) and also WSMs(type-I and type-II), using a quasi-classical Boltzmann formalism. The planarNernst effect manifests in a configuration when the applied temperaturegradient, magnetic field, and the measured voltage are all co-planar, and is ofdistinct origin when compared to the anomalous and conventional Nernst effects.Our findings, specifically a 3D map of the planar Nernst coefficient in type-IDirac semimetals (Na$_3$Bi, Cd$_3$As$_2$ etc) and type-II DSM (PdTe$_2$, VAI3etc), can be verified experimentally by an in-situ 3D double-axis rotationextracting the full $4\pi$ solid angular dependence of the Nernst coefficient.

Transverse thermopower in Dirac and Weyl semimetals