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Thermoelectric transport in double-Weyl semimetals

We study the thermoelectric properties of a double-Weyl fermion system, possibly realized in $\mathrm{HgCr_2Se_4}$ and $\mathrm{SrSi_2}$, by a semi-classical Boltzmann transport theory. We investigate different relaxation processes including short-range disorder and electron-electron interaction on the thermoelectric transport coefficients. It is found that the anisotropy of the band dispersion for in-plane and out-of-plane momentum directions affects the relaxation time for transport in different directions. The transport also exhibits an interesting directional dependence on the chemical potential and model parameters, differing from a simple isotropic quadratic or linearly dispersing electron gas. By applying a static magnetic field along the linearly dispersing direction, the longitudinal and transverse electrical and thermal magnetoconductivity show a similar dependence on the in-plane cyclotron frequency to the linear dispersing Weyl nodes. By including internode scattering, we find that the chiral anomaly contribution to the thermoelectric coefficients doubles that of a linearly dispersing Weyl node in both the semi-classical and quantum regimes. A magnetic field applied along the quadratically dispersing direction will split the double Weyl point into two single Weyl points with the same chirality.