Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals

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We compute the thermoelectric and thermal transport coefficients in the weakly disordered non-Fermi liquid phase of the Luttinger semimetals at zero doping, where the decay rate associated with the (strong) Coulomb interactions is much larger than the electron-impurity scattering rate. To this end, we implement the Mori-Zwanzig memory matrix method, that does not rely on the existence of long-lived quasiparticles in the system. We find that the thermal conductivity at zero electric field scales as κ¯∼T−n (with 0≲n≲1) at low temperatures, whereas the thermoelectric coefficient has the temperature dependence given by α∼Tp (with 1/2≲p≲3/2). These unconventional properties turn out to be key signatures of this long sought-after non-Fermi liquid state in the Luttinger semimetals, which is expected to emerge in strongly correlated spin-orbit coupled materials like the pyrochlore iridates. Finally, our results indicate that these materials might be good candidates for achieving high figure-of-merit for thermoelectric applications.