Phonon-drag thermopower in 3D Dirac semimetals

Abstract

A theory of low-temperature phonon-drag thermopower Sg in three-dimensional (3D) Dirac semimetals has been developed considering screened electron–phonon deformation potential coupling. Numerical investigations of Sg, in the boundary scattering regime for phonons, are made in 3D Dirac semimetal Cd3As2, as a function of temperature T and electron concentration ne. Sg is found to increase rapidly for about T < 1 K and nearly levels off for higher T. It is also seen that Sg increases (decreases) with decreasing ne at lower (higher) T (<2 K). A screening effect is found to be very significant, strongly affecting T and ne dependence for about <1 K and becoming negligible at higher temperature. In the Bloch–Gruneisen (BG) regime the power laws Sg ~ T8 (T4) and Sg ~ with (without) screening are obtained. These laws with respect to T and ne are, respectively, characteristics of 3D phonons and Dirac 3D electrons. Comparison with diffusion thermopower Sd shows that Sg dominates (and is much greater than) Sd for about T > 0.2 K. Herring’s law Sgμp ~ T −1, relating phonon limited mobility μp and Sg in the BG regime, is shown to be valid in 3D Dirac semimetals. The results obtained here are compared with those in 3D semiconductors, low-dimensional semiconductor heterojunctions and graphene. We conclude that ne-dependent measurements, rather than T-dependent ones, provide a clearer signature of the 3D Dirac semimetal phase.