Phonon-drag thermopower in 3D Dirac semimetals

A theory of low-temperature phonon-drag thermopower S-g in three-dimensional (3D) Dirac semimetals has been developed considering screened electron-phonon deformation potential coupling. Numerical investigations of S-g, in the boundary scattering regime for phonons, are made in 3D Dirac semimetal Cd3As2, as a function of temperature T and electron concentration n(e). S-g 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 S-g similar to T-8 (T-4) and S-g similar to n(e)(-5/3)(n(e)(-1/3)) with (without) screening are obtained. These laws with respect to T and n(e) are, respectively, characteristics of 3D phonons and Dirac 3D electrons. Comparison with diffusion thermopower S-d shows that S-g dominates (and is much greater than) S-d for about T > 0.2 K. Herring's law S-g mu(p) similar to T-1, relating phonon limited mobility mu(p) and S-g 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.