Quantum Hall and magneto-Seebeck effects in three-dimensional Dirac and Weyl semimetals

Large and non-saturating magneto-Seebeck coefficient S_xx as a function of magnetic field B is predicted [Sci. Adv. 4, eeat2621 (2018)] to occur in three-dimensional (3D) Dirac/Weyl semimetal (DWS). This is because by keeping the number of charge carriers n₀ constant, the Hall resistivity is given by the classical formula ρ_yx=B/n₀e (e is the elementary charge), while the thermoelectric Hall coefficient α_xy approaches a finite value at the quantum limit (QL), where only the zeroth Landau level is occupied [PRB 99, 155123 (2019)]. Therefore, within the dissipationless limit, S_xx≈ρ_yx·α_xy∝B. On the other hand, saturating S_xx is observed in 3D DWS ZrTe₅, where 3D quantum Hall effect (QHE) occurs [Nat. Commun. 12, 3197 (2021)]. It was proposed [PRL 125, 206601 (2020)] that charge density wave (CDW) plays a decisive role in 3D QHE. However, transport measurement in ZrTe₅ do not indicate the signs of CDW.

In our talk, we discuss the magneto-Seebeck effect in 3D DWS. We found that by keeping the chemical potential constant, both ρ_yx and α_xy exhibit plateaus at the QL. We analytically show that the Hall plateau is given by ρ_yx∝λ_F^z (λ_F^z is the Fermi wavelength parallel to B), as has been recently observed in ZrTe₅ as a hallmark of 3D QHE. In this condition, the massless fermions are transformed into a Fermi liquid (FL) system. Particularly, we found that the S_xx of the FL phase is expressed by the harmonic sum of the Fermi and thermal de Broglie wavelengths, scaled by the magnetic length.