Two topological thermoelectric effects, the nonlinear anomalous Ettingshausen effect and the quantized thermoelectric Hall effect, were investigated in the two-dimensional (2D) organic Dirac fermion (DF) system a-(BEDT-TTF)₂I₃.

(1) Nonlinear anomalous Ettingshausen effect (AEE)

So far, we have experimentally confirmed that the weak charge ordering (CO) state of α-(BEDT-TTF)₂I₃, which is the region close to the 2D massless DF phase in the CO phase, is a 2D massive DF state with a small CO gap. Because the finite Berry curvature dipole was expected in the massive DF state with tilted Dirac cones, we experimentally searched for the nonlinear anomalous Hall effect (AHE) in the current-carrying state in the weak CO state at zero magnetic field, and successfully observed it.

Here, we newly proposed a novel current-induced thermoelectric phenomenon, the nonlinear AEE, which is a thermoelectric analogue of the nonlinear AHE [1]. The thermoelectric Berry curvature dipole was introduced to explain this thermoelectric effect instead of the Berry curvature dipole. The nonlinear AEE is a phenomenon in which a temperature gradient proportional to the square current is induced in the direction perpendicular to the current. It exhibits rectifying characteristics (nonreciprocity). The generated transverse heat current flows unidirectionally even under an AC current. The nonlinear AEE occurs simultaneously with the nonlinear AHE as shown in Fig. 1. We estimated that the nonlinear AEE is sufficiently observable in the current-carrying state in the weak CO state of α-(BEDT-TTF)₂I₃.

Fig. 1. Schematic of the current-induced topological transport phenomena, nonlinear anomalous Hall and Ettingshausen effects, in the current-carrying state in the thermally isolated 2D massive Dirac fermion system. Λ (Θ) indicates the (thermoelectric) Berry curvature dipole.

(2) Quantized thermoelectric Hall effect (QTHE)

The high-performance thermoelectricity, that is boundless increase of the Seebeck coefficient S_xx, has been theoretically and experimentally investigated in 3D topological semimetals with nodal points (Dirac/Weyl semimetals) at the high-magnetic-field quantum limit. Recently, more advantageous thermoelectric effect called QTHE was proposed in the 2D massless DF system at the clean limit. The thermoelectric conductivity αxy takes a quantized constant value of (4log2)k_Be/h, which is independent of temperature, magnetic field, and carrier density. It causes the boundless increase of S_xx even at low temperatures. α-(BEDT-TTF)₂I₃ was considered as one of candidate materials.

We investigated the thermoelectricity of the 2D massless DF system in real α-(BEDT-TTF)₂I₃ under high magnetic fields [2]. Because of its small electron group velocity, the Zeeman splitting becomes relatively important and cannot be ignored in α-(BEDT-TTF)₂I₃. We showed that the Zeeman splitting of the n = 0 Landau level suppresses the QTHE: α_xy decreases from the quantized value at low temperatures leaving a shoulder-like structure, and S_xx decreases after linear increase at high magnetic fields leaving a hump-like structure (Fig. 2). These features were observed in our previous experiment. In contrast to 3D nodal-point semimetals with robust gapless features, it is difficult to realize the QTHE in real 2D Dirac fermion systems due to the Zeeman gap in the n = 0 Landau level under high magnetic fields. 

Fig. 2. The magnetic field dependence of the Seebeck coefficient of the 2D massless Dirac fermion system at a fixed carrier density around the charge neutrality point. The solid and dashed curves are for cases with and without the Zeeman effect.

References

• [1] T. Osada and A. Kiswandhi, J. Phys. Soc. Jpn. 90, 053704 (2021).
• [2] T. Osada, J. Phys. Soc. Jpn. 90, 113703 (2021).

Authors

• T. Osada, A. Kiswandhi, M. Sato, K. Uchida, and T. Taen