The thermoelectric Hall effect is the generation of a transverse heat current upon applying an electric field in the presence of a magnetic field. Here we demonstrate that the thermoelectric Hall conductivity α xy in the three-dimensional Dirac semimetal ZrTe 5 acquires a robust plateau in the extreme quantum limit 1 arXiv:1904.02157v2 [cond-mat.mtrl-sci] of magnetic field. The plateau value is independent of the field strength, disorder strength, carrier concentration, or carrier sign. We explain this plateau theoretically and show that it is a unique signature of three-dimensional Dirac or Weyl electrons in the extreme quantum limit. We further find that other thermoelectric coefficients, such as the thermopower and Nernst coefficient, are greatly enhanced over their zero-field values even at relatively low fields. SUPPLEMENTARY NOTE 1: EXPERIMENTAL DETAILS SUPPLEMENTARY FIG. 1: Optical image of our experimental setup. A chip heater (outlined by red dashed line) and a copper heat sink are mounted on the thermal bath by varnish and silver paste, respectively. A copper film is deposited on top of the heater to reduce temperature nonuniformity. Silver paste is used to make electrical contacts. 25 µm gold wires are used for electrical leads due to their small Seebeck coefficient. A Type-E thermocouple measures the temperature difference between the hot end of sample and the thermal bath, with one joint attaching to the sample and the other attaching to the pad on the thermal bath. SUPPLEMENTARY FIG. 2: Schematics of two-point measurement (left) and four-point measurement (right) setups.The optical image of our measurement setup is shown in Supplementary Fig. 1. We use a two-point method to measure the temperature difference between the hot end and cold end of the sample (see Supplementary Fig. 2, left). Normally, two Type-E thermocouples are attached to the heater stage and the heat sink, respectively. The differential of the measured values between two stages is ΔT=(TH-T0)-(TL-T0)=TH-TL. Here, TH, TL and T0 are the temperature of the hot end, the heat sink and the thermal bath, respectively. In our experiment, only one

Thermoelectric materials can recover electrical energy from waste heat and vice versa, which are of great significance in green energy harvesting and solid state refrigerator. The thermoelectric figure of merit (zT) quantifies the energy conversion efficiency, and a large Seebeck or Nernst effect is crucial for the development of thermoelectric devices. Here we present a significantly large Nernst thermopower in topological semimetal ZrTe5, which is attributed to both strong Berry curvature and bipolar transport. The largest in-plane 𝑆 𝑥𝑦 (when B//b) approaches 1900 𝜇𝑉/𝐾 at T=100K and B=13T, and the out-of-plane 𝑆 𝑥𝑧 (when B//c) reaches 5000 𝜇𝑉/𝐾. As a critical part of 𝑧 𝑁 𝑇, the linearly increased in-plane 𝑆 𝑥𝑦 and resistivity 𝜌 𝑦𝑦 regard to B induces an almost linear increasing transversal 𝑧 𝑁 𝑇 without saturate under high fields. The maximum 𝑧 𝑁 𝑇 of 0.12 was obtained at B=13 T and T= 120K, which significantly surmounts its longitudinal counterpart under the same condition.

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We have investigated the magneto-transport properties of β-Bi4I4 bulk crystal, which was recently theoretically proposed and experimentally demonstrated to be a topological insulator. At low temperature T and magnetic field B, a series of Shubnikov-De Haas(SdH) oscillations are observed on the magnetoresistivity (MR). The detailed analysis reveals a light cyclotron mass of 0.1 me, and the field angle dependence of MR reveals that the SdH oscillations originate from a convex Fermi surface. In the extreme quantum limit (EQL) region, there is a metal-insulator transition occurring soon after the EQL. We perform the scaling analysis, and all the isotherms fall onto a universal scaling with a fitted critical exponent  ≈ 6.5. The enormous value of critical exponent  implies this insulating quantum phase originated from strong electron-electron interactions in high fields. However, in the far end of EQL, both the longitudinal and Hall resistivity increase exponentially with B, and the temperature dependence of the MR reveals an energy gap induced by the high magnetic field, signifying a magnetic freeze-out effect. Our findings indicate that bulk β-Bi4I4 is an excellent candidate for a 3D topological system for exploring EQL physics and relevant exotic quantum phases.