Nernst effect in semimetals: the effective mass and the figure of merit

Transport properties in non-Fermi liquid phases of nodal-point semimetals

In this review, we survey the current progress in computing transport properties in semimetals which harbour non-Fermi liquid (NFL) phases. We first discuss the widely-used Kubo formalism, which can be applied to the effective theory describing the stable NFL phase obtained via a renormalization group procedure and, hence, is applicable for temperatures close to zero (e.g. optical conductivity). For finite-temperature regimes, which apply to the computations of the generalized DC conductivity tensors, we elucidate the memory matrix approach. This approach is based on an effective hydrodynamic description of the system, and is especially suited for tackling transport calculations in strongly-interacting quantum field theories, because it does not rely on the existence of long-lived quasiparticles. As a concrete example, we apply these two approaches to find the response of the so-calledLuttinger-Abrikosov-Benelavskii phaseof isotropic three-dimensional Luttinger semimetals, which arises under the effects of long-ranged (unscreened) Coulomb interactions, with the chemical potential fine-tuned to cut exactly the nodal point. In particular, we focus on the electric conductivity tensors, thermal and thermoelectric response, Raman response, free energy, entropy density, and shear viscosity.

Large oscillatory thermal hall effect in kagome metals

The thermal Hall effect recently provided intriguing probes to the ground state of exotic quantum matters. These observations of transverse thermal Hall signals lead to the debate on the fermionic versus bosonic origins of these phenomena. The recent report of quantum oscillations (QOs) in Kitaev spin liquid points to a possible resolution. The Landau level quantization would most likely capture only the fermionic thermal transport effect. However, the QOs in the thermal Hall effect are generally hard to detect. In this work, we report the observation of a large oscillatory thermal Hall effect of correlated Kagome metals. We detect a 180-degree phase change of the oscillation and demonstrate the phase flip as an essential feature for QOs in the thermal transport properties. More importantly, the QOs in the thermal Hall channel are more profound than those in the electrical Hall channel, which strongly violates the Wiedemann-Franz (WF) law for QOs. This result presents the oscillatory thermal Hall effect as a powerful probe to the correlated quantum materials.

Large transverse thermoelectric effect induced by the mixed-dimensionality of Fermi surfaces

Transverse thermoelectric effect, the conversion of longitudinal heat current into transverse electric current, or vice versa, offers a promising energy harvesting technology. Materials with axis-dependent conduction polarity, known as p × n-type conductors or goniopolar materials, are potential candidate, because the non-zero transverse elements of thermopower tensor appear under rotational operation, though the availability is highly limited. Here, we report that a ternary metal LaPt2B with unique crystal structure exhibits axis-dependent thermopower polarity, which is driven by mixed-dimensional Fermi surfaces consisting of quasi-one-dimensional hole sheet with out-of-plane velocity and quasi-two-dimensional electron sheets with in-plane velocity. The ideal mixed-dimensional conductor LaPt2B exhibits an extremely large transverse Peltier conductivity up to ∣αyx∣ = 130 A K-1 m-1, and its transverse thermoelectric performance surpasses those of topological magnets utilizing the anomalous Nernst effect. These results thus manifest the mixed-dimensionality as a key property for efficient transverse thermoelectric conversion.

Measurement setup for Nernst and Seebeck effect at high temperatures and magnetic fields tested on elemental bismuth and full-Heusler compounds

In this work, a measurement setup to study the Seebeck and Nernst effect at high temperatures and high magnetic fields is introduced and discussed. The measurement system allows for simultaneous measurements of both thermoelectric effects up to 700 K and magnetic fields up to 12 T. Based on theoretical concepts, measurement equations are derived that counteract constant spurious offset voltages and, therefore, inhibit systematic errors in the measurement setup. The functionality is demonstrated on polycrystalline samples of elemental bismuth as well as various full-Heusler materials, exhibiting an anomalous Nernst effect. In all samples, the measured Seebeck and Nernst coefficients align excellently with the reported values. This allows future research to substantially extend the measured temperature and field intervals, commonly limited to temperatures below room temperature. For the first time, the thermoelectric and thermomagnetic properties of these materials are reported up to temperatures of 560 K.

Nernst response, viscosity and mobile entropy in vortex liquids

In a liquid of superconducting vortices, a longitudinal thermal gradient generates a transverse electric field. This Nernst signal peaks at an intermediate temperature and magnetic field, presumably where the entropy difference between the vortex core and the superfluid environment is largest. There is a puzzling similarity of the amplitude of this peak across many different superconductors. This peak can be assimilated to a minimum in the viscosity to entropy density ratio of the vortex liquid. Expressed in units ofℏkB, this minimum is one order of magnitude larger than what is seen in common liquids. Moreover, the entropy stocked in the vortex core isnotidentical to the entropy bound to a moving magnetic flux line. Due to a steady exchange of normal quasi-particles, entropy can leak from the vortex core. A slowly moving vortex will be peeled off its entropy within a distance of the order of a superconducting coherence length, provided that theΔEFratio is sufficiently large.

Large Transverse and Longitudinal Magneto-Thermoelectric Effect in Polycrystalline Nodal-Line Semimetal Mg3 Bi2

Topological semimetals provide new opportunities for exploring novel thermoelectric phenomena, owing to their exotic and nontrivial electronic structure topology around the Fermi surface. Herein, the discovery of large transverse and longitudinal magneto-thermoelectric (MTE) effects in Mg₃ Bi₂ is reported and predicted to be a type-II nodal-line semimetal in the absence of spin-orbit coupling (SOC). The maximum transverse power factor is 2182 μW m^-1 K^-2 at 13.5 K and 6 Tesla. The longitudinal power factor reaches up to 3043 μW m^-1 K^-2 , which is 20 times higher than that in a zero-strength magnetic field and is also comparable to state-of-the-art MTE materials. By compensating the Mg loss in Mg-rich conditions for tuning the carrier concentration close to intrinsic state, the sample fabricated in this study exhibits a large linear non-saturating magnetoresistance of 940% under a field of 14 Tesla. Using density functional calculations, the authors attribute the underlying mechanism to the parent linear-dispersed nodal-line electronic structure without SOC and the anisotropic Fermi surface shape with SOC, highlighting the essential role of high carrier mobility and open electron orbits in the moment space. This work offers a new avenue toward highly efficient MTE materials through defect engineering in polycrystalline topological semimetals.

Thermoelectric properties plus phonon and de Haas-van Alphen frequencies of hole/electron-doped [Formula: see text]

We investigate temperature, pressure, and localization dependence of thermoelectric properties, phonon and de Haas-van Alphen (dHvA) frequencies of the anti-ferromagnetic (AFM) CeIn[Formula: see text] using density functional theory (DFT) and local, hybrid, and band correlated functionals. It is found that the maximum values of thermopower, power factor, and electronic figure of merit of this compound occur at low (high) temperatures provided that the 4f-Ce electrons are (not) localized enough. The maximum values of the thermopower, power factor, electronic figure of merit (conductivity parameters), and their related doping levels (do not) considerably depend on the localization degree and pressure. The effects of pressure on these parameters substantially depend on the degree of localization. The phonon frequencies are calculated to be real which shows that the crystal is dynamically stable. From the phonon band structure, the thermal conductivity is predicted to be homogeneous. This prediction is found consistent with the thermal conductivity components calculated along three Cartesian directions. In analogous to the thermoelectric properties, it is found that the dHvA frequencies also depend on both pressure and localization degree. To ensure that the phase transition at Néel temperature cannot remarkably affect the results, we verify the density of states (DOS) of the compound at the paramagnetic phase constructing a non-collinear magnetic structure where the angles of the spins are determined so that the resultant magnetic moment vanishes. The non-collinear results reveal that the DOS and whence the thermoelectric properties of the compound are not changed considerably by the phase transition. To validate the accuracy of the results, the total and partial DOSs are recalculated using DFT plus dynamical mean-field theory (DFT+DMFT). The DFT+DMFT DOSs, in agreement with the hybrid DOSs, predict the Kondo effect in this compound.

Seebeck-driven transverse thermoelectric generation

When a temperature gradient is applied to a closed circuit comprising two different conductors, a charge current is generated via the Seebeck effect¹. Here, we utilize the Seebeck-effect-induced charge current to drive 'transverse' thermoelectric generation, which has great potential for energy harvesting and heat sensing applications owing to the orthogonal geometry of the heat-to-charge-current conversion^2-9. We found that, in a closed circuit comprising thermoelectric and magnetic materials, artificial hybridization of the Seebeck effect into the anomalous Hall effect¹⁰ enables transverse thermoelectric generation with a similar symmetry to the anomalous Nernst effect^11-27. Surprisingly, the Seebeck-effect-driven transverse thermopower can be several orders of magnitude larger than the anomalous-Nernst-effect-driven thermopower, which is clearly demonstrated by our experiments using Co₂MnGa/Si hybrid materials. The unconventional approach could be a breakthrough in developing applications of transverse thermoelectric generation.

Experimental setup for the Seebeck and Nernst coefficient measurements

A new experimental setup is designed for the measurement of Seebeck and Nernst coefficients on the single crystal flakes and polycrystalline samples. The setup utilizes the multifunctional probe assembly of the physical property measurement system by Quantum Design, Inc. and can measure in the temperature range of 1.8 K-380 K up to 8 T magnetic fields. The experimental measurement was fully automated through a computer using the code written in LabVIEW software. The setup is capable of measurements on samples as small as 2 × 1 mm² in size and thickness as small as a few micrometers, which is quite important for the crystal flakes grown using the vapor transport method. The determination of the coefficients is based on the quasi-static approach, with the thermal gradient of 0.2 K-1.2 K across the sample in the measured temperature range of 1.8 K-300 K. The sensitivity of the instrument is better than 0.1 µV/K, and the accuracy is better than ∼0.5 µV/K, which can be further improved with the better quality of electrical contacts on the sample. The Seebeck and Nernst coefficient measurements performed on some well-studied semimetallic (bismuth), thermoelectric (Bi₂Se₃), and superconducting (FeTe_0.5Se_0.5) systems are also presented.

Nernst effect in metals and superconductors: a review of concepts and experiments

The Nernst effect is the transverse electric field produced by a longitudinal thermal gradient in the presence of a magnetic field. At the beginning of this century, Nernst experiments on cuprates were analyzed assuming that: (i) the contribution of quasi-particles to the Nernst signal is negligible; and (ii) Gaussian superconducting fluctuations cannot produce a Nernst signal well above the critical temperature. Both these assumptions were contradicted by subsequent experiments. This paper reviews experiments documenting multiple sources of a Nernst signal, which, according to the Bridgman relation, measures the flow of transverse entropy caused by a longitudinal particle flow. Along the lines of Landauer's approach to transport phenomena, the magnitude of the transverse magneto-thermoelectric response is linked to the quantum of thermoelectric conductance and a number of material-dependent length scales: the mean free path, the Fermi wavelength, the de Broglie thermal wavelength and the superconducting coherence length. Extremely mobile quasi-particles in dilute metals generate a widely-documented Nernst signal. Fluctuating Cooper pairs in the normal state of superconductors have been found to produce a detectable Nernst signal with an amplitude conforming to the Gaussian theory, first conceived by Ussishkin, Sondhi and Huse. In addition to these microscopic sources, mobile Abrikosov vortices, mesoscopic objects simultaneously carrying entropy and magnetic flux, can produce a sizeable Nernst response. Finally, in metals subject to a magnetic field strong enough to truncate the Fermi surface to a few Landau tubes, each exiting tube generates a peak in the Nernst response. The survey of these well-established sources of the Nernst signal is a helpful guide to identify the origin of the Nernst signal in other controversial cases.

Thermoelectric probe for the Rashba spin-orbit interaction strength in a two dimensional electron gas

The thermoelectric coefficients of a two dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) are presented here. In the absence of a magnetic field, thermoelectric coefficients are enhanced due to the Rashba SOI. In the presence of a magnetic field, the thermoelectric coefficients of spin-up and spin-down electrons oscillate with different frequencies and produces beating patterns in the components of the total thermoelectric power and the total thermal conductivity. We also provide analytical expressions for the thermoelectric coefficients to explain the formation of the beating pattern. We obtain a simple relation which determines the strength of the Rashba SOI if the magnetic fields corresponding to any two successive beat nodes are known from the experiment.

Giant Nernst effect and bipolarity in the quasi-one-dimensional metal Li0.9Mo6O17

The Nernst coefficient for the quasi-one-dimensional metal, Li{0.9}Mo{6}O{17}, is found to be among the largest known for metals (ν≃500  μV/KT at T∼20  K), and is enhanced in a broad range of temperature by orders of magnitude over the value expected from Boltzmann theory for carrier diffusion. A comparatively small Seebeck coefficient implies that Li{0.9}Mo{6}O{17} is bipolar with large, partial Seebeck coefficients of opposite sign. A very large thermomagnetic figure of merit, ZT∼0.5, is found at high field in the range T≈35-50  K.

Giant Nernst-Ettingshausen oscillations in semiclassically strong magnetic fields

We consider the Nernst-Ettingshausen (NE) effect in the presence of semiclassically strong magnetic fields for a quasi-two-dimensional system with a parabolic or linear dispersion of carriers. We show that the occurring giant oscillations of the NE coefficient are coherent with the recent experimental observation in graphene, graphite, and bismuth. In the 2D case we find the exact shape of these oscillations and show that their magnitude decreases (increases) with enhancement of the Fermi energy for Dirac fermions (normal carriers). With a crossover to the 3D spectrum the phase of the oscillations shifts, their amplitude decreases, and the peaks become asymmetric.

The Nernst effect and the boundaries of the Fermi liquid picture

Following the observation of an anomalous Nernst signal in cuprates, the Nernst effect has been explored in a variety of metals and superconductors during the past few years. This paper reviews the results obtained during this exploration, focusing on the Nernst response of normal quasi-particles as opposed to the one generated by superconducting vortices or by short-lived Cooper pairs. Contrary to what has been often assumed, the so-called Sondheimer cancelation does not imply a negligible Nernst response in a Fermi liquid. In fact, the amplitude of the Nernst response measured in various metals in the low-temperature limit is scattered over six orders of magnitude. According to the data, this amplitude is roughly set by the ratio of electron mobility to Fermi energy, in agreement with the implications of semi-classical transport theory.

Thermoelectric response near a quantum critical point: the case of CeCoIn5

We present a study of thermoelectric coefficients in CeCoIn5 down to 0.1 K and up to 16 T in order to probe the thermoelectric signatures of quantum criticality. In the vicinity of the field-induced quantum critical point, the Nernst coefficient nu exhibits a dramatic enhancement without saturation down to the lowest measured temperature. The dimensionless ratio of the Seebeck coefficient to the electronic specific heat shows a minimum at a temperature close to threshold of the quasiparticle formation. Close to Tc(H), in the vortex-liquid state, the Nernst coefficient behaves anomalously in puzzling contrast with other superconductors and standard vortex dynamics.

Oscillating Nernst-Ettingshausen effect in bismuth across the quantum limit

In elemental bismuth, 10(5) atoms share a single itinerant electron. Therefore, a moderate magnetic field can confine electrons to the lowest Landau level. We report on the first study of metallic thermoelectricity in this regime. The main thermoelectric response is off-diagonal with an oscillating component several times larger than the nonoscillating background. When the first Landau level attains the Fermi energy, both the Nernst and the Ettingshausen coefficients sharply peak, and the latter attains a temperature-independent maximum. These features are yet to be understood. We note a qualitative agreement with a theory invoking current-carrying edge excitations.