Anomalous Nernst Effect in the Dirac Semimetal Cd_{3}As_{2}

Multipocket synergy towards high thermoelectric performance in topological semimetal TaAs2

Charge-carrier compensation in topological semimetals amplifies the Nernst signal and simultaneously degrades the Seebeck coefficient. In this study, we report the simultaneous achievement of both a large Nernst signal and an unsaturating magneto-Seebeck coefficient in a topological nodal-line semimetal TaAs2 single crystal. The unique dual-high transverse and longitudinal thermopowers are attributed to multipocket synergy effects: the combination of a strong phonon-drag effect and the two overlapping highly dispersive conduction and valence bands with electron-hole compensation and high mobility, promising a large Nernst effect; the third Dirac band causes a large magneto-Seebeck effect. High transverse and longitudinal power factors of ~3100 and ~50 μW cm-1 K-2, respectively, are achieved, surpassing those of other topological semimetals and mainstream semiconductors. Our study presents a feasible approach for optimizing the longitudinal and transverse thermopowers in topological semimetals simultaneously and demonstrates the potential of TaAs2 for low temperature solid-state cooling.

A magneto-thermoelectric with a high figure of merit in topological insulator Bi88Sb12

High thermoelectric performance is generally achieved by synergistically optimizing two or even three of the contradictorily coupled thermoelectric parameters. Here we demonstrate magneto-thermoelectric correlation as a strategy to achieve simultaneous gain in an enhanced Seebeck coefficient and reduced thermal conductivity in topological materials. We report a large magneto-Seebeck effect and high magneto-thermoelectric figure of merit of 1.7 ± 0.2 at 180 K and 0.7 T in a single-crystalline Bi88Sb12 topological insulator. This result fills a gap of a high performance below 300 K and is promising for low-temperature thermoelectric applications. The large magneto-Seebeck response is attributed to the ultrahigh mobility and the Dirac band dispersion. The application of a low magnetic field to achieve a high thermoelectric performance can be extended to topological materials with similar features that are rapidly emerging because it synergistically optimizes the thermoelectric parameters.

Crystal Chemistry and Design Principles of Altermagnets

Altermagnetism was very recently identified as a new type of magnetic phase beyond the conventional dichotomy of ferromagnetism (FM) and antiferromagnetism (AFM). Its globally compensated magnetization and directional spin polarization promise new properties such as spin-polarized conductivity, spin-transfer torque, anomalous Hall effect, tunneling, and giant magnetoresistance that are highly useful for the next-generation memory devices, magnetic detectors, and energy conversion. Though this area has been historically led by the thin-film community, the identification of altermagnetism ultimately relies on precise magnetic structure determination, which can be most efficiently done in bulk materials. Our review, written from a materials chemistry perspective, intends to encourage materials and solid-state chemists to make contributions to this emerging topic through new materials discovery by leveraging neutron diffraction to determine the magnetic structures as well as bulk crystal growth for exploring exotic properties. We first review the symmetric classification for the identification of altermagnets with a summary of chemical principles and design rules, followed by a discussion of the unique physical properties in relation to crystal and magnetic structural symmetry. Several major families of compounds in which altermagnets have been identified are then reviewed. We conclude by giving an outlook for future directions.

Hybridizing anomalous Nernst effect in artificially tilted multilayer based on magnetic topological material

Transverse thermoelectric conversion holds significant potential in addressing complex challenges faced by classical Seebeck/Peltier modules. A promising transverse thermoelectric phenomenon is the anomalous Nernst effect originating from nontrivial band structures in magnetic topological materials. However, the currently reported performance of the anomalous Nernst effect in topological materials, e.g., Co2MnGa, remains insufficient for practical thermoelectric applications. Here, we unveil an unconventional availability of the anomalous Nernst effect by integrating magnetic topological materials into artificially tilted multilayers, known to exhibit the structure-induced transverse thermoelectric conversion due to the off-diagonal Seebeck effect. Our experiments reveal that the transverse thermoelectric performance in Co2MnGa-based artificially tilted multilayers is improved through the hybrid action of the anomalous Nernst and off-diagonal Seebeck effects, with the magnetization-dependent performance modulation being one order of magnitude greater than the performance achievable with the anomalous Nernst effect alone. This synergy underscores the importance of hybrid transverse thermoelectric conversion and paves a way for advancing thermoelectric applications using magnetic materials.

Geometry, anomaly, topology, and transport in Weyl fermions

Weyl fermions are one of the simplest objects that link ideas in geometry and topology to high-energy physics and condensed matter physics. Although the existence of Weyl fermions as elementary particles remains dubious, there is mounting evidence of their existence as quasiparticles in certain condensed matter systems. Such systems are termed Weyl semimetals (WSMs). Needless to say, WSMs have emerged as a fascinating class of materials with unique electronic properties, offering a rich playground for both fundamental research and potential technological applications. This review examines recent advancements in understanding electron transport in WSMs. We begin with a pedagogical introduction to the geometric and topological concepts critical to understanding quantum transport in Weyl fermions. We then explore chiral anomaly, a defining feature of WSMs, and its impact on transport phenomena such as longitudinal magnetoconductance and planar Hall effect. The Maxwell-Boltzmann transport theory extended beyond the standard relaxation-time approximation is then discussed in the context of Weyl fermions, which is used to evaluate various transport properties. Attention is also given to the effects of strain-induced gauge fields and external magnetic fields in both time-reversal broken and inversion asymmetric inhomogeneous WSMs. The review synthesizes theoretical insights, experimental observations, and numerical simulations to provide a comprehensive understanding of the complex transport behaviors in WSMs, aiming to bridge the gap between theoretical predictions and experimental verification.

Experimental progress in Eu(Al,Ga)4topological antiferromagnets

The non-trivial magnetic and electronic phases occurring in topological magnets are often entangled, thus leading to a variety of exotic physical properties. Recently, the BaAl4-type compounds have been extensively investigated to elucidate the topological features appearing in their real- and momentum spaces. In particular, the topological Hall effect and the spin textures, typical of the centrosymmetric Eu(Al,Ga)4family, have stimulated extensive experimental and theoretical research. In this topical review, we discuss the latest findings on the Eu(Al,Ga)4topological antiferromagnets and related materials, arising from a wide range of experimental techniques. We show that Eu(Al,Ga)4represents a suitable platform to explore the interplay between lattice-, charge-, and spin degrees of freedom, and associated emergent phenomena. Finally, we address some key questions open to future investigation.

Extremely Large Anomalous Hall Conductivity and Unusual Axial Diamagnetism in a Quasi-1D Dirac Material La3MgBi5

Anomalous Hall effect (AHE), one of the most important electronic transport phenomena, generally appears in ferromagnetic materials but is rare in materials without magnetic elements. Here, a study of La3MgBi5 is presented, whose band structure carries multitype Dirac fermions. Although magnetic elements are absent in La3MgBi5, the signals of AHE can be observed. In particular, the anomalous Hall conductivity is extremely large, reaching 42,356 Ω-1 cm-1 with an anomalous Hall angle of 8.8%, the largest one that has been observed in the current AHE systems. The AHE is suggested to originate from the combination of skew scattering and Berry curvature. Another unique property discovered in La3MgBi5 is the axial diamagnetism. The diamagnetism is significantly enhanced and dominates the magnetization in the axial directions, which is the result of the restricted motion of the Dirac fermion at the Fermi level. These findings not only establish La3MgBi5 as a suitable platform to study AHE and quantum transport but also indicate the great potential of 315-type Bi-based materials for exploring novel physical properties.

Extraordinary Thermoelectric Properties of Topological Surface States in Quantum-Confined Cd3As2 Thin Films

Topological insulators and semimetals have been shown to possess intriguing thermoelectric properties promising for energy harvesting and cooling applications. However, thermoelectric transport associated with the Fermi arc topological surface states on topological Dirac semimetals remains less explored. This work systematically examines thermoelectric transport in a series of topological Dirac semimetal Cd3As2 thin films grown by molecular beam epitaxy. Surprisingly, significantly enhanced Seebeck effect and anomalous Nernst effect are found at cryogenic temperatures when the Cd3As2 layer is thin. In particular, a peak Seebeck coefficient of nearly 500 µV K-1 and a corresponding thermoelectric power factor over 30 mW K-2 m-1 are observed at 5 K in a 25-nm-thick sample. Combining angle-dependent quantum oscillation analysis, magnetothermoelectric measurement, transport modeling, and first-principles simulation, the contributions from bulk and surface conducting channels are isolated and the unusual thermoelectric properties are attributed to the topological surface states. The analysis showcases the rich thermoelectric transport physics in quantum-confined topological Dirac semimetal thin films and suggests new routes to achieving high thermoelectric performance at cryogenic temperatures.

Tunable positions of Weyl nodes via magnetism and pressure in the ferromagnetic Weyl semimetal CeAlSi

The noncentrosymmetric ferromagnetic Weyl semimetal CeAlSi with simultaneous space-inversion and time-reversal symmetry breaking provides a unique platform for exploring novel topological states. Here, by employing multiple experimental techniques, we demonstrate that ferromagnetism and pressure can serve as efficient parameters to tune the positions of Weyl nodes in CeAlSi. At ambient pressure, a magnetism-facilitated anomalous Hall/Nernst effect (AHE/ANE) is uncovered. Angle-resolved photoemission spectroscopy (ARPES) measurements demonstrated that the Weyl nodes with opposite chirality are moving away from each other upon entering the ferromagnetic phase. Under pressure, by tracing the pressure evolution of AHE and band structure, we demonstrate that pressure could also serve as a pivotal knob to tune the positions of Weyl nodes. Moreover, multiple pressure-induced phase transitions are also revealed. These findings indicate that CeAlSi provides a unique and tunable platform for exploring exotic topological physics and electron correlations, as well as catering to potential applications, such as spintronics.

Thermoelectric properties of ballistic Normal-Weyl semimetal-Normal junction

Weyl semimetals are a new class of topological materials possessing outstanding physical properties. We investigate the thermoelectric properties of a ballistic Weyl semimetal specimen connected to two normal contacts. We introduce a model to evaluate the thermoelectric coefficients of the junction and analyze its features along two distinct directions, one along the chiral axis of the Weyl semimetal and the other perpendicular to it. We demonstrate that the thermoelectric response of this junction depends on whether it is along the chiral axis of the Weyl semimetal or not. Electrical and thermal conductances of this junction reveal considerable dependence on the length and chemical potential of the Weyl semimetal layer. In particular, we observe that, decreasing the chemical potential in the normal contacts enhances the Seebeck coefficient and thermoelectric figure of merit of the junction to substantial values. Hence, we unveil that a ballistic junction of Weyl semimetal can serve as a fundamental segment for application in future thermoelectric devices for thermal energy harvesting.

Magnetoelectric tuning of spin, valley, and layer-resolved anomalous Nernst effect in transition-metal dichalcogenides bilayers

The anomalous Nernst coefficient (ANC) for transition-metal dichalcogenide (TMD) bilayers is studied with a focus on the interplay between layer pseudospin, spin, and valley degrees of freedom when electric and exchange fields are present. Breaking the inversion and time reversal symmetries via respectively electric and exchange fields results for bilayer TMDs in a spin-valley-layer polarized total ANC. Conditions are determined for controlling the spin, valley, and layer-resolved contributions via electric field tuning. Our results demonstrate the control of layer degree of freedom in bilayer TMDs magnetoelectrically which is of relevance for possible applications in spin/valley caloritronics.

Enhanced photonic spin Hall effect in Dirac semimetal metamaterial enabled by zero effective permittivity

With the recent discovery of three dimensional Dirac semimetals, their integrations with the optoelectronic devices allow the novel optical effects and functionalities. Here, we theoretically report the photonic spin Hall effect in a periodic structure, where three dimensional Dirac semimetals and the dielectric materials are assembled into the stack. The incident angle and frequency dependent spin shift spectrum reveals that the spin shifts of the transmitted wave in this structure emerge the obvious peaks and valleys for the horizontal polarized wave and their magnitudes and positions display a distinct dependence on the incident angle around the specific frequency. These observations originate from its zero value of the effective perpendicular permittivity and its greatly reduced transmission in the multilayered structure, whose mechanism is different from those in the previous works. Moreover, both the peaks and valleys of the transmitted spin shift are significantly sensitive to the Fermi energy of three dimensional Dirac semimetals, whose magnitudes and positions can be tuned by varying it. Our results highlight the vital role of three dimensional Dirac semimetals in their applications of the spin photonic devices and pave the way to explore the tunable photonic spin Hall effect by engineering their Fermi energies.

Local thermoelectric response from a single Néel domain wall

Spatially resolved thermoelectric detection of magnetic systems provides a unique platform for the investigation of spintronic and spin caloritronic effects. Hitherto, these investigations have been resolution-limited, confining analysis of the thermoelectric response to regions where the magnetization is uniform or collinear at length scales comparable to the domain size. Here, we investigate the thermoelectric response from a single trapped domain wall using a heated scanning probe. Following this approach, we unambiguously resolve the domain wall due to its local thermoelectric response. Combining analytical and thermal micromagnetic modeling, we conclude that the measured thermoelectric signature is unique to that of a domain wall with a Néel-like character. Our approach is highly sensitive to the plane of domain wall rotation, which permits the distinct identification of Bloch or Néel walls at the nanoscale and could pave the way for the identification and characterization of a range of noncollinear spin textures through their thermoelectric signatures.

In-plane magnetotransport phenomena in tilted Weyl semimetals

The nontrivial Berry curvature and chiral anomaly result in plenty of interesting magnetotransport and magneto-thermoelectric transport phenomena in Weyl semimetals, two of which are the planar Hall effect and planar Nernst effect. Based on the semi-classical Boltzmann theory, we theoretically study the in-plane magnetotransport coefficients (including electric conductivity, thermoelectric conductivity and Nernst thermopower) for both type-I and type-II Weyl semimetals using a linearized low-energy Hamiltonian. We find that for tilt-coplanar setup where the electric field (or temperature gradient) is applied along the tilted direction of the Weyl nodes, the planar Hall conductivity (or planar Nernst thermopower) shows a magnetic field linear dependence. And these linear responses do no obey the reportedcosθsinθdependence on the angleθbetween the magnetic and electric field for planar Hall effect. For tilt-perpendicular setup where the applied field (Eor∇T) and magnetic field are perpendicular to the tilted direction, the planar Hall conductivity (or planar Nernst thermopower) mainly follows a magnetic field quadratic dependence, and it satisfies thecosθsinθcharacteristic. There are also anomalous Hall effect and anomalous Nernst effect in the plane perpendicular to the tilted direction of the two oppositely tilted Weyl nodes. These findings can be verified experimentally by changing the direction and magnitude of the in-plane magnetic field.

Ultrafast photothermoelectric effect in Dirac semimetallic Cd3As2 revealed by terahertz emission

The thermoelectric effects of topological semimetals have attracted tremendous research interest because many topological semimetals are excellent thermoelectric materials and thermoelectricity serves as one of their most important potential applications. In this work, we reveal the transient photothermoelectric response of Dirac semimetallic Cd₃As₂, namely the photo-Seebeck effect and photo-Nernst effect, by studying the terahertz (THz) emission from the transient photocurrent induced by these effects. Our excitation polarization and power dependence confirm that the observed THz emission is due to photothermoelectric effect instead of other nonlinear optical effect. Furthermore, when a weak magnetic field (~0.4 T) is applied, the response clearly indicates an order of magnitude enhancement on transient photothermoelectric current generation compared to the photo-Seebeck effect. Such enhancement supports an ambipolar transport nature of the photo-Nernst current generation in Cd₃As₂. These results highlight the enhancement of thermoelectric performance can be achieved in topological Dirac semimetals based on the Nernst effect, and our transient studies pave the way for thermoelectric devices applicable for high field circumstance when nonequilibrium state matters. The large THz emission due to highly efficient photothermoelectric conversion is comparable to conventional semiconductors through optical rectification and photo-Dember effect.

Many topological semimetals are excellent thermoelectric materials, but previous studies were limited to steady-state properties. Here, the authors observe a transient thermoelectric response in Cd₃As₂ by detecting the resulting THz emission, with an enhanced response when a small magnetic field is applied.

Exchange-biased topological transverse thermoelectric effects in a Kagome ferrimagnet

Kagome metal TbMn6Sn6 was recently discovered to be a ferrimagnetic topological Dirac material by scanning tunneling microscopy/spectroscopy measurements. Here, we report the observation of large anomalous Nernst effect and anomalous thermal Hall effect in this compound. The anomalous transverse transport is consistent with the Berry curvature contribution from the massive Dirac gaps in the 3D momentum space as demonstrated by our first-principles calculations. Furthermore, the transverse thermoelectric transport exhibits asymmetry with respect to the applied magnetic field, i.e., an exchange-bias behavior. Together, these features place TbMn6Sn6 as a promising system for the outstanding thermoelectric performance based on anomalous Nernst effect.

Giant anomalous Nernst signal in the antiferromagnet YbMnBi2

A large anomalous Nernst effect (ANE) is crucial for thermoelectric energy conversion applications because the associated unique transverse geometry facilitates module fabrication. Topological ferromagnets with large Berry curvatures show large ANEs; however, they face drawbacks such as strong magnetic disturbances and low mobility due to high magnetization. Herein, we demonstrate that YbMnBi2, a canted antiferromagnet, has a large ANE conductivity of ~10 A m-1 K-1 that surpasses large values observed in other ferromagnets (3-5 A m-1 K-1). The canted spin structure of Mn guarantees a non-zero Berry curvature, but generates only a weak magnetization three orders of magnitude lower than that of general ferromagnets. The heavy Bi with a large spin-orbit coupling enables a large ANE and low thermal conductivity, whereas its highly dispersive px/y orbitals ensure low resistivity. The high anomalous transverse thermoelectric performance and extremely small magnetization make YbMnBi2 an excellent candidate for transverse thermoelectrics.

Topological phase and thermoelectric properties of bialkali bismuthide compounds (Na, K)2RbBi from first-principles

We report the topological phase and thermoelectric properties of bialkali bismuthide compounds (Na, K)₂RbBi, as yet hypothetical. The topological phase transitions of these compounds under hydrostatic pressure are investigated. The calculated topological surface states andZ₂topological index confirm the nontrivial topological phase. The electronic properties and transport coefficients are obtained using the density functional theory combined with the Boltzmann transport equation. The relaxation times are determined using the deformation potential theory to calculate the electronic thermal and electrical conductivity. The calculated mode Grüneisen parameters are substantial, indicating strong anharmonic acoustic phonons scattering, which results in an exceptionally low lattice thermal conductivity. These compounds also have a favorable power factor leading to a relatively flat p-type figure-of-merit over a broad temperature range. Furthermore, the mechanical properties and phonon band dispersions show that these structures are mechanically and dynamically stable. Therefore, they offer excellent candidates for practical applications over a wide range of temperatures.

Large magnon-induced anomalous Nernst conductivity in single-crystal MnBi

Thermoelectric modules are a promising approach to energy harvesting and efficient cooling. In addition to the longitudinal Seebeck effect, transverse devices utilizing the anomalous Nernst effect (ANE) have recently attracted interest. For high conversion efficiency, it is required that the material have a large ANE thermoelectric power and low electrical resistance, which lead to the conductivity of the ANE. ANE is usually explained in terms of intrinsic contributions from Berry curvature. Our observations suggest that extrinsic contributions also matter. Studying single-crystal manganese-bismuth (MnBi), we find a high ANE thermopower (∼10 μV/K) under 0.6 T at 80 K, and a transverse thermoelectric conductivity of over 40 A/Km. With insight from theoretical calculations, we attribute this large ANE predominantly to a new advective magnon contribution arising from magnon-electron spin-angular momentum transfer. We propose that introducing a large spin-orbit coupling into ferromagnetic materials may enhance the ANE through the extrinsic contribution of magnons.

Giant magnetoresistance and topological Hall effect in the EuGa4antiferromagnet

We report on systematic temperature- and magnetic field-dependent studies of the EuGa₄binary compound, which crystallizes in a centrosymmetric tetragonal BaAl₄-type structure with space groupI4/mmm. The electronic properties of EuGa₄single crystals, with an antiferromagnetic (AFM) transition atT_N∼ 16.4 K, were characterized via electrical resistivity and magnetization measurements. A giant nonsaturating magnetoresistance was observed at low temperatures, reaching∼7×104% at 2 K in a magnetic field of 9 T. In the AFM state, EuGa₄undergoes a series of metamagnetic transitions in an applied magnetic field, clearly manifested in its field-dependent electrical resistivity. BelowT_N, in the ∼4-7 T field range, we observe also a clear hump-like anomaly in the Hall resistivity which is part of the anomalous Hall resistivity. We attribute such a hump-like feature to the topological Hall effect, usually occurring in noncentrosymmetric materials known to host topological spin textures (as e.g., magnetic skyrmions). Therefore, the family of materials with a tetragonal BaAl₄-type structure, to which EuGa₄and EuAl₄belong, seems to comprise suitable candidates on which one can study the interplay among correlated-electron phenomena (such as charge-density wave or exotic magnetism) with topological spin textures and topologically nontrivial bands.

Berry curvature generation detected by Nernst responses in ferroelectric Weyl semimetal

The quest for nonmagnetic Weyl semimetals with high tunability of phase has remained a demanding challenge. As the symmetry-breaking control parameter, the ferroelectric order can be steered to turn on/off the Weyl semimetals phase, adjust the band structures around the Fermi level, and enlarge/shrink the momentum separation of Weyl nodes which generate the Berry curvature as the emergent magnetic field. Here, we report the realization of a ferroelectric nonmagnetic Weyl semimetal based on indium-doped Pb_{1- x} Sn _x Te alloy in which the underlying inversion symmetry as well as mirror symmetry are broken with the strength of ferroelectricity adjustable via tuning the indium doping level and Sn/Pb ratio. The transverse thermoelectric effect (i.e., Nernst effect), both for out-of-plane and in-plane magnetic field geometry, is exploited as a Berry curvature-sensitive experimental probe to manifest the generation of Berry curvature via the redistribution of Weyl nodes under magnetic fields. The results demonstrate a clean, nonmagnetic Weyl semimetal coupled with highly tunable ferroelectric order, providing an ideal platform for manipulating the Weyl fermions in nonmagnetic systems.

Strong Anisotropy and Bipolar Conduction-Dominated Thermoelectric Transport Properties in the Polycrystalline Topological Phase of ZrTe5

ZrTe₅ has unique features of a temperature-dependent topological electronic structure and anisotropic crystal structure and has obtained intensive attention from the thermoelectric community. This work revealed that the sintered polycrystalline bulk ZrTe₅ possesses both (020) and (041) preferred orientations. The transport properties of polycrystalline bulk p-type ZrTe₅ exhibits an obvious anisotropic characteristic, that is, the room-temperature resistivity and thermal conductivity, possessing anisotropy ratios of 0.71 and 1.49 perpendicular and parallel to the pressing direction, respectively. The polycrystalline ZrTe₅ obtained higher ZT values in the direction perpendicular to the pressing direction, as compared to that in the other direction. The highest ZT value of 0.11 is achieved at 350 K. Depending on the temperature-dependent topological electronic structure, the electronic transport of p-type ZrTe₅ is dominated by high-mobility electrons from linear bands and low-mobility holes from the valence band, which, however, are merely influenced by valence band holes at around room temperature. Furthermore, external magnetic fields are detrimental to thermoelectric properties of our ZrTe₅, mainly arising from the more prominent negative effects of electrons under fields. This research is instructive to understand the transport features of ZrTe₅ and paves the way for further optimizing their ZTs.

Topological Quantum Materials from the Viewpoint of Chemistry

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin-orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.

Unconventional Transverse Transport above and below the Magnetic Transition Temperature in Weyl Semimetal EuCd_{2}As_{2}

As exemplified by the growing interest in the quantum anomalous Hall effect, the research on topology as an organizing principle of quantum matter is greatly enriched from the interplay with magnetism. In this vein, we present a combined electrical and thermoelectrical transport study on the magnetic Weyl semimetal EuCd_{2}As_{2}. Unconventional contribution to the anomalous Hall and anomalous Nernst effects were observed both above and below the magnetic transition temperature of EuCd_{2}As_{2}, indicating the existence of significant Berry curvature. EuCd_{2}As_{2} represents a rare case in which this unconventional transverse transport emerges both above and below the magnetic transition temperature in the same material. The transport properties evolve with temperature and field in the antiferromagnetic phase in a different manner than in the paramagnetic phase, suggesting different mechanisms to their origin. Our results indicate EuCd_{2}As_{2} is a fertile playground for investigating the interplay between magnetism and topology, and potentially a plethora of topologically nontrivial phases rooted in this interplay.

Magneto-transport phenomena of type-I multi-Weyl semimetals in co-planar setups

Having the chiral anomaly (CA) induced magneto-transport phenomena extensively studied in single Weyl semimetal as characterized by topological charge n = 1, we here address the transport properties in the context of multi-Weyl semimetals (m-WSMs) where n > 1. Using semiclassical Boltzmann transport formalism with the relaxation time approximation, we investigate several intriguing transport properties such as longitudinal magneto-conductivity (LMC), planar Hall conductivity (PHC), thermo-electric coefficients (TECs) and planar Nernst coefficient (PNC) for m-WSMs in the co-planar setups with external magnetic field, electric field and temperature gradient. Starting from the low-energy model, we show analytically that at zero temperature both LMC and PHC vary cubically with topological charge as n ³ while the finite temperature (T ≠ 0) correction is proportional to (n + n ²)T ². Interestingly, we find that both the longitudinal and transverse TECs vary quadratically with topological charge as n ² and the PNC is found to vary non-monotonically as a function of n. Our study hence clearly suggests that the inherent properties of m-WSMs indeed show up distinctly through the CA and the chiral magnetic effect induced transport coefficients in two different setups. Moreover, in order to obtain an experimentally realizable picture, we simultaneously verify our analytical findings through the numerical calculations using the lattice model of m-WSMs.

Two-dimensional topological insulators exfoliated from Na3Bi-like Dirac semimetals

Topological insulation is widely predicted in two-dimensional (2D) materials realized by epitaxial growth or van der Waals (vdW) exfoliation. Such 2D topological insulators (TI's) host many interesting physical properties such as the quantum spin Hall effect and superconductivity. Here, we extend the search of 2D TI's into the exfoliatable non-vdW 2D crystals. We find that three-dimensional Dirac semimetals A3Bi (A = Na, K, Rb) (P3[combining macron]c1) can be exfoliated into 2D materials with exfoliation energies of 0.479-0.990 J m-2. Our careful examination of the topological invariants of exfoliated A3Bi monolayers/multilayers by using two well-established approaches reveals that bilayer and tetralayer Na3Bi are 2D TI's. It is found that the band gap of 2D TI's can be significantly increased by external strain. We further find that the predicted 2D TI's possess interesting hidden Rashba-like spin textures. Our results suggest a new arena to search for two-dimensional topological insulators and spintronic materials.

AC measurement of the Nernst effect of thin films at low temperatures

We describe an alternating current method to measure the Nernst effect in superconducting thin films at low temperatures. The Nernst effect is an important tool in the understanding of superconducting fluctuations and, in particular, vortex motion near critical points. However, in most materials, the Nernst signal in a typical experimental setup rarely exceeds a few μV, in some cases being as low as a few nV. DC measurements of such small signals require extensive signal processing and protection against stray pickups and offsets, limiting the sensitivity of such measurements to >1 nV. Here, we describe a method utilizing a one-heater-two-thermometer setup with the heating element and thermometers fabricated on-chip with the sample, which helped to reduce the thermal load and temperature lag between the substrate and the thermometer. Using AC heating power and 2ω measurement, we are able to achieve sub-nanovolt sensitivity in 20 nm-30 nm thin superconducting films on a glass substrate, compared to a sensitivity of ∼10 nV using DC techniques on the same setup.

Topological electronic state and anisotropic Fermi surface in half-Heusler GdPtBi

Half-Heusler alloys possess unique and desirable physical properties due to their thermoelectricity, magnetism, superconductivity, and weak antilocalization effects. These properties have become of particular interest since the recent discovery of topological Weyl semimetal state for which the electronic bands are dispersed linearly around one pair of Weyl nodes, with opposite chirality (i.e., chiral anomaly). Here, we report the transport signatures of topological electronic state in a half-Heusler GdPtBi single crystal. We show that the non-trivial π Berry phase, negative magnetoresistance and giant planner Hall effect arise from the chiral anomaly and that the Shubnikov-de Haas oscillation frequency in GdPtBi is angle-dependent with an anisotropic Fermi surface (FS). All transport signatures not only demonstrate the topological electronic state in half-Heusler GdPtBi crystals, but also describe the shape of the anisotropy FS.

Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals

Dirac and Weyl semimetals are three-dimensional electronic systems with the Fermi level at or near a band crossing. Their low energy quasi-particles are described by a relativistic Dirac Hamiltonian with zero effective mass, challenging the standard Fermi liquid (FL) description of metals. In FL systems, electrical and thermo–electric transport coefficient are linked by very robust relations. The Mott relation links the thermoelectric and conductivity transport coefficients. In a previous publication, the thermoelectric coefficient was found to have an anomalous behavior originating in the quantum breakdown of the conformal anomaly by electromagnetic interactions. We analyze the fate of the Mott relation in the system. We compute the Hall conductivity of a Dirac metal as a function of the temperature and chemical potential and show that the Mott relation is not fulfilled in the conformal limit.

Finite-temperature violation of the anomalous transverse Wiedemann-Franz law

The Wiedemann-Franz (WF) law has been tested in numerous solids, but the extent of its relevance to the anomalous transverse transport and the topological nature of the wave function, remains an open question. Here, we present a study of anomalous transverse response in the noncollinear antiferromagnet Mn₃Ge extended from room temperature down to sub-kelvin temperature and find that the anomalous Lorenz ratio remains close to the Sommerfeld value up to 100 K but not above. The finite-temperature violation of the WF correlation is caused by a mismatch between the thermal and electrical summations of the Berry curvature and not by inelastic scattering. This interpretation is backed by our theoretical calculations, which reveals a competition between the temperature and the Berry curvature distribution. The data accuracy is supported by verifying the anomalous Bridgman relation. The anomalous Lorenz ratio is thus an extremely sensitive probe of the Berry spectrum of a solid.

Signatures of the Magnetic Entropy in the Thermopower Signals in Nanoribbons of the Magnetic Weyl Semimetal Co3Sn2S2

Weyl semimetals exhibit interesting electronic properties due to their topological band structure. In particular, large anomalous Hall and anomalous Nernst signals are often reported, which allow for a detailed and quantitative study of subtle features. We pattern single crystals of the magnetic Weyl semimetal Co₃Sn₂S₂ into nanoribbon devices using focused ion beam cutting and optical lithography. This approach enables a very precise study of the galvano- and thermomagnetic transport properties. Indeed, we found interesting features in the temperature dependency of the anomalous Hall and Nernst effects. We present an analysis of the data based on the Mott relation and identify in the Nernst response signatures of magnetic fluctuations enhancing the anomalous Nernst conductivity at the magnetic phase transition.

Largely Suppressed Magneto-Thermal Conductivity and Enhanced Magneto-Thermoelectric Properties in PtSn4

Highly conductive topological semimetals with exotic electronic structures offer fertile ground for the investigation of the electrical and thermal transport behavior of quasiparticles. Here, we find that the layer-structured Dirac semimetal PtSn₄ exhibits a largely suppressed thermal conductivity under a magnetic field. At low temperatures, a dramatic decrease in the thermal conductivity of PtSn₄ by more than two orders of magnitude is obtained at 9 T. Moreover, PtSn₄ shows both strong longitudinal and transverse thermoelectric responses under a magnetic field. Large power factor and Nernst power factor of approximately 80-100 μW·cm^-1·K^-2 are obtained around 15 K in various magnetic fields. As a result, the thermoelectric figure of merit zT is strongly enhanced by more than 30 times, compared to that without a magnetic field. This work provides a paradigm for the decoupling of the electron and hole transport behavior of highly conductive topological semimetals and is helpful for developing topological semimetals for thermoelectric energy conversion.

Anomalous Thermoelectric Effects of ZrTe_{5} in and beyond the Quantum Limit

Thermoelectric effects are more sensitive and promising probes to topological properties of emergent materials, but much less addressed compared to other physical properties. We study the thermoelectric effects of ZrTe_{5} in a magnetic field. The presence of the nontrivial electrons leads to the anomalous Nernst effect and quasilinear field dependence of thermopower below the quantum limit. In the strong-field quantum limit, both the thermopower and Nernst signal exhibit exotic peaks. At higher magnetic fields, the Nernst signal has a sign reversal at a critical field where the thermopower approaches zero. We propose that these anomalous behaviors can be attributed to the gap closing of the zeroth Landau bands in topological materials with the band inversion. Our understanding to the anomalous thermoelectric properties in ZrTe_{5} opens a new avenue for exploring Dirac physics in topological materials.

Strongly correlated oxides for energy harvesting

We review recent advances in strongly correlated oxides as thermoelectric materials in pursuit of energy harvesting. We discuss two topics: one is the enhancement of the ordinary thermoelectric properties by controlling orbital degrees of freedom and orbital fluctuation not only in bulk but also at the interface of correlated oxides. The other topic is the use of new phenomena driven by spin-orbit coupling (SOC) of materials. In 5d electron oxides, we show some SOC-related transport phenomena, which potentially contribute to energy harvesting. We outline the current status and a future perspective of oxides as thermoelectric materials.

Thermopower and Unconventional Nernst Effect in the Predicted Type-II Weyl Semimetal WTe2

WTe₂ is one of a series of recently discovered high mobility semimetals, some of whose properties are characteristic of topological Dirac or Weyl metals. One of its most interesting properties is the unsaturated giant magnetoresistance that it exhibits at low temperatures. An important question is the degree to which this property can be ascribed to a conventional semimetallic model in which a highly compensated, high mobility metal exhibits large magnetoresistance. Here, we show that the longitudinal thermopower (Seebeck effect) of semimetallic WTe₂ exfoliated flakes exhibits periodic sign changes about zero with increasing magnetic field that indicates distinct electron and hole Landau levels and nearly fully compensated electron and hole carrier densities. However, inconsistent with a conventional semimetallic picture, we find a rapid enhancement of the Nernst effect at low temperatures that is nonlinear in magnetic field, which is consistent with Weyl points in proximity to the Fermi energy. Hence, we demonstrate the role played by the Weyl character of WTe₂ in its transport properties.

Generation of a Nernst Current from the Conformal Anomaly in Dirac and Weyl Semimetals

We show that a conformal anomaly in Weyl and Dirac semimetals generates a bulk electric current perpendicular to a temperature gradient and the direction of a background magnetic field. The associated conductivity of this novel contribution to the Nernst effect is fixed by a beta function associated with the electric charge renormalization in the material. We discuss the experimental feasibility of the proposed phenomenon.

Towards the manipulation of topological states of matter: a perspective from electron transport

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we review the progress of the characterization and manipulation of topological phases from the electron transport perspective and also the intriguing chiral/Majorana states that stem from them. We then discuss the future directions of research into these topological states and their potential applications.

Magnetic-field enhanced high-thermoelectric performance in topological Dirac semimetal Cd3As2 crystal

Thermoelectric materials can be used to convert heat to electric power through the Seebeck effect. We study magneto-thermoelectric figure of merit (ZT) in three-dimensional Dirac semimetal Cd₃As₂ crystal. It is found that enhancement of power factor and reduction of thermal conductivity can be realized at the same time through magnetic field although magnetoresistivity is greatly increased. ZT can be highly enhanced from 0.17 to 1.1 by more than six times around 350 K under a perpendicular magnetic field of 7 T. The huge enhancement of ZT by magnetic field arises from the linear Dirac band with large Fermi velocity and the large electric thermal conductivity in Cd₃As₂. Our work paves a new way to greatly enhance the thermoelectric performance in the quantum topological materials.

Anisotropic thermal and electrical transport of Weyl semimetal TaAs

We report on anisotropic electrical, thermal as well as thermoelectric properties of the prototypical Weyl semimetal TaAs. Compared to the normal metallic behavior along a axis, TaAs is more electrically resistive along c axis and exhibits a semiconductor-like resistivity upturn below [Formula: see text] K. In the same temperature range, the thermal conductivity along c axis shows a pronounced maximum of 183 [Formula: see text] characteristic of a crystalline solid, three times higher than that of a axis. The thermoelectric power, while exhibiting enhanced values around room temperature, becomes diminished in a substantial range of temperature ([Formula: see text] K) for both axes. Together with the enhanced Nernst signals, this hints at a dominating ambipolar diffusion as is frequently seen in a compensated semimetal. An in-depth investigation of the anisotropic transport quantities is expected to yield deep insights into the propagating Weyl fermions in TaAs.

Nontrivial Berry phase in magnetic BaMnSb2 semimetal

The subject of topological materials has attracted immense attention in condensed-matter physics because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones either not tilted (type I) or tilted (type II). Although both Dirac and Weyl fermions have massless nature with the nontrivial Berry phase, the formation of Weyl fermions in 3D semimetals require either time-reversal or inversion symmetry breaking to lift degeneracy at Dirac points. Here we demonstrate experimentally that canted antiferromagnetic BaMnSb₂ is a 3D Weyl semimetal with a 2D electronic structure. The Shubnikov-de Hass oscillations of the magnetoresistance give nearly zero effective mass with high mobility and the nontrivial Berry phase. The ordered magnetic arrangement (ferromagnetic ordering in the ab plane and antiferromagnetic ordering along the c axis below 286 K) breaks the time-reversal symmetry, thus offering us an ideal platform to study magnetic Weyl fermions in a centrosymmetric material.