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[Yutaka Iwasaki](https://orcid.org/0000-0002-7317-4939), Fabian Garmroudi, [Naohito Tsujii](https://orcid.org/0000-0002-6181-5911), Ernst Bauer, Andrej Pustogow, [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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[Scattering-tuned metal thermoelectrics, a new paradigm](https://mdr.nims.go.jp/datasets/c05c9d91-e1b1-4587-b23a-cbe848995245)

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Scattering-tuned metal thermoelectrics, a new paradigmApplied PhysicsExpress      APEX REVIEW • OPEN ACCESSScattering-tuned metal thermoelectrics, a newparadigmTo cite this article: Yutaka Iwasaki et al 2026 Appl. Phys. Express 19 070104 View the article online for updates and enhancements.You may also likeEnhanced energy dependence of carrierdensity of states, relaxation time, andgroup velocity in highly asymmetric bandsyields large Seebeck coefficientsShihao Han, Bing Lv, Qinghang Tang etal.-Thermoelectric properties of periodicquantum structures in the Wigner–RodeformalismAdithya Kommini and Zlatan Aksamija-Transport properties and valence bandfeature of high-performance(GeTe)85(AgSbTe2)15 thermoelectricmaterialsY Chen, C M Jaworski, Y B Gao et al.-This content was downloaded from IP address 144.213.253.16 on 03/08/2026 at 01:09https://doi.org/10.35848/1882-0786/ae84a0/article/10.1088/1361-648X/ae06e3/article/10.1088/1361-648X/ae06e3/article/10.1088/1361-648X/ae06e3/article/10.1088/1361-648X/ae06e3/article/10.1088/1361-648X/aaa110/article/10.1088/1361-648X/aaa110/article/10.1088/1361-648X/aaa110/article/10.1088/1367-2630/16/1/013057/article/10.1088/1367-2630/16/1/013057/article/10.1088/1367-2630/16/1/013057/article/10.1088/1367-2630/16/1/013057/article/10.1088/1367-2630/16/1/013057/article/10.1088/1367-2630/16/1/013057/article/10.1088/1367-2630/16/1/013057/article/10.1088/1367-2630/16/1/013057aaaScattering-tuned metal thermoelectrics, a new paradigmYutaka Iwasaki1†, Fabian Garmroudi2† , Naohito Tsujii1†, Ernst Bauer3, Andrej Pustogow3 , and Takao Mori1,4*1National Institute for Materials Science, Tsukuba, Ibaraki 987-6543, Japan2Materials Physics Applications - Quantum, Los Alamos National Laboratory, Los Alamos, 87545 NM, United States of America3Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria4University of Tsukuba, Japan*E-mail: MORI.Takao@nims.go.jp†These authors contributed equally to this work.Received April 24, 2026; revised June 10, 2026; accepted June 29, 2026; published online July 20, 2026In contrast to conventional semiconductor materials, this review outlines a new strategy for metals to be high-performance thermoelectricmaterials. We have proposed “intrinsic energy filtering” as a strategy to overcome the inherently low Seebeck coefficients in metals. This strategyinvolves engineering electronic structures where a dispersive conduction band and a localized flat band coexist near the Fermi level, creatingstrong energy dependence in the carrier relaxation time, thereby generating a large Seebeck coefficient S. Effectiveness has manifested indistinct material systems; Ni–Au alloys, where disorder-mediated s–d interband scattering achieves exceptionally high power factors∼34 mW m−1 K−2. Ni3Ge exhibits a relatively large S∼−80 μV K−1 through interband scattering. The strategy was further extended to theKagome metal Ni3In, with topological flat bands, revealing that Zener tunneling can suppress S, and we outline strategies to circumvent thisquantum transport phenomenon. These developments point to a new horizon for the development of next-generation thermoelectric materials,unlocked by the precise control of scattering mechanisms. © 2026 The Author(s). Published on behalf of The Japan Society of Applied Physics byIOP Publishing Ltd1. IntroductionThermoelectric power generation is a unique technology thatcan convert waste heat into useful electrical power by solid-state devices without moving parts, and has thereforeattracted attention for the expectation of improving energyefficiency and the possible contribution to the developmentof carbon-neutral society.1,2) Recently, thermoelectric powergeneration is also expected to be utilized as the power sourceof IoT sensors.3–5) The thermoelectric device, which is oftenreferred toas a thermoelectric module, consists of arrays of n-type and p-type thermoelectric materials. Actually, theprinciple is the same as the Peltier module, which canfunction as a heat pump by passing an electric currentthrough the device.The conversion efficiency of a power generation device isdescribed asT TTzTzT T T1 11, 1H CHave1 2ave1 2C H( )( ) ( )( )///=++ +where TH and TC are the temperature at the hot and the coldsides, respectively. zT represents the dimensionless figureof merit of thermoelectric materials and is defined by zT =S2T/ρκ, with S, T, ρ, κ being the Seebeck coefficient,absolute temperature, electrical resistivity, and thermalconductivity, respectively. Here, the thermal conductivitycan be divided into two terms, κ = κlatt + κelec, where κlattand κelec are the thermal conductivities due to lattice(phonon) and electrons. zTave in Eq. (1) indicates thetemperature-average of zT. With the increase of zT, theconversion efficiency η monotonically increases and even-tually reaches the Carnot efficiency η = (TH − TC)/TH.Thus, developing thermoelectric materials with high zT isimportant. However, increasing zT is challenging becauseof the trade-off between S, ρ, κ.6–9)A lot of works have been devoted to overcome this issue. Asa result, state of the art TE materials record zT of nearly 3.10–13)One of the guiding principles is to utilize semiconductors withlow thermal conductivity. This has been achieved by variousways of phonon-engineering, including using materials withcomplex crystal structures or large unit cells,13–15) withweak-bonding units that can bring anharmonic latticevibrations,16–21) or by introducing nano structures to reducethe phonon mean free path.22–25)Now, we consider the electronic requirements, namely, thestrategies to achieve high Seebeck coefficients and highpower factors (PFs), S2/ρ. First of all, a semi-classicalapproach has been adopted to describe electronic transportin materials. From the Mott formula, the Seebeck coefficientof a degenerate system is described asS, 2k Te Ek TeNE3ln3ln ln2B2F2B2F( )| |( )| |( )=+==Here, σ(ε), N(ε), and τ represent the spectral conductivity,electronic density of states (DOS), and the carrier scatteringtime, respectively.26,27) Normally for semiconductors, thecarrier scattering time τ can mostly be regarded as a constantwithin the narrow energy window of kBT. Thus, the secondterm in Eq. (2) is neglected. Therefore, it is required that theDOS hasa sharp energy dependence around EF to exhibit alarge Seebeck coefficient. Carrier-doped semiconductors aretherefore suitable, as N(E) shows a sudden change near theband edge. In contrast, normal metals such as Cu and Ag arenot good TE materials because the energy dependence oftheDOS is very small at EF. Up to now, semiconductor-basedTE materials have been very promising to achieve high zTand high conversion efficiency. On the other hand, the PF,S2/ρ, is a direct measure of the output power, and has beenanother fundamental factor to measure the performance ofContent from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution ofthis work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.070104-1© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdApplied Physics Express 19, 070104 (2026) APEX REVIEWhttps://doi.org/10.35848/1882-0786/ae84a0https://crossmark.crossref.org/dialog/?doi=10.35848/1882-0786/ae84a0&domain=pdf&date_stamp=2026-07-20https://orcid.org/0000-0002-0088-1755https://orcid.org/0000-0001-9428-5083https://orcid.org/0000-0003-2682-1846mailto:MORI.Takao@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://doi.org/10.35848/1882-0786/ae84a0TE materials. Historically, there have been well known highPF materials in intermetallic alloys and compounds but thesesystemswere not extensively studied for TE application,mostly because of their low zT due to high thermalconductivity. However, when it comes to the power genera-tion from abundant waste heat resources, PF can be a morecritical and practical factor than zT, as it is related to theupper limit of the minable power density per area.28) This isespecially true when one can use cooling water or efficientcooling tools for the low temperature part. Then, interme-tallic compounds and transition metal alloys could becomevery attractive as candidates for high power-factor TEmaterials. In addition to the high output power density, thesemetallic TE materials have other advantages; includingmechanical robustness, thermal stability, easy processabilityand manufacturability, and so on. Furthermore, recently, thepossibility of active cooling with Peltier devices29,30) isattracting attention due to the rapidly increasing heatproblems in data centers and power devices.31) In this case,a high thermal conductivity is also advantageous to transferthe heat out of the hot devices via thermal conductionthrough the legs, as well as further enhancing heat pumpingcapabilities via active cooling by the Peltier effect, which isdirectly proportional to PF. Thus, metallic TE materials withhigh PF and high thermal conductivity are now of greatinterest to contribute as possible solutions to the heatproblems in society. Metallic thermoelectric materials canbe roughly classified into several categories. We will brieflydescribe them below.(a) Intermetallic compounds with an energy gap or apseudo gap at the Fermi levelIntermetallic compounds are mostly metallic, butsome of them are semiconductors or semimetals. Thisincludes silicides, such as Mg2Si, SrSi2, CrSi2, FeSi2,Ru2Si3, MoSi2, etc.32) In addition, FeGa3, FeAl2, andRuAl2 are also known to show semimetallic behaviorwith pseudo gaps, and are thereby studied as candidatesof TE materials.33–35) Furthermore, this class involvesthe full Heusler Fe2VAl and Fe2TiSi, and half-Heuslercompounds like (Hf,Zr)NiSn, TiCoSb, NbFeSb, and soon.36–40) It is well known that for these Heusler seriesthe valence-electron concentration (VEC) per atom is agood factor to predict the electronic state,41) andVEC = 6 is the magic number for which the Fermilevel of the Heusler compounds is situated withinthe energy gap or the pseudo-gap. This empiricalrelation can be further applied to design double- ortriple-Heusler systems; like Ti2FeNiSb242,43) orMg2VNi3Sb3,44) etc. In this case, increased number ofatoms inside the enlarged unit cell causes significantreduction in the lattice thermal conductivity, therebyachieving larger figure of merit.For these intermetallic TE materials with an energygap or a pseudo gap, the carrier concentration can beoptimized by the elemental substitution. Thus, the basicstrategy to enhance the TE performance is almostsimilar to the case of classical TE semiconductors. Inthe case of the Fe-based Heusler alloy, however, thedopant element sometimes modifies the band-edgestructure. The effects of non-stoichiometry and/or theanti-site defect especially give a significant effect onthe electronic structure near the Fermi level, therebylarge improvements in the PF are sometimesachieved due to the resonant level evolution, whichwere not expected from the rigid-band like VECdependence.45–49) Thus, electronic structure calcula-tions give good guidelines.50–52)(b) Metals or intermetallic compounds with strong elec-tronic correlationAnother classification of the metallic TE materials ismetallic compounds which have simple Fermi surfaces,but possess large electronic DOS near the Fermi level.This quite often is the case for the strongly-correlatedelectron systems. Intermetallic compounds with Ce,Sm, Eu, and Yb can have intermediate valence statelike Ce3+↔4+ or Yb2+↔3+ through the hybridization ofconduction electrons and the 4 f levels, which gives riseto a steep quasi-particle band called Kondo resonancenear EF. Here, the physical properties are basicallydescribed by a single quasi-particle band with signifi-cantly enhanced effective mass m*, ranging fromtypically tens to several hundreds order of magnitudelarger than that of the free electron. Indeed, a largeSeebeck coefficients for metallic compounds of S =−90 μV K−1 for YbAl3, and larger than 100 μV K−1 forCePd3 were reported.53–55) Other intermediate valencecompounds such as Sm4Bi3 and EuCu2Si2 also showrelatively large Seebeck coefficients for metals.55)Furthermore, a good universal scaling is observedbetween S/T and the electronic specific heat coefficientγ in a wide range of correlated electron systems,56)indicating that the above-mentioned Fermi liquid de-scription well holds. On top of these relatively largeSeebeck coefficients, the metallic nature with periodiclattice enables very low electrical resistivity. As aresult, very large PFs have been observed; exceeding10 mW K−2 m−1 even at room temperature.57)The origin of the large PF in these intermediatevalence compounds can basically be understood interms of the steep DOS at EF due to the Kondoresonance. Wei et al. carefully compared the resultsof magneto thermoelectric effect and other physicalquantities for YbAl3 and suggested that the largeSeebeck coefficient of YbAl3 is understood by a simplenarrow-band model.27,58) In case of 4f-based inter-mediate valence compounds, a Lorenzian type quasi-particle band, N ff f2 2( )+, is assumed to develop,where Γf and εf are the width of the 4 f band and itsdistance from the Fermi level. Again, when the energydependence of τ is not significant, the second term ofEq. (2) can be omitted, then the temperature depen-dence of Seebeck coefficient is expressed as:59)SkeTT3 3. 3ff f2B2 2 2 2| | ( )( )/=±+ +Although phenomenological, this formula agrees wellwith the Seebeck coefficients in a wide temperature rangefor many compounds including YbAl3,58) CeNi5Sn,Ce2Ni2Ga,59) Yb3Si5,60) and so on. The fitting with Eq. (3)yields the values of Γf and εf, and the former should becomparable with the energy parameters like Kondo070104-2© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 070104 (2026) APEX REVIEWtemperature TK estimated from other physical measurements.Good agreement between Γf and TK is indeed observed inthese compounds, indicating the validity of the universalbehavior of Fermi liquid system.In case of these intermediate valence compounds, optimi-zation by carrier doping is not effective unfortunately,because of the large carrier concentration and large DOS.Instead, controlling the c–f hybridization to tune the para-meters Γf and εf can be effective to modify the TEperformance. Typically, this is actually done through sub-stituting elements with smaller or larger ionic radii to varychemical pressure on the system. In CePd3−xPtx61) andYb(Si1−xGex)2−δ or Yb3(Si,Ge)5,62) the substitution leadsto expansion of the unit cell, which causes a negativechemical pressure, and results in improved TE performance.Hence, the large PF in this class of materials can be basicallyunderstood in terms of a single-band (intra band) phenom-enon, although the origin of the heavy quasiparticle bandderives from a multi-body effect.For Yb3Si5, a moderately large PF of 5 to 6 mW K−2 m−1at T = 72 K for sintered samples has been obtained.60,63) Onthe other hand, a very large PF of 40 mW K−2 m−1 wasobserved at low temperatures by using a single-crystallinesample.64) Similarly, a PF of 34 mW K−2 m−1 was reportedfor YbAl3 at 80 K.65) There can be much room forfurther improvement for low temperature thermoelectricapplications.In case of compounds with large DOS near EF, theelectronic state can be affected by strong magnetic interac-tion, or quite often the compounds are magnetically ordered.Then, in addition to the normal diffusion thermopower, themagnon (spin wave) drag thermopower can sometimes bemore dominant, as observed in ferromagnetic Fe, Co, andNi.66,67) The Heusler compound Fe2VAl is also known to beclose to magnetic ordering, and indeed ferromagnetic statecan be induced by slight doping.68) A weak ferromagnetismwas observed in Cr- and Fe-doped Fe2VAl alloys, and a clearindication of spin-fluctuation drag thermopower was ob-served, causing 20% or much higher enhancement in PF.69)The merit of spin-fluctuation is that the interaction isavailable in wide temperature ranges even above theferromagnetic transition temperature. In addition to thesecoherent magnetic excitation, Kondo-like local interactionwith magnetic moments and carriers can also be found toyield enhanced PF.66,70) Here, the carrier scattering by theother band may also be relevant, which will be introduced indetail below.(c) Metallic compounds with significant inter-band scat-teringThe last class includes transition metal alloys andcompounds and is based on a very new and intriguingconcept, which is the main topic of this review article. Thedistinct difference in this class from the previous ones isthat the energy dependence in the scattering time τ issignificant, and therefore the second term in Eq. (2) playsthe dominant role. This mechanism was shown to beessential in the heavy fermion compound CeCu2Si2, whichlies in the vicinity of quantum critical regime.27) Now, itbecomes increasingly a promising guideline as a numberof high PF materials have been discovered. Theseinclude inorganic semimetals, such as MoTe271,72) andTa2PdSe6.73,74) In the former system, a critical scatteringdue to the polar-non polar structural transition is relevant tothe asymmetry in the carrier mobility and the enhancedSeebeck coefficient, which results in a large PF of30 mW K−2 m−1.71,72) In the latter, an extraordinarily highPF of 240 mW K−2 m−1 has been recorded at lowtemperature,73) where the multiple bands with significantlydifferent carrier mobilities are considered to be the sourceof strongly asymmetric scattering time.75) Furthermore,even in the well-known TE materials with high PFs, suchas the chalcopyrite CuFeS276,77) and the CoSb3-basedskutterudites,78,79) the energy dependence of the scat-tering-time is being considered to be significant.80,81)Thus, the utilization of the “scattering-time engi-neering” emerges as the new paradigm for the develop-ment of thermoelectric materials, in addition to the“phonon engineering” and the “band engineering.” Fromthe viewpoint of materials design, however, controllingthe carrier scattering time is highly difficult. In thisreview, therefore, recently proposed practical strategiesare summarized. Details will be explained later, therebyonly a brief introduction is given here. Essentially, the TEcompounds in this class should contain multiband struc-tures around EF which embody different roles. Thereshould be at least one dispersive band, which contributesto the electronic transport with a high mobility. On theother hand, there should be another (other) band(s) withrather non-dispersive DOS. Thus, carrier’s life timebecomes very short through the inter band scattering inthe narrow energy window where the two bandsoverlap.82) Outside of the overlapped energy region, onthe other hand, tau should have only a weak energydependence due to the dispersive band. Further, theFermi level can be tuned so the energy comes close tothe non-dispersive band by filling carriers in the disper-sive band. This mechanism allows the energy-filtering oflow energy carriers, or selective scattering of minoritycarriers in semimetals. Thus, this mechanism can poten-tially result in ultra-high PFs.To illustrate the overall logic of this new paradigm, Fig. 1summarizes the conceptual pathway from the initial bandstructure to the resulting thermoelectric performance, along-side the fundamental limitations. As depicted, while theengineered interband scattering creates a steep energydependence in the relaxation time to boost the PF, thisstrategy must also navigate constraints imposed by quantumtransport. Specifically, phenomena such as Zener tunnelingat band crossing points can introduce additional conductionchannels σWTE that smear the transport distribution, therebysuppressing the Seebeck coefficient. Based on this concep-tual pathway, proposed candidates for the origins of non-dispersive bands are as follows: (i) heavily doped impuritieslike in Ni–Au alloy,83) (ii) intrinsically narrow 3 d bands,84)which potentially can be finely tuned to the EF, and (iii)geometrically frustrated orbitals like in Kagome lattice.85)Because of the difficulty of calculating the carrier lifetime,this mechanism was not well studied. However, recentdevelopment in the microscopic theory of TEphenomena52,86) may enable the precise treatment of thisproblem, with the help of precise calculation of the electronicstructure of materials.070104-3© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 070104 (2026) APEX REVIEWIn the following section, this category of TE compoundswill be introduced. These metallic TE materials are new andhave been relatively unstudied until recently, both experi-mentally and theoretically. However, they actually haveexhibited ultra-high PF of the range of 10–30 mW K−2 m−1around room temperature. Hence, these materials have greatpotential of advancing the TE conversion from both largelimitless waste heat sources which have some built-in robustcooling mechanism for the cold side, and also the activecooling technology which can be applicable to the explo-sively increasing number of data centers and power devices.2. Interband scattering as novel paradigm ofboosting TE performance of metalsDistinct from traditional semiconductor-centric approaches,a key research theme in recent years has been how to achievehigh thermoelectric performance specifically a large PF inmechanically robust and low-cost metallic materials.Conventionally, common metals like Cu or Al have beenconsidered unsuitable for thermoelectric applications due totheir large carrier density and symmetric band structurearound the Fermi level, where cancelation of electron andhole contributions results in a low Seebeck coefficient (S). Inthis section, we review an innovative material designstrategy that overturns this conventional wisdom and ex-amine its effectiveness and limitations based on our series ofstudies.83–85)The “Intrinsic Energy Filtering” strategy utilized inNi1−xAux alloys83) involves designing the electronic struc-ture of metals from the perspective of interband scattering,thereby realizing selective carrier scattering in bulk systems,similar to theoretical predictions for nanostructured mate-rials. Specifically, two ordered materials that demonstratedthe success of this strategy are Ni3Ge with an L12 structure84)and the Kagome metal Ni3In, which is predicted to be atopological flat-band (TFB) material.85) These studies havenot only brought about a breakthrough in the field of metallicthermoelectrics but have also opened new horizons inunderstanding charge transport in multiband metals featuringboth dispersive and flat bands.The performance of thermoelectric materials is determinedby the S, κ, and electrical conductivity σ = 1/ρ. In particular,the PF (S2σ) is a crucial indicator representing the quality ofcharge transport. According to the theory proposed byMahan and Sofo, an ideal thermoelectric material shouldhave a transport distribution function σ(E) with a sharp,delta-function-like peak near the Fermi level (EF).87) Thisimplies that if only charge carriers with specific energycontribute to transport, both a large S and high σ can beachieved simultaneously.The “Energy Filtering” strategy we implemented in recentworks83–85) is a concrete design guideline for optimizing thetransport distribution in metals. Its core lies in the coex-istence of a sharp peak derived from a flat band (FB) and adispersive band (DB) that supplies conduction carriers nearEF in the electronic DOS D(E) (see Fig. 2). Under thiselectronic structure, low-energy conduction carriers in theDB are strongly scattered into the FB, where abundantscattering states exist (interband scattering). Consequently,the relaxation time for low-energy carriers becomes extre-mely short. Conversely, carriers with higher energy are lessaffected by this scattering and thus possess a longer relaxa-tion time. This strong energy dependence of the relaxationtime τ(E) forms a steep edge in the transport distributionfunction σ(E), generating a large electron–hole asymmetrydespite the material being a metal, resulting in the manifes-tation of a boost of S.3. Ultrahigh power factors in intermetallic alloysThomas Johann Seebeck first discovered the thermoelectriceffect in metals more than 200 years ago, but since the mid-20th century, research has predominantly focused on semi-conducting materials. Semiconductors inherently display alarge Seebeck effect since the transport function σ(E)Fig. 1. Conceptual pathway of scattering engineering and the fundamental limitations imposed by quantum transport in metallic thermoelectrics. (Top)The “scattering-time engineering” paradigm. (Bottom) Performance suppression due to Zener tunneling.070104-4© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 070104 (2026) APEX REVIEWdisplays large relative asymmetry near a band edge. This canbe rationalized even from the simple Mott formula, whichapproximates the Seebeck coefficient by the relative asym-metry in σ(E) via SEd EdE E E1F( )( )=. SinceE1F( ) is large neara band gap, even a small term d EdE( ) will result in a large S.On the other hand, the conductivity σ itself will be small,creating a tradeoff. Therefore, to realize a large PF (andultimately zT) it is crucial to obtain a large S stemming froma large d EdE( ) , sometimes referred to as the “electronic qualityfactor” or “weighted mobility” in the field.88,89) Hence, theabsolute asymmetry in σ(E) must be large. In other words,the properties of the band edge must be such that the Seebeckwill remain large even for higher doping and larger σ(EF).However, since TE performance in semiconductors istypically optimized at values of σ(EF) still far from thoseseen in good metals, heat transport is dominated by phononsκlatt ≫ κelec, requiring substantial tuning with respect to theirlattice thermal conductivity. In many metals, on the otherhand, κelec is sufficiently larger than κlatt, particularly at hightemperatures since κlatt decreases with temperature due tophonon-phonon Umklapp scattering, whereas κelec = LσT(with L being the Lorenz number). This substantiallysimplifies the expression for the dimensionless figure ofmerit in metals to zT S L2/ . We extracted thermoelectricproperty data for several metallic materials from the litera-ture and plotted S versus L as seen in Fig. 3. Indeed, manymetals satisfy zT S L2/ , reducing the multidimensionaloptimization problem encountered in semiconductors to thesingular challenge of obtaining a large Seebeck coefficient inmetals.From Fig. 3, it becomes clear that, next to intermediate-valence systems such as YbAl3 and CePd3, the highest S inmetals is realized in binary alloys containing group 10 and11 elements. Indeed, it has long been known that binaryalloys containing nickel and copper (e.g. constantan) orpalladium and silver display an unusually large Seebeckeffect, resulting in their application in temperature sensing asthermocouples. The underlying origin of their high Seebeckcoefficient is rooted in a combination of almost fully filled dshells and partially filled s states (see Fig. 4). This creates aband structure that looks similar to the one sketched inFig. 1, where charge carriers can scatter from the s bands intothe more localized d states (s–d scattering) below EF, whileno such transitions are allowed above EF (due to the lack of asubstantial d DOS). Interestingly, while the interbandtransitions are mostly mediated by phonons in pristine,ordered compounds, such as Ni3Ge and Ni3In,84,85) thedominant scattering mechanism in highly concentratedAxB1−x alloys (A = group 10 transition metal andB = group 11 element) is disorder, resulting in the famouslytemperature-independent resistivity in alloys such as con-stantan. The fact that interband transitions are mediated bydisorder and not phonons implies that the Fermi surface andFermi wavevector must be large enough such that interbandFig. 2. Schematic diagram illustrating energy filtering. The density ofstates D(E) shows the coexistence of a flat band (FB) and a dispersiveband (DB). Interband scattering suppresses the contribution of low-energycarriers, forming a sharp edge in the relaxation time τ(E) around EF.Fig. 3. Wiedemann–Franz scaling of figure of merit with Seebeckcoefficient. When electrons dominate the heat transport over phonons, zTsimplifies to zT = S2/L, which is experimentally observed across theelemental metals and various binary metallic alloy systems.Semiconductors require tuning of the lattice thermal conductivity toapproach the “metallic limit.” (This figure is reproduced from Ref. 83under the Creative Commons Attribution 4.0 International License.)Fig. 4. Density of states of the group 10 and group 11 elements.Transition metals from the Ni group have almost fully filled d shells,creating a steep edge in their DOS just above the Fermi level. On theother hand, the DOS of the Cu group has fully filled d states and ischaracterized by an almost energy-independent behavior due to the broads band. In binary alloys, the d edge can be tuned due to the difference inchemical potential between group 10 and 11 elements. (This figure isreproduced from Ref. 83 under the Creative Commons Attribution 4.0International License.)070104-5© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 070104 (2026) APEX REVIEWtransitions are allowed even without momentum transfer ofphonons. This should be kept in mind when designing newmetallic alloy systems for thermoelectrics. In alloys, wherephonons are too short-lived and damped to dominate carrierscattering, Fermi surface geometries must be such that staticdisorder can yield transitions into states that are at most |k| =kF away in momentum space.Which combination of group 10 and 11 elements realizesthe largest S? In order to predict the maximum performanceand optimal alloy configuration, we systematically investi-gated the DOS of all possible combinations between Ni, Pdand Pt with Cu, Ag and Au (see Fig. 5) by means of alloy-averaged density functional theory (DFT) calculations inthe Kohn–Korringa–Rostoker formalism and coherent po-tential approximation. Our theoretical predictions revealedthat alloys comprising Ni and Au realize the highest S,which was experimentally confirmed. This way, we dis-covered record-high PFs among bulk materials atT > 300 K, with PF reaching up to 34 mW m−1 K−2 inNi0.1Au0.9 at 560 K and ultrahigh average values up to30 mW m−1 K−2 in an extremely broad temperature range300–1100 K.4. Materials screening yields flat bands and highthermopower in Ni3Ge and Ni3InIn our systematic quest for cheap, abundant candidatematerials, our first clean compound to demonstrate theeffectiveness of this intrinsic energy filtering strategy wasNi3Ge. Through large-scale computational materialsscreening using DFT, we identified the intermetallic com-pound Ni3Ge with an L12 structure as an ideal candidate forrealizing this paradigm. As shown in the band structure ofNi3Ge in Fig. 6(a), a FB derived from the localized 3 dorbitals of Ni atoms exists just 20 meV above EF along theΓ–X direction, overlapping with a dispersive conductionband present at the R point. Figure 6(b) shows the D(E), thesquared group velocity v2(E), and a model of τ(E) assumingsignificant interband scattering, where τ(E) ∝ D−1(E).D−1(E) exhibits a steep peak just above EF, which generatesthe asymmetric transport distribution function σ(E).Fig. 5. Composition-dependent figure of merit for alloys of all combinations between the group 10 and 11 elements. Theoretical results were obtainedby assuming zT = S2/L and S calculated from a simple τ(E) ∝ D−1(E) interband scattering model using the alloy-averaged D(E) from density functionaltheory KKR–CPA calculations. (This figure is reproduced from Ref. 83 under the Creative Commons Attribution 4.0 International License.)Fig. 6. (a) The band structure of Ni3Ge features both a flat band (FB, blue line along the Γ–X direction) and a dispersive band (DB, green line) existsat the R point. (b) Density of states D(E), squared group velocity v2(E), and the relaxation time model assuming τ(E) ∝ D−1(E). D−1(E) exhibits a sharppeak in the energy region just above the Fermi energy EF.070104-6© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 070104 (2026) APEX REVIEWIn Ref. 84 we synthesized stoichiometric and Sb-dopedNi3Ge samples. As shown in Fig. 7, undoped Ni3Geexhibited a very large negative Seebeck coefficient ofSmax = −80 μV K−1 at 600 K, despite its metallic electricalresistivity of ρ = 80 μΩ cm. The Sb-doped Ni3Ge0.9Sb0.1, inwhich EF was optimized, achieved an exceptionally high PF11 mW m−1 K−2 in the temperature range from room tem-perature to 400 K. This value surpasses that of most high-performance thermoelectric materials. Furthermore, the Scalculated using the semi-classical Boltzmann transportequation and a simple model assuming τ(E) ∝ D−1(E)reproduced the experimental S well. Indeed, S obtained bycalculating the electron–phonon interaction using densityfunctional perturbation theory within the relaxation timeapproximation (RTA) aligns well with both experiment andthe τ(E) ∝ D−1(E) model. This strongly supports the conclu-sion that the proposed energy filtering mechanism is actuallyrealized in clean bulk compounds through intrinsic phonon-mediated interband scattering. Note that in NiAu alloys andconstantan83,90–92) interband transitions are predominantlymediated via impurity scattering, but in both cases theelectron–hole asymmetry emerges from the phase space ofinterband transitions.Aiming to apply the energy filtering strategy demonstratedin Ni3Ge to a more ideal platform, we conducted a high-throughput computational materials screening and found thatthe Kagome metal Ni3In was suitable.85) The “TFB” of Ni3Inis an extremely narrow feature in the DOS arising fromdestructive phase interference of electron hopping pathscaused by the geometric frustration of d-orbitals orbitals.Figure 8 shows (a) the band structure of Ni3In, (b) the Scalculated assuming τ(E) ∝ D−1(E), and (c) the calculateddimensionless figure of merit zT alongside other metallicthermoelectric materials. Since the flat band of Ni3In has aneven narrower bandwidth than the d-orbital derived band ofNi3Ge, a large S exceeding −100 μV K−1 and high thermo-electric performance (zT > 1) were theoretically predicted.However, the experimental results significantly fell short ofthese theoretical predictions. We synthesized Ni3In1−xSnx byalloying Ni3In with Ni3Sn to tune the position of the TFBrelative to EF and measured the thermoelectric properties. Themeasured S for all samples was smaller than that of Ni3Ge,with an absolute value of at most 50 μV K−1. Furthermore,neither the semi-classical transport model of τ(E) ∝ D−1(E),which was successful for Ni3Ge, nor the RTA calculatingelectron–phonon interactions from first principles calculation(BTE–RTA) could explain the experimental results at all.To unravel this significant discrepancy between theory andexperiment, we introduced calculations using the Wignertransport formalism-based RTA (WTE-RTA), a moreFig. 7. (a) Experimental Seebeck coefficients (S) of Ni3Ge compared with theoretical values calculated using different models including relaxationtime approximation (RTA), τ(E) ∝ D−1(E) and constant relaxation time (CRTA). (b) Temperature dependence of the power factor (PF) for Ni3Ge1−ySby.(This Figure is reproduced from Ref. 84 under the Creative Commons Attribution 4.0 International License.)Fig. 8. (a) Band structure of Ni3In. (b) Experimental Seebeck coefficients (S) of Ni3In1−xSnx and other metallic thermoelectric materials (NixAu1−x,NixCu1−x) compared with calculated values assuming τ(E) ∝ D−1(E). (c) Theoretical values of the dimensionless figure of merit zT. (This Figure isreproduced from Ref. 85 under the Creative Commons Attribution 4.0 International License.)070104-7© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 070104 (2026) APEX REVIEWadvanced theoretical framework that extends beyond semi-classical Boltzmann transport theory (Fig. 9). The resultsrevealed the existence of a new quantum transport phenom-enon previously unconsidered in thermoelectric transport:“Zener Tunneling.”The electronic structure of Ni3In contains Dirac coneswith linear band dispersion in addition to the TFB. As shownin Fig. 9(b), calculations using the WTE identified that anextra conduction channel exists where electrons tunneldirectly between these Dirac bands. This is the primarycause for the weakening of the electron–hole asymmetrycreated by energy filtering, thereby suppressing the S. Thisdemonstrated that the performance of thermoelectric mate-rials can be governed by pure quantum effects that cannot becaptured by the conventional semi-classical picture. Tosuppress this troublesome Zener tunneling and realize alarge S in Ni3In, methods such as separating the Dirac coneand the TFB by applying strain to the material or throughelemental substitution are conceivable. Moreover, the avail-ability of Ni3In single crystals provides the unique opportu-nity to investigate anisotropy effects of interband scattering—and possibly also direction-dependence of the Wignercontribution to transport. Having said that, low-frequencyspectroscopic studies of charge transport, e.g. by opticalreflectivity in the infrared and THz ranges, will be highlyinformative to elucidate the intriguing mechanisms at play.5. High performance metallic thermoelectricssummaryThe series of studies described above has brought two majoradvancements to the field of metallic thermoelectric materials.First, by proposing the clear design strategy of “IntrinsicEnergy Filtering” and experimentally proving its effectivenessin Ni3Ge, we demonstrated that metallic materials can indeedbecome high-performance thermoelectric materials. Second, inthe process of expanding this strategy to TFB materials, weelucidated the importance of the quantum transport phenom-enon “Zener Tunneling,” which cannot be explained byconventional semi-classical transport theory, thereby indi-cating the necessity of a new theoretical perspective in thedesign of metallic thermoelectric materials. Through thesestudies, we are further advancing the search for materials withstrong energy dependence of relaxation times, and computa-tionally we have identified several candidate materials thatexhibit large S values exceeding 100 μV K−1, which will besubject to future experimental endeavours.6. OutlookAs described in this review, the emergence of metallicthermoelectric materials as viable thermoelectric materialsis exciting for various important reasons.First of all, there is the huge increase of exploratory phasespace to search for new attractive materials, which waspreviously confined largely to semiconducting materials.The other fundamentally interesting aspect is the noveland powerful thermoelectric enhancement mechanism de-monstrated, namely, how utilizing different character energybands (e.g. flat and sharp near the Fermi level) with differentscattering time dependences, could result in intrinsic carrierfiltering effects to enhance the Seebeck coefficient, withoutrelying on construction of composite materials with suitablyfunctioning interfaces which can be complex and sometimeschallenging for reproducibility.Furthermore, two attractive directions for applicability ofmetallic thermoelectric materials are also shown.Firstly, for the Ni3Ge-type materials, very large PFs of∼10 mW m−1 K−2 and not too high thermal conductivitycan yield competitive zT values, to try to further enhance forconventional thermoelectric applications. It further should bementioned that for the metallic materials, the high thermo-electric performance tends to manifest at relatively lowtemperature including room temperature.Secondly, for the materials of Ni–Au-type, the hugePFs > 30 mW m−1 K−2 and high thermal conductivitymake them interesting candidates for the active coolingapplication, which is becoming increasingly important asthe heating problems related to semiconductors, data centers,etc., become critical. Further tuning of the PF and thermalconductivity should be possible, and can lead to attractivematerials for this relatively new application.We think that this review on the new frontiers shown inmetallic thermoelectrics will inspire further intense researchexplorations and discovery of even higher performancematerials to come. Altogether, the recent discovery of high-performance metallic thermoelectrics provides an invaluablestimulus for the vast fields of thermoelectricity and condensed-matter research in general. We expect exciting and unexpectedresults both from experimental and theoretical investigations.Fig. 9. (a) Experimental Seebeck coefficients (S) of Ni3In compared with calculations using various relaxation time models based on Boltzmanntransport theory (BTE), and quantum transport calculations based on Wigner transport theory (WTE). (b) Mapping of the Zener tunneling contributionderived from Wigner transport onto the band structure of Ni3In. (This Figure is reproduced from Ref. 85 under the Creative Commons Attribution 4.0International License.)070104-8© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 070104 (2026) APEX REVIEWAcknowledgmentsWe thank support from JST Mirai Program Grant No.JPMJMI19A1. Institutional support from the JSPS WPIAcademy Program is also acknowledged. 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His research interests span elec-tronic and thermal transport in thermoelectricmaterials, the design and discovery of novelquantum states of matter, and the synthesis andcrystal growth of new materials.Naohito Tsujii has been a principal researcherat the Research Center for MaterialsNanoarchitectonics (MANA), NIMS, sinceApril 2014. He received his Ph.D. from thegraduate school of science, Kyoto University, in1999. He worked at the National ResearchInstitute for Metals, Tsukuba, from 1999 to2001. After that he is working for NIMS. Hisresearch interests include thermoelectric mate-rials and intermetallic compounds with strongelectronic correlation.Ernst Bauer received his Ph.D. from TU Wienin 1984, where he advanced to AssociateProfessor in 1997 and University Professor in2009. His research focuses on superconduc-tivity, thermoelectric materials, and stronglycorrelated electron systems under extreme con-ditions. He has published over 550 papers, 10+book chapters and was honored with the 2023ICT “Outstanding Achievement Award” inSeattle.Andrej Pustogow studied physics at LMUMunich and ETH Zurich. After completing hisPh.D. with distinction Summa Cum Laude atthe University of Stuttgart in 2017, he con-ducted postdoctoral research at the Universityof California, Los Angeles, supported by aFeodor Lynen Fellowship of the Alexander vonHumboldt Foundation. Since 2020 he has beena professor at TU Wien, where he completed hishabilitation in Experimental Physics in 2025.His research is dedicated to developing novel pathways towards acomprehensive understanding and control of electronic properties in solid-state systems, ranging from quantum magnetism and unconventionalsuperconductivity to electronic correlations and modern thermoelectricmaterials.Takao Mori received his Ph.D. at U. Tokyo,Dept. Physics. He is a Field Director at NationalInstitute for Materials Science (NIMS) andProfessor of U. Tsukuba Graduate School, andelected Board Member, present President of theInternational Thermoelectric Society (ITS).Mori’s research interests are, broadly speaking,to find ways to control structures and propertiesof inorganic materials. He is especially involvedin development of thermoelectric materials &devices, and thermal management technologies.Mori is a Senior Editor of Materials Today Physics, Advisory BoardMember of JSSC, J. Materiomics, PRX Energy, Joule, Device. He is aProgram Manager of JST Mirai Large-scale Program. Mori has publishedover 600 papers, 25 book chapters, 40 patents.070104-10© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 070104 (2026) APEX REVIEWhttps://doi.org/10.7566/JPSJ.87.024707https://doi.org/10.1073/pnas.93.15.7436https://doi.org/10.1126/sciadv.abc0726https://doi.org/10.1002/adma.202001537https://doi.org/10.1016/j.nanoen.2015.09.003https://doi.org/10.1016/j.ijheatmasstransfer.2022.123181https://doi.org/10.1016/0040-6031(93)80410-C 1. Introduction 2. Interband scattering as novel paradigm of boosting TE performance of metals 3. Ultrahigh power factors in intermetallic alloys 4. Materials screening yields flat bands and high thermopower in Ni3Ge and Ni3In 5. High performance metallic thermoelectrics summary 6. Outlook Acknowledgments A8