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Fabian Garmroudi, Simone Di Cataldo, Michael Parzer, Jennifer Coulter, [Yutaka Iwasaki](https://orcid.org/0000-0002-7317-4939), Matthias Grasser, Simon Stockinger, Stephan Pázmán, Sandra Witzmann, Alexander Riss, Herwig Michor, Raimund Podloucky, Sergii Khmelevskyi, Antoine Georges, Karsten Held, [Takao Mori](https://orcid.org/0000-0003-2682-1846), Ernst Bauer, Andrej Pustogow

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[Energy filtering–induced ultrahigh thermoelectric power factors in Ni3Ge](https://mdr.nims.go.jp/datasets/73c2aa3b-d8b6-4b3a-bbb4-64a585189c17)

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Energy filtering–induced ultrahigh thermoelectric power factors in Ni3GeGarmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e1 of 11M AT E R I A L S  S C I E N C EEnergy filtering–induced ultrahigh thermoelectric power factors in Ni3GeFabian Garmroudi1,2*, Simone Di Cataldo3, Michael Parzer1, Jennifer Coulter4, Yutaka Iwasaki5, Matthias Grasser1, Simon Stockinger1, Stephan Pázmán1, Sandra Witzmann1, Alexander Riss1, Herwig Michor1, Raimund Podloucky5, Sergii Khmelevskyi6, Antoine Georges4,7,8,9, Karsten Held1, Takao Mori5,10, Ernst Bauer1, Andrej Pustogow1*Traditional thermoelectric materials rely on low thermal conductivity to enhance their efficiency but suffer from inherently limited power factors. Innovative pathways to optimize electronic transport are thus crucial. Here, we achieve ultrahigh power factors in Ni3Ge-based systems through an unconventional thermoelectric materials de-sign principle. When overlapping flat and dispersive bands are engineered to the Fermi level, charge carriers can undergo intense interband scattering, yielding an energy filtering effect similar to what has long been predicted in certain nanostructured materials. Via a multistep DFT-based screening method developed here, we find a family of L12-ordered binary compounds with ultrahigh power factors up to 11 mW m−1 K−2 near room temperature, which are driven by an intrinsic phonon-mediated energy filtering mechanism. Our comprehensive experimental and theoretical study of these intriguing materials paves the way for understanding and designing high-performance scattering-tuned metallic thermoelectrics.INTRODUCTIONWaste heat is ubiquitous and the majority of it occurs in a decentral-ized and low-grade form (1). Thermoelectrics (TEs) present a prom-ising solution for harvesting a small fraction of this heat, for example, to power trillions of autonomous sensor systems and smart devices expected to be installed with the upcoming Internet of Things (2). Ef-ficient TE materials require a large power factor ( PF = S2σ ) and low thermal conductivity ( κ ), which together determine the dimension-less figure of merit zT = S2σκ−1T ; here, S , σ and T denote the Seebeck coefficient, electrical conductivity, and temperature, respectively. De-spite substantial advancements in the discovery of TE materials with high zT (3–5), integrating these materials into practical applications remains an unresolved key challenge (6), and, so far, only Bi2Te3-based systems, found 70 years ago (7), are commercially available.A major bottleneck is that many of the current high-performance materials have mechanical and thermal stability issues—an unfor-tunate consequence following from the fact that conventional TE materials design focuses on maximizing structural and chemical complexity to restrict lattice-driven heat transport (8, 9). On the other hand, an optimization approach that focuses on high zT aris-ing from high PF rather than from low κ will more effectively lead to materials with a real-world impact. Among all TE materials, robust and stable half-Heusler compounds with high PF are currently among prime candidates for making it into practical applications (10) despite their zT being substantially smaller than that of other high-performance TE materials.Enhancing PF , however, is much less straightforward and particu-larly difficult due to the inherent trade-off between S and σ—arguably the toughest challenge in designing TE materials. Consequently, the power factor of most semiconductors is usually far below 10 mW m−1 K−2, with rare exceptions found in few half- and full-Heusler compounds (11, 12). A number of dedicated strategies to overcome this limitation have been developed, e.g., aligning multiple conduc-tion or valence bands (band convergence) (13), modulation doping (14), or even using magnetic interactions (15). Another enhance-ment concept that has received great interest is energy filtering. It has long been predicted that in certain nanocomposites, electronic scattering could be leveraged to filter out low-energy charge carriers (16, 17), but verification of this concept has been an outstanding experi-mental challenge (18, 19), and exploitation for practical purposes remains severely limited (20, 21) up until today.Here, we use intrinsic energy filtering (IEF) as an innovative strat-egy for achieving high PF driven by selective carrier scattering in flat-band (FB) materials (Fig. 1). More specifically, when flat and dispersive bands (DBs) are engineered to the Fermi level EF , charge carriers from the DB can transition into the FB in the overlapping energy range by scattering off impurities, phonons, or even other electrons. This enables a large Seebeck effect even in metals with a high carrier concentration that would otherwise display a negligibly small S . The effectiveness of IEF is largely determined by the density of states (DOS), which gives the total available phase space for possible interband transitions and by the respective scattering potentials (22).RESULTSWe developed a multistep screening method, solely based on the DOS calculated by density functional theory (DFT), to search for materials with the potential for IEF (Fig. 2A). Our goal is to maximize IEF by engineering non-DBs (very sharp DOS) right below/above EF in a 1Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria. 2Materials Physics Applications–Quantum, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. 3Dipartimento di Fisica, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, Italy. 4Center for Computational Quantum Physics, Flatiron Institute, New York 10010, USA. 5International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Tsukuba, Japan. 5Institute of Materials Chemistry, Universität WienUniversität Wien, 1090 Vienna, Austria. 6Vienna Scientific Cluster Research Center, TU Wien, 1040 Vienna, Austria. 7Collège de France, PSL University, 75005 Paris, France. 8Department of Quantum Matter Physics, University of Geneva, 1211 Geneva, Switzerland. 9Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau, France. 10Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan.*Corresponding author. Email: f.​garmroudi@​gmx.​at (F.G.); pustogow@​ifp.​tuwien.​ac.​at (A.P.)Copyright © 2025 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY). Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025mailto:f.​garmroudi@​gmx.​atmailto:pustogow@​ifp.​tuwien.​ac.​atmailto:pustogow@​ifp.​tuwien.​ac.​athttp://crossmark.crossref.org/dialog/?doi=10.1126%2Fsciadv.adv7113&domain=pdf&date_stamp=2025-08-01Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e2 of 11metallic background of dispersive conduction bands. This requires a metallic material with nonhybridizing, localized states (e.g., 3d or-bitals). If this is the case, then the energy of these localized d orbitals depends mainly on the relative chemical potential of the two atomic species (weighted by composition) and only minorly on the details of the crystal structure.Following this idea, we start in step 1 with a rough screening of fictitious binary systems using a simple cubic unit cell and A1B3 composition (Materials and Methods). The DOSs of all possible compounds with A being a transition metal ranging from Mn to Zn and B being any element from Li to La were calculated by DFT. As shown in Fig. 2B, the sharp peaks associated with localized 3d states are mostly unperturbed, except for a shift in energy. Initial screening highlights binary systems with Fe, Co, or Ni as the transition metal providing the non-DBs and B elements from the alkali metals, alka-line earths, or the third and fourth main groups as promising. At this point, it is worth mentioning that the search for FB hosting materials is a highly active field of research, with several alternative strategies being explored beyond the use of localized 3d (or f) orbit-als. For example, destructive phase interference in frustrated lattices (23) and the formation of moiré superlattices, such as in twisted bi-layer graphene (24), have emerged as promising routes, and even dedicated FB databases have been developed (25, 26). Thus, we reckon that our screening method has potential for future improvement and expansion by making use of these recently developed FB catalogues.The second step of our screening consisted of a series of variable-composition crystal structure prediction calculations (Materials and Methods) for the most promising pairs of elements emerging from the initial screening in step 1. We focused on Co- and Ni-based bina-ries with third and fourth main group elements, which are experi-mentally more convenient than alkalis and alkaline earths and exhibit a plethora of stable phases. Figure 2C shows the calculated formation 400 600 8000510T (K)PF (mW m−1 K−2)Ni3Ge1−ySbyy = 0.05y = 0y = 0.1qkk′PhononsConduction electronsFlat-band electronsq = |k  k′ |Fig. 1. High power factor from electron-phonon interband scattering. Sche-matic of phonon-mediated interband scattering and energy filtering of low-energy carriers in metallic Ni3Ge, leading to high PF > 10 mW m−1 K−2 ( zT ≈ 0.3 ) around room temperature.Element BElement AAT (K)0 100 200 300 400 500 600−120−100−80−60−40−200S (µV K−1)NixAu1−xNixCu1−xPdxAg1−xNi3Sn (nisnite)DNi3GeFeBe3 FeB3 FeC3 FeN3 FeO3 FeF3 FeNa3 FeMg3DOS (eV−1)020-3 3 Energy, E EF(eV)0FeLi3CoBe3 CoB3 CoC3 CoN3 CoO3 CoF3 CoNa3 CoMg3CoLi3NiBe3 NiB3 NiC3 NiN3 NiO3 NiF3 NiNa3 NiMg3NiLi3E (eV/atom)Ni SnNi3Sn4Ni3SnSnNiC1 23minFBDBEEEF0((()ED((()E00Energy filteringB−0.4−0.3−0.2−0.10.00.1Ni5Sn3NiSnx0.0 0.2 0.4 0.6 0.8 1.0020020DOS scanStabilityEEFig. 2. Density of states screening for high-performance metallic TEs enabled by IEF. (A) Schematic of IEF in gapless systems hosting a combination of flat (blue) and dispersive (green) bands at the Fermi level EF . In step 1, a broad range of 255 fictitious binary cubic systems was scanned with a fixed stoichiometry (A1B3), where A is a transition metal from Mn to Zn, providing localized 3d states and B is any element from Li to La. (B) DFT-calculated energy-dependent DOS near EF for selected A1B3 bina-ries from step 1. In step 2, a more detailed screening of Ni binaries was performed with variable-composition crystal structure prediction calculations, taking into account thermodynamic stability. (C) Formation energy as a function of atomic fraction for the binary Ni-Sn system identified in step 2. In a last step, the temperature-dependent Seebeck coefficient S(T ) was calculated using an interband scattering model, which estimates τ−1(E) ∝ D(E) as per Fermi’s golden rule. (D) Seebeck coefficient of two systems, L12-ordered Ni3Ge and Ni3Sn, identified from our multistep screening, compared to groups 10 and 11 transition metal alloys ( x = 0.5).Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e3 of 11energies of the binary Ni-Sn system. Among the more than 40 ther-modynamically stable compounds we found, particularly promis-ing is the family of A3B compounds, crystallizing in the L12-ordered Cu3Au structure, where A is a Ni-group element and B is Ge, Sn, or Pb. These gapless materials exhibit intriguing low-dimensional elec-tronic structures, with remarkably flat, atomic-like bands in certain Brillouin zone directions, yet they have entirely flown under the radar of the TE community, which has thus far heavily focused on narrow-gap semiconducting systems.In a third step, we used a simple interband scattering model, wherein the carrier scattering rate is estimated to be proportional to the DOS (as per Fermi’s golden rule) τ−1(E) ∝ D(E) , to calculate the temperature-dependent Seebeck coefficient S(T) of our newly found candidate materials. The same model has previously been shown to work well for similar systems, such as binary group 10 and 11 transi-tion metal alloys (27) and the chiral semimetal CoSi (28). Figure 2D displays S(T) of L12-ordered Ni3Ge and Ni3Sn estimated in this manner. The latter is in fact a natural mineral (“nisnite”), which has been found in Canadian mines, where it is believed to have formed under elevated pressure and temperature conditions (2.5 to 4.5 kbar and 563 to 673 K) in Earth’s crust (29). While nisnite would be the most promising candidate, it can only be synthesized under high pressure. On the other hand, Ni3Ge is stable at ambient pressure and across the entire tempera-ture range up to its melting point at around 1400 K, and it also cheaper than Pd- and Pt-containing systems, whose electronic structures and estimated S(T) curves are shown in fig. S10. All these factors motivated us to perform an in-depth experimental and theoretical study of Ni3Ge.Figure 3 summarizes the distinguished electronic structure fea-tures of Ni3Ge. In Fig. 3A, it can be seen that most of the DOS can be attributed to the 3d states of Ni. Most prominently, around EF , there are two dispersive conduction bands: one slightly above EF at Γ and another partially filled one at the R point (Fig. 3B). In addi-tion, an exceptional FB occurs along Γ–X, which remains rather flattened along other k directions as well. This yields peculiar low-dimensional features (tubes) in the Fermi surface (Fig. 3C), which are accompanied by the doubly degenerate pocket at R. We note that both the Fermi surface tubes and the FB along Γ–X, from which they originate, display notable similarity to the electronic structures found in some full-Heusler compounds, where very large power fac-tors were previously predicted theoretically (30).Similar to the Heusler compounds, it can be shown that these low-dimensional electronic structure features originate from a lack Wave vectorEEF (eV)XRFBX XRZ = XR−1.0−0.50.00.51.0A B C−8 2 4DOS (states eV −1  f.u. −1 )05101520 Ge statesNi d statesTotal DOSE EF (eV)25Ni dxy+ dzy + dzxNi dx y   + dz  2 22CB Ni3GeGeNia = 3.57 ÅaxyzD E F2  (°)20 40 60 80 100Intensity (104 counts)0246810Bragg peakYobs. Ycalc.Ycalc.Yobs.12Ni3Gexyz−6 −4 −2 0Fig. 3. Electronic structure and atomic-like flat bands in L12-ordered Ni3Ge. (A) Total and partial DOS of Ni3Ge, showing dominant Ni 3d states near EF . (B) Band struc-ture of Ni3Ge with orbital-decomposed Ni 3d states, revealing a flat band along the Γ–X direction, just 20 meV above EF . (C) Fermi surface of Ni3Ge, showing low-dimensional tubular features along Γ–X and a doubly degenerate pocket at the R point, corresponding to partially filled conduction bands. (D) Crystal structure of Ni3Ge, crystallizing in the ordered Cu3Au-type structure. (E) Charge density n(r) for the flat band at X, illustrating localized dxy orbitals within the xy planes. (F) X-ray diffraction pattern of Ni3Ge, with Rietveld refinement confirming successful synthesis of single-phase L12-ordered Ni3Ge.Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e4 of 11of dd hopping in certain crystal directions. Figure 3D shows the highly ordered Cu3Au-type crystal structure of Ni3Ge, where Ni atoms form an octahedron inside a cube with Ge atoms at the corners. An extended version shows that there are Ni layers sepa-rated by a lattice parameter of a = 0.357 nm comparable to that of elemental fcc Ni ( a = 0.352 nm). In Fig. 3E, we plot the charge density n(r) of the FB at X, as obtained from our DFT calculations. The shape of n(r) resembles atomic-like dxy orbitals, signifying that there is no dd hopping across the layers and that the bonding for these electronic states is two dimensional. The same holds true, mutatis mutandis, for the yz and xz planes. We successfully syn-thesized phase-pure Ni3Ge in the Cu3Au structure (Fig. 3F) and studied the TE properties in a broad temperature range (2 to 860 K) as discussed next.In Fig. 4, we demonstrate how IEF occurs from interband scatter-ing in Ni3Ge and manifests itself in all of the temperature-dependent transport properties. First, the rapid variation and steep edge in the DOS associated with the FB is depicted in Fig. 4A (DOS of Ni3Sn is shown for comparison as well). The temperature-dependent chem-ical potential μ(T) and the derivative of the Fermi-Dirac distribu-tion (−df∕dE) at 500 K, about where S displays its maximum values, are plotted over the DOS, highlighting that the entire relevant energy range can be readily excited at temperatures accessible by our trans-port measurements. The steep edge in the DOS implies that also the scattering phase space varies rapidly as a function of energy. Figure 4B compares the energy-dependent carrier relaxation time, estimated solely from the DOS via τ(E) ∝ D−1(E) , with advanced ab initio calcu-lations of electron-phonon interactions and scattering rates in the relaxation time approximation (RTA) (31) (details in Materials and Methods). It is evident that the simple D−1(E) model captures the energy-dependent behavior of τ(E) well, reproducing its sharp peak just above EF . Below the Fermi level, the dispersive conduction band at R and the flat bands overlap (Fig. 3B), and τ(E) drops rapidly due to interband scattering.Notably, in pristine Ni3Ge, interband scattering is intrinsically mediated via phonons (as sketched in Fig. 1) and possibly electron-electron correlations, which differs markedly from the mechanism in binary NixCu1−x and NixAu1−x alloys, where extrinsic impurity/disorder scattering occurs between s-like conduction electrons and randomly distributed Ni atoms in the alloy (fig. S12) (27). This has some implications because phonons can transfer their momentum onto the charge carriers. When the phonon wave vector q is small (at low temperatures), extensive interband transitions between carrier pockets at different points in the Brillouin zone is severely limited, as ABCE EF (eV)0.401234−0.4 0.4T (K)01000(E) (102  fs)DOS (states eV−1 f.u.−1)T = 500 K(T)02468 Ni3SnNi3Ge ( cm)020406080100120H (cm2  V−1 s−1)DEF0100200300400500600T (K) RTA × 1.45 RTAMobile states actviated0 200 400 600 800 1000T (K)0 200 400 600 800 1000RTA, 300 K(E) ~ D −1 (E)Ni3Ge Ni3Ge(W m–1 K–1)L/L01.02.0eL/L00 200 400 600 800 1000051015202530S (V K−1)−100−80−60−40−200200 200 400 600 800 1000Ni3Ge(E) ~ D −1 (E)ExperimentRTACRTANi3GeT 3 (104 K3)(cm)H−1Bloch-Wilson lawNi3Ge 1.51.52.02.53.03.54.04.52.02.53.03.50 2 4 6 8 10 12 14H−1 (10−3  cm−2 V s)−0.2 −0.0 0.2−0.4 −0.2 −0.0 0.2Fig. 4. Flat-band induced conductivity edge and electronic transport signatures of energy filtering in Ni3Ge. (A) DOS of Ni3Ge and Ni3Sn as calculated by DFT, show-ing a sharp step near EF . The dotted line marks the temperature-dependent chemical potential μ(T ) , and the green area represents the derivative of the Fermi-Dirac dis-tribution (−df∕dE) at 500 K, about where ∣S ∣ reaches its maximum. (B) Energy-dependent electron lifetimes, obtained from ab initio calculations of electron-phonon interaction and scattering matrix elements in the RTA and using a simple D−1(E) model. (C to F) Temperature-dependent Seebeck coefficient S(T ) , electrical resistivity ρ(T ) , thermal conductivity κ(T ) , and Hall mobility μH(T ) of Ni3Ge with theoretical calculations in the CRTA (green dashed line), the RTA (green solid line), and the D−1(E) model (blue solid line). Blue shaded area in (C) refers to the contribution from IEF. Inset in (F) shows that the scattering rate follows a cubic behavior at low temperatures, as expected for electron-phonon interband scattering (Bloch-Wilson law).Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e5 of 11they are far apart in reciprocal space. This is indeed apparent in the low-temperature behavior of S(T) , which starts off with a small posi-tive slope that is not captured in the D−1(E) model. Once T reaches about one-third of the Debye temperature ΘD ≈ 460(20) K, high-q phonons can scatter low-energy charge carriers from the R point into the FB, yielding a sign reversal and a strong enhancement of ∣S(T)∣ . This is in agreement with our phonon phase space calculations (fig. S9), revealing that, at 300 K, the strongest contribution comes from acous-tic (and to a lesser extent optical) phonons along the high-symmetry band paths Γ–X, Γ–R, and Γ–M with the right momenta to scatter charge carriers from the pockets around R into the FB states around the high-symmetry line Γ–X. Experimental S(T) data can be excel-lently reproduced by our RTA calculations in the entire temperature range because they incorporate electron-phonon scattering, whereas the D−1(E) model gives very good agreement only above ΘD ∕3 , where all phonon modes are accessible. On the contrary, when S(T) is calculated in the commonly used constant RTA (CRTA), where τ(E) is treated as a constant that drops out in the Boltzmann transport expression for S(T) , the experimental trend is not reproduced, and absolute values are severely underestimated. This highlights the piv-otal role of IEF by phonon-mediated interband scattering processes in enabling a large Seebeck effect in metallic Ni3Ge. The blue shaded area in Fig. 4C corresponds to the contribution of IEF, which yields a ≈ 300 % enhancement of ∣S ∣ at the temperature where it reaches its maximum. The deviation from CRTA becomes even greater at 300 K, where the Seebeck effect is entirely attributed to intrinsic phonon-mediated energy filtering.Figure 4D shows the temperature-dependent electrical resistivity ρ(T) of Ni3Ge. The RTA framework qualitatively reproduces the tem-perature dependence of ρ(T) but underestimates the absolute values by about a factor of 1.4 to 1.5. Since our samples are polycrystalline, this discrepancy could be related to grain boundary scattering, al-though this seems unlikely given the quite large residual resistivity ratio ρ300K ∕ρ4K ≈ 26 . Another possibility could be that the FB at EF leads to a renormalization of the electron-phonon coupling and/or the quasiparticle effective mass, which is not captured by our DFT-based calculations. These effects would be much more relevant for the resistivity because global enhancement factors of the scattering rate drop out in the Boltzmann transport expression for S(T) (31).Additional proof for the importance of phonon-mediated inter-band scattering is seen in the low-temperature behavior of ρ(T) , the Hall mobility μH(T) (inset Fig. 4F) and even in the thermal conduc-tivity κ(T) (Fig. 4E), which shows a shoulder-like feature around 200 K (blue vertical arrow) in agreement with theoretical calculations predicting a peak in the temperature-dependent Lorenz number ow-ing to thermal activation of carriers across the scattering-induced conductivity edge. The electronic thermal conductivity in the D−1(E) model (blue line in Fig. 4E) was calculated via the Wiedemann-Franz law by taking the electrical resistivity (blue line in Fig. 4D) and the Lorenz number, which were calculated by solving the respective transport integrals and using the same transport function corre-sponding to the calculated Seebeck coefficient in Fig. 4C. The lattice part contributes to the difference between the blue curve and ex-perimental data, κph = κ − κel , and reaches around 2.6 W m−1 K−1 at room temperature. This value is substantially smaller than the elec-tronic contribution κel ≈ 15 W m−1 K−1, meaning that the dimen-sionless figure of merit of these metallic systems, zT ≈ S2 ∕L , depends in good approximation mainly on the Seebeck coefficient and the Lorenz number, both of which can be calculated without any free pa-rameters from first principles.As described by the well-known Bloch-Grüneisen law, the scat-tering rate for electron-phonon scattering becomes linear at high temperatures, and at low temperatures, τ−1(T) follows a power law Tn , where n = 5 for common metals and n = 3 in the case of strong interband scattering (Bloch-Wilson limit) (32). ρ(T) and μ−1H(T) , both of which are reflecting the scattering rate as the carrier concen-tration is almost temperature independent (fig. S11), follow a cubic power law at low temperatures (inset Fig. 4F).To tune the position of EF with respect to the atomic-like flat band, we investigated the effects of chemical doping in Ni3Ge (Fig. 5). Similar to semiconductors, tuning the position of EF relative to the scattering-induced conductivity edge is crucial to assess optimal per-formance in scattering-tuned metals. Myriad materials crystallize in the Cu3Au structure, with 1247 entries in the Inorganic Crystal Structure Database as of November 2024, allowing for outstanding tunability and flexibility, e.g., when it comes to adjusting EF through aliovalent alloying. For example, Al substitution at the Ge site in Ni3Ge1-xAlx lowers EF , shifting it into the higher DOS, while Sb dop-ing in Ni3Ge1-xSbx raises EF above the edge into the DBs. Figure 5A shows that the Sommerfeld coefficient γ , extracted from low tem-perature–specific heat measurements (fig. S13A), follows a trend con-sistent with the DOS calculated by DFT, assuming a rigid-band shift of EF , which confirms the effectiveness of the doping. We find, how-ever, that the experimental γ values are enhanced compared to DFT predictions, even when accounting for electron-phonon coupling cal-culated by density functional perturbation theory (fig. S7C), yielding λDFT < 0.1 versus λexp ≈ 0.74(9) . This suggests a renormalization of either λep or the effective mass by many-body effects, affecting ρ(T) and γ , but not S(T).Figure 5B displays ρ(T) − ρ0 , for Ni3Ge1−xAlx and Ni3Ge1−xSbx. Electron doping (Ge/Sb) reduces the slope of ρ(T) , while hole dop-ing (Ge/Al) steepens it, reflecting shifts of EF into the dispersive and flat bands, respectively. At higher temperatures, the slopes of ρ(T) de-crease, associated with thermal activation of mobile carriers above the conductivity edge. This shoulder, indicated by vertical black arrows in Fig. 5B, shifts to higher temperatures with Al doping (as EF moves away from the conductivity edge) and to lower temperatures with Sb doping (as EF approaches the conductivity edge). We are even able to experimentally reconstruct the scattering-induced conduc-tivity edge in the energy-dependent transport distribution function σ(E) by carefully analyzing ρ(T) of the doped samples (Fig. 5C). At low temperatures, the aforementioned Bloch-Wilson limit yields ρ(T) ∼ BT3 , where B is determined by the carrier velocities and DOS, encapsulated in σ(EF) and by other physical parameters, such as the electron-phonon coupling constant λep . Assuming that the latter do not change markedly with doping, σ(EF) can be extracted from the cubic fits of our experimental data, in excellent agreement with the theoretical estimate of σ(E).The temperature-dependent power factor, Seebeck coefficient, thermal conductivitiy, and zT of Ni3Ge1−xAlx and Ni3Ge1−xSbx are shown in figs. S14 (A to D). S(T) decreases with Al doping as electron-hole asymmetry diminishes (cf. Fig. 5C), while Sb doping causes a slight shift of the maximum Seebeck coefficient to lower tempera-tures. The maximum PF , exceeding 10 mW m−1 K−2, is achieved in Ni3Ge0.9Sb0.1 near the Sb solubility limit at 300 to 400 K, with a peak zT ≈ 0.3 , which is exceptionally large among metallic systems. As shown in fig. S14E, these values are—apart from the recently discovered Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e6 of 11Ni-Au alloys (27)—substantially larger than those found in the few known systems (33–37), where IEF enhances TE performance (com-parison to semiconductors (38–42) in fig. S15).DISCUSSIONIn conclusion, we developed a multistep DFT-based screening method for identifying gapless TEs with the potential for IEF. When flat and DBs overlap, charge carriers can be selectively immobilized through interband scattering. This process is largely dictated by the DOS, which determines the total available scattering phase space. Taking the DOS as a simple descriptor for IEF, we found a family of binary metallic compounds, crystallizing in the Cu3Au-type structure, with ultrahigh PF > 10 mW m−1 K−2 in Ni3Ge1−xSbx around room tem-perature ( PFmax ≈ 11 mW m−1 K−2 at 375 K).In the future, an important question to address will be how to further pile up and sharpen the DOS to enhance the phase space for interband scattering, e.g., by further flattening the bands or via band convergence. Different from semiconducting systems, however, σ(E) should not be locally enhanced but reduced by the converged bands. Graziosi et al. (22) recently derived a set of design criteria from a two-parabolic band model, showing that, aside from the DOS effective mass asymmetry, the respective deformation potentials and the band overlap are also crucial parameters to maximize the effectiveness of interband scattering for metallic TEs. Another route toward flat bands at the Fermi level are f electron systems, particularly those based on Ce and Yb, where the Kondo effect can mix localized f states into the Fermi surface. Intermediate valence systems, such as CePd3 (43) and YbAl3 (44), have long been known for their enhanced Seebeck coeffi-cient and have ultrahigh power factors as well. However, if the f elec-trons are too localized, little to no TE enhancement can be expected, especially at higher temperatures. To enable large-scale predictions of promising f electron materials, a theoretical framework—likely be-yond standard DFT—is needed to reliably and efficiently capture the hybridization between localized f states and conduction electrons.Furthermore, an interesting direction to explore would be to se-lectively filter out high energy charge carriers further above EF to create a boxcar-shaped σ(E) (Fig. 6). As suggested by recent theo-retical studies (45, 46), this would be the optimal transport func-tion, superior to the delta function proposed originally by Mahan and Sofo in their seminal work (47). Here, we demonstrated that immobilizing low-energy carriers just below EF is crucial for enhancing S . Engineering flat bands further above EF , on the other hand, can filter out charge carriers that most strongly contrib-ute to thermal transport, while retaining a high σ (48). This way, the Lorenz number L could be reduced well below the Sommerfeld value L0 =(π2∕3)(kB∕e)2 , which would further enhance zT , particu-larly in these gapless systems as κe ≫ κl.With the development of increasingly advanced materials data-bases (25), the advent of machine-learning–assisted material discov-ery (49), and substantial progress in theoretical transport calculations beyond the CRTA (31, 50, 51), the search for high-performance TEs with IEF has become more viable and accessible than ever. Our work demonstrates that a simple, easily computed property like the DOS can be a powerful tool for identifying promising can-didate materials and confirms that TE materials with ultrahigh PF = 101 − 102 mW m−1 K−2, long thought to be rare exceptions, can be readily designed and may be far more common than initially ex-pected when exploring gapless metallic systems instead of the typi-cally studied narrow-gap semiconductors.MATERIALS AND METHODSSynthesis of starting materialsHigh-purity bulk elements (Ni, 99.99%; Ge, 99.999%; Al, 99.999%; Sb, 99.999%) were carefully weighed in stoichiometric amounts, and polycrystalline ingots were produced using high-frequency induc-tion melting in a water-cooled copper coldboat under an argon at-mosphere. It is worth mentioning that although Sb is typically prone to evaporation due to its low vapor pressure, this was not a concern 0 200 400 600 8000 (µ cm)0204060801001200.2 0.1 0.0 0.1 0.2 (mJ mol−1 K−2)02468101214 Ni3Ge1−xAlxNi3Ge1−ySbyy = 0.05y = 0.10x,y = 0x = 0.20x = 0.10Solubility limitx y0.20.050.1Ni3Ge1−xAlxNi3Ge1−ySbyDFTT (K)A B C DB −1  (107−1m−1 K3 )−0.4 0.4(E) (106−1 m−1) 05101501T = 500 KE  EF (eV)CRTA(E) ~ D −1 (E)(T) ~ BT 30.12x y0.10.2PF max(mW m−1K−2)Ni3Ge1−xAlxxSolubility limitNi3Ge1−ySby0246810120.1 0.0 0.1 0.2y−0.2 0.0 0.2Fig. 5. Tuning the Fermi level with respect to the FB states of Ni3Ge. (A) Sommerfeld coefficient γ , extracted from the specific heat C ∕T  at T → 0 of p-doped Ni3Ge1−xAlx and n-doped Ni3Ge1−xSbx compared with DFT calculations assuming rigid band–like doping. (B) Temperature-dependent electrical resistivity of Ni3Ge1−xAlx and Ni3Ge1−xSbx, showing a consistent decrease in resistivity as the nominal valence electron concentration increases, pushing EF into more DBs and away from the flat band. Moreover, a shoulder-like feature in ρ(T ) , corresponding to thermal activation of dispersive-band charge carriers across the conductivity edge, appears and is shifted toward higher/lower temperatures with Al/Sb doping [arrows in (B)]. (C) Energy-dependent transport distribution function from DFT, assuming a constant relaxation time (CRTA; dashed line) and τ(E) ∝ D−1(E) (solid line), with interband scattering filtering out low-energy carriers (blue shaded area). The step-like feature in σ(E) can be experimentally reconstructed by determining σ(EF)∝ B−1 from the cubic power law ρ(T ) ∼ BT3 at low temperatures. (D) Compostition-dependent maximum power factor of Ni3Ge1−xAlx and Ni3Ge1−ySby.Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e7 of 11for the materials used in this process and the mass loss was negligi-bly small for all samples ( δm∕m < 0.001 ). Although Ni3Ge-based compounds melt almost congruently into a single phase, small im-purities were observed directly after the melt synthesis. After annealing the samples at 973 K for several days, the samples were homoge-nized and phase-pure specimen were obtained, which also showed a notably higher Seebeck coefficient than those measured directly after the melt synthesis (fig. S16A). We note that, owing to the sub-stantial compositional range of the cubic Ni3Ge phase in the binary Ni-Ge phase diagram (fig. S16B), prolonged annealing is crucial to obtain a homogeneous, stoichiometric phase distribution across the sample. Off-stoichiometric specimens can emerge either by chang-ing the composition from a 3:1 stoichiometry or directly after the melt synthesis as certain regions crystallize with slightly off-stoichiometric compositions. Stoichiometric samples subjected to extended anneal-ing at the appropriate temperatures (973 to 1073 K), however, show very consistent and reproducible TE properties (fig. S16A). After an-nealing, the sample ingots were cut using a high-speed cutting ma-chine (Accutom from Struers). Rectangular samples with a typical geometry of 10 mm by 1.5 mm by 1.5 mm were obtained, and off-cuts of the samples were crushed and ground by hand to a fine pow-der to be used for powder x-ray diffraction measurements.Structural characterizationX-ray powder diffraction measurements were conducted at the Institute of Solid State Physics, TU Wien, using an in-house diffractometer (AERIS by PANalytical). These measurements used standard Cu K α ra-diation, with data collected in the Bragg-Brentano geometry over the angular range 20° < 2θ < 100°. Rietveld refinements on the obtained powder patterns were performed using the program PowderCell.High-temperature transport measurementsThe bar-shaped samples were mounted in a commercial setup (ZEM3 by ULVAC-RIKO), and the electrical resistivity and Seebeck coeffi-cient were measured as a function of temperature. The setup oper-ates from room temperature up to 860 K (or higher) and uses an infrared furnace. The sample chamber is evacuated and filled with He exchange gas to ensure thermal coupling to the sample. Figure S1A showcases the measurement principle and setup, where the sample is placed and mechanically fixed between two Pt elec-trodes. A temperature gradient is generated across the sample by a heater at the bottom. The temperature difference ΔT and voltage ΔV  are measured by two thermocouples TC1 and TC2 with an ap-proximate distance d = 3 mm between TC1 and TC2. Because spu-rious voltages can occur, the measurement is typically conducted N times at N different values of ΔT , and a linear regression is performed to determine the Seebeck coefficient, which—after subtraction of Swire , that is, the Seebeck coefficient of the thermocouple—comes out as the slope of the linear fit. Usually, N = 3 and ΔT = 10, 15 , and 20 K is assumed to reach a desired threshold of accuracy. Note that this represents the temperature difference with respect to the bottom heater. The real temperature difference measured at the sample is usually an order of magnitude smaller. In addition, the resistivity can be deter-mined simultaneously at each temperature by making use of a four-probe technique.Temperature-dependent measurements of the thermal conduc-tivity κ(T) in the temperature range 300 K up to ~760 K have been conducted by making use of a commercially available laser/light flash setup (LFA 500 by Linseis). Pictures of the setup and sample holder and a schematic of the measurement principle are shown in fig. S2. The thermal conductivity is given by κ = D ρm C , where D denotes the thermal diffusivity, ρm denotes the material density, and C denotes the specific heat. The thermal diffusivity and the specific heat can be simultaneously measured by the device, while the mate-rial density exists as an input parameter that can be determined via Archimedes’ principle. The specific heat is measured via a differen-tial scanning calorimetry method by making use of an appropriate reference sample. Figure S2C shows a sketch of the measurement principle for the thermal diffusivity. In the LFA 500, a xenon flash lamp heats the sample from the sample bottom. The absorbed heat is conducted through the sample and reaches the top surface, where the temperature rises and heat is radiated from a small hole. The sig-nal is then picked up by a detector further away from the sample and converted to a voltage, which is recorded as a function of time. Fig-ure S2C depicts a typical measurement curve, where the signal in-tially spikes due to ballistic heat transport, after the light/laser flash is fired, followed by a steady increase up to a maximum value. The time to the half maximum t1∕2 is directly related to the thermal diffu-sivity D via t1∕2 ∝ d2 ∕D , where d is the thickness of the sample (usu-ally 1 to 2 mm).Low-temperature transport measurementsThe TE characterization at low temperatures was carried out at on the same rectangular bar-shaped sample pieces that were used for the high-temperature measurements. The temperature-dependent electrical re-sistivity was measured using a custom-built sample probe, which can be immersed in a bath cryostat at TU Wien, Austria. The sample was contacted with thin gold wires in a four-probe configuration using a spot-welding device. It was then mounted on a sample puck with GE Varnish as the adhesive, and the probe was inserted directly into a bath cryostat, which is barely filled with liquid He. As the cryostat warms up, owing to thermal coupling to the environment, measurements are taken continuously whenever the temperature changes by 1 K. This is done by making use of an a.c. resistance bride (LakeShore 370).The low-temperature Seebeck coefficient was measured with a separate custom-made setup at TU Wien, Austria. The tempeature minFB 1 FB 2DBEE0(E(()EE(E(()EE00L L0|S|  03 kBT1.5 kBTE(E(()EEµeS( df/dE)(E )2( df/dE)(E )( df/dE)0DσFig. 6. Toward the optimal transport function via interband scattering. Filter-ing low-energy charge carriers with a FB just below EF (i) enables a large Seebeck effect, while filtering high-energy charge carriers further above EF with another FB (ii) restricts electronic heat transport without affecting the electrical conductivity, which reduces the Lorenz number and enhances zT .Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e8 of 11differences and voltages are measured by making use of two chromel—constantan (Ni0.9Cr0.1─Ni0.45Cu0.55) thermocouples, which are sol-dered to both ends of the sample. In addition, two strain gauges with a resistance of ~120 ohms serve as heaters, attached to the bot-tom of each sample end using GE Varnish. This configuration al-lows for “seesaw heating” (52), enabling the cancellation of spurious voltage contributions by switching the temperature difference during each measurement. The measurements are conducted in an evac-uated sample chamber, where helium exchange gas can be introduced to provide a thermal coupling to the cryogen.The thermal conductivity at low temperatures was measured using a steady-state method with a custom-built sample probe in a flow cryostat at TU Wien, Austria. A heater was attached to the top surface of the sample using a thermally conductive epoxy resin (STYCAST 2850FT). Two bundles of copper wires were first tightly fixed to the sample, to each of which a thermocouple was then soldered. The bot-tom of the sample was mounted on a copper heat sink, and measure-ments were conducted in a high vacuum of ~10−5 mbar.Measurements of the Hall effect at 2 < T < 300 K were carried out in a commercially available setup [Physical Property Measure-ment System (PPMS) by Quantum Design] and from 300 < T < 580 K in a home-built setup. For the latter, magnetic fields reaching up to 10 T can be achieved via a superconducting magnet and a closed cycle refrigerator, which is thermally decoupled from the sample chamber through a high vacuum (~10−5 mbar). Because the signal for these metallic samples is quite small, we fabricated specimen with a reduced thickness by polishing the samples down to ~20 μm (see fig. S3A), which was possible due to the excellent mechanical prop-erties of these materials. Measurements were carried out making use of the van der Pauw technique (see fig. S3B).Low-temperature thermodynamic measurementsThe temperature-dependent specific heat and magnetic susceptibil-ity (see Fig. 4A and fig. S13) from down to 2 K and up to 320 K were measured in a commercially available setup (PPMS by Quantum De-sign) making use of a standard relaxation-type calorimetry technique and a vibrating sample magnetometer (VSM), respectively.Screening calculationsIn this section, we describe in further detail the screening method and provide the specific computational parameters relevant to the respec-tive calculations. In general, for screening calculations we obtained the locally-relaxed structure, the total energy, and the DOS by means of DFT as implemented in the Vienna Ab Initio Simulation Package (VASP) (53). We used projector-augmented wave pseudopotentials provided in VASP (54) and the Perdew-Burke-Ernzerhof (PBE) cor-rected for solids (PBEsol) exchange-correlation functional (55). Fur-ther details specific of each calculation are given below.The first screening step was performed by fixing the crystal struc-ture to a simple cubic unit cell with AB3 composition. The purpose of this step is not to identify directly the correct structure, but rather to find pairs of atoms for which the relative chemical potentials are in the correct ballpark to place the strongly localized transition metal 3d states in the vicinity of the Fermi energy. Note that in binary transition metal alloys, where Ni atoms are embedded in face-centered cubic Cu or Au lattices, the optimal concentration for the highest Seebeck co-efficient is around Ni0.45Cu0.55 and Ni0.43Au0.63. The power factor is even maximized at Ni-poorer compositions, for instance, Ni0.1Au0.9. This suggests that an initial starting guess of AB3 is not unreasonable, although future screenings with AB or AB3 might be worthwhile to investigate. Within the cubic unit cell, the atoms A and B occupy the 1a and 3c Wyckoff positions, respectively. Using this structure as a template, we proceeded to generate all possible combinations of the following atoms1) A site: Fe, Co, Ni, Cu, Zn.2) B site: Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Rb, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, I, Cs, Ba, La.For each combination, we relaxed the crystal structure and com-puted the DOS using four DFT steps, using the output of one calcula-tion as input for the successive one. In the following, we provide a summary of the computational parameters for these DFT calculations.1. Structural relaxation at fixed volume (energy cutoff on plane waves: pseudopotential default; smearing of 0.40 eV; k-point density of 0.30 Å−1)2. Structural relaxation at variable volume (energy cutoff on plane waves: 600 eV; smearing of 0.30 eV; k-point density of 0.30 Å−1)3. Self-consistent calculation at the equilibrium volume (energy cutoff on plane waves: 600; smearing of 0.20 eV; k-point density of 0.25 Å−1)4. Non–self-consistent calculation on a dense k-mesh (energy cutoff on plane waves: 600; smearing of 0.20 eV; k-point density of 0.20 Å−1)5. Postprocessing and extraction of DOSAn example of the result from the first screening for Ni as A is shown in fig. S4. We note that although Ni1Ge3, shown in fig. S4, is not the structure investigated in the paper (which is Ni3Ge1), the sharp peak of the Ni-3d states is nonetheless present about 1 eV below the Fermi energy.From the initial step, based on the position of the sharp 3d transi-tion metal states relative to the Fermi energy, we established that the following pairs of atoms were promising: Mn-Mg, Fe-Ca, Fe-Zn, Co-Cd, Co-Cs, Co-Ga, Co-Mg, Co-Sn, Co-Zn, Co-Pb, Co-Hg, Ni-Hg, Ni-B, Ni-Ca, Ni-Ge, Ni-In, Ni-K, Ni-Rb, Ni-Sb, Ni-Si, Ni-Sn, Ni-Pb, Cu-Cs, and Cu-Sc.Starting from the pool of pairs of atoms identified in step 1, we performed crystal structure prediction calculations. To this end, we used the variable-composition evolutionary algorithm implemented in the USPEX code (56, 57).For these calculations, we used a population size of 80 individu-als for the first generations and 40 individuals for all the subsequent ones. Each calculation was run until the same structures were found on the convex hull for 4 generations or for a maximum of 20 gen-erations. Each structure underwent a six-step relaxation with pro-gressively tighter constraints, until forces on atoms were lower than 1 e−2 eV/Å. A summary of all the convex hulls is shown in fig. S5, and an enlargement for the Ni-Ge system is shown in fig. S6. Each point corresponds to a crystal structure, each with its own energy. Compositions on the convex hull are stable with respect to any other possible decomposition.In Table 1, we summarize all binary compositions, which appear as thermodynamically stable in our structure searches. The respective crystal structures can be found in the crystallographic information file (CIF) format as accompanying data in the form of a compressed file.Electron and phonon structure calculationsElectronic structure and phonon and electron-phonon calculations were performed using Quantum ESPRESSO (58, 59), after re-relaxing the crystal structure appropriately.Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e9 of 11In particular, we employed optimized norm-conserving Vanderbilt pseudopotentials (60), with a cutoff of 80 rydberg (Ry) for the plane waves expansion of the Kohn-Sham wavefunctions. The ground-state charge density was obtained using a Monkhorst-Pack mesh of 16 × 16 × 16 and a smearing of 0.02 Ry. We note that this mesh is denser than what is typically required with structures of similar vol-ume. Because of the sharp features of the Fermi surface of this struc-ture, however, this was required to achieve a convergence of the total energy to about 1 meV/atom. We found the equilibrium volume to be especially sensitive to this convergence.Phonon dispersions, DOSs and electron-phonon coupling (see fig. S7) were computed from linear response theory in the frame-work of density functional perturbation theory (DFPT) (61, 62). In particular, the Eliashberg function α2F(ω) , that is, the electron-phonon spectral function was obtained from the double-delta inte-gral of the matrix element over the Fermi surface, as in equation 18 of (61).From the Eliashberg function, we can obtain the cumulative in-tegral of the electron-phonon coupling coefficient λep(ω) as the first inverse momentfrom which we also have the total value λep = λep(ωmax) . We note, however, that λep obtained this way, interestingly, does not account for the enhancement of the Sommerfeld coefficient of the specific heat (Fig. 4A), suggesting that many-body effects beyond DFT and DFPT might become important when EF is placed in the vicinity of the flat band edge.The bands, Fermi surface, and DOS were obtained via non–self-consistent calculations. For the Fermi surface and DOS, we used a 36 × 36 × 36 mesh in reciprocal space. Phonon properties were com-puted from the converged self-consistent charge density using a 6 × 6 × 6 grid for the phonon momenta. In addition, electron-phonon properties were computed by integrating the electronic states over a 24 × 24 × 24 × grid, with a smearing of 200 meV. The phonon dis-persion alongside the atom-projected phonon DOS and Eliashberg function of Ni3Ge are displayed in fig. S7.Electronic transport calculationsTransport calculations were performed using the Phoebe code (31), an open-source package for electron and phonon Boltzmann transport equation solutions. Transport calculations were performed using the RTA. The CRTA result was also calculated as a point of comparison.Electron-phonon coupling calculations were performed using the JDFTx code (63), with associated DFT calculations with the GBRV pseudopotentials (64) parameterized for the PBE exchange-correlation functional (65).λep(ω) = 2ωmax∫0α2F(ω�)ω�dω� (1)Table 1. Summary of compositions for which we found thermodynamically stable structures. The corresponding crystal structures are provided in the CIF format with the accompanying data.Element pair Stable compositionsCo-Cd NoneCo-Cs NoneCo- Ga Co3Ga4, CoGa, CoGa2Co- Mg NoneCo- Sb CoSn2Co- Zn CoZn5, Co2Zn3, CoZn3Cu-Cs NoneCu- Sc Cu2Sc, Cu5Sc, Cu4Sc, CuSc Fe-Ca None Fe- Zn NoneCo-Hg NoneNi-Hg None Mn- Mg NoneNi- B Ni4B, Ni2B, NiB, NiB8Ni-Ca NiCa3, NiCa2, NiCa, Ni2Ca, Ni5CaNi- Ge Ni3Ge, NiGeNi-In NiInNi- K NoneNi- Rb NoneNi- Sb Ni6Sb, Ni5Sb, Ni3Sb, NiSbNi- Si Ni3Si, Ni4Si3, Ni2Si, NiSi2Ni- Sn Ni3Sn, Ni5Sn3, Ni3Sn4, NiSnCo- Pb NoneNi- Pb NoneDownloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025Garmroudi et al., Sci. Adv. 11, eadv7113 (2025)     1 August 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e10 of 11Here, electron phonon scattering rates were calculated using Wannier interpolation of the electron-phonon matrix elements, as described in (31). The scattering rates were then calculated aswhere m is a band index, ν is a phonon mode index, q and k are pho-non and electron wave vectors, with k� = k + q , ω and ϵ are phonon and electron energies, and n and f are Bose-Einstein and Fermi-Dirac occupation factors, respectively. From these lifetimes, we pre-dicted RTA-level transport properties asfor the electrical conductivity tensor andto calculate S , where one can apply the inverse of the conductivity tensor calculated as above to isolate S . For CRTAs, the expressions are identical, with the exception of τkm → τconstant = 10 fs. Transport calculations were performed with 75 × 75 × 75 k-point sampling for the integration of the Brillouin zone, adaptive smearing to approxi-mate the Dirac delta functions, and the electronic states contribut-ing to the calculation were selected by a threshold on occupation, using a Fermi window of width �f∕�T = 1 × 10−10.The phonon phase space, which is the likelihood for a phonon to participate in a scattering event with charge carriers on the Fermi-Dirac–broadened Fermi surface, was calculated via the fol-lowing expressionwith the Dirac delta distribution functions enforcing energy and momentum conservation. Equation 5 is plotted for different high-symmetry paths of Ni3Ge in fig. S9.Supplementary MaterialsThis PDF file includes:Figs. S1 to S16ReferencesREFERENCES AND NOTES  1. C . Forman, I. K. Muritala, R. Pardemann, B. Meyer, Estimating the global waste heat potential. Renew. Sustain. Energy Rev. 57, 1568–1579 (2016).  2. V . Pecunia, S. R. P. Silva, J. D. Phillips, E. 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Prokofiev from Institute of Solid State Physics, TU Wien is acknowledged for fruitful discussions regarding sample synthesis. Funding: F.G., M.P., A.R.,  E.B., Y.I., and T.M. acknowledge financial support by the Japan Science and Technology Agency (JST) program MIRAI (JPMJMI19A1). F.G. further acknowledges a Director’s Postdoctoral Fellowship through the Laboratory and Directed Research & Development (LDRD) program. A.P. acknowledges support from OeAD-GmbH (CZ 08/2023 and HR 05/2024). We also acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme. The Flatiron Institute is a division of the Simons Foundation. Author contributions: F.G., S.D.C., M.P., and A.P. conceived the idea for the study. S.D.C. performed the high-throughput DFT screening calculations and calculations of the electron and phonon structure of Ni3Ge. F.G. and M.P. designed the experimental work. J.C. performed ab initio electronic transport calculations in the RTA and CRTA. M.G., S.S., S.P. and S.W. synthesized and investigated doped Ni3Ge samples at high temperatures. F.G. measured the low-temperature transport properties of pristine Ni3Ge and modelled the transport properties with the  D−1(E) model. H.M. and F.G. measured and analyzed the specific heat and magnetic susceptibility.  R.P. performed DFT electronic structure and CRTA electronic transport calculations of Ni3Ge and other isovalent family members of the same structure. S.K. calculated alloy-averaged  DOSs of doped Ni3Ge samples. A.G., K.H., T.M., E.B. and A.P. supervised the work. F.G., together with A.P., wrote the manuscript. F.G., S.D.C., M.P., J.C., Y.I., A.R., H.M., R.P., S.K., A.G., K.H., T.M., E.B. and A.P. discussed the contents and edited the manuscript. Competing interests: F.G., S.D.C., M.P., A.P., E.B., Y.I., and T.M. have filed a patent with JST (2024-159799)  on 17 September 2024. The other authors declare that they have no competing interests.  Data and materials availability: All data needed to evaluate the conclusions in the paper  are present in the paper and/or the Supplementary Materials.Submitted 14 January 2025 Accepted 26 June 2025 Published 1 August 2025 10.1126/sciadv.adv7113Downloaded from https://www.science.org at National Institute for Materials Science on August 03, 2025 Energy filtering–induced ultrahigh thermoelectric power factors in Ni3Ge INTRODUCTION RESULTS DISCUSSION MATERIALS AND METHODS Synthesis of starting materials Structural characterization High-temperature transport measurements Low-temperature transport measurements Low-temperature thermodynamic measurements Screening calculations Electron and phonon structure calculations Electronic transport calculations Supplementary Materials This PDF file includes: REFERENCES AND NOTES Acknowledgments