High-performance non-Fermi-liquid metallic thermoelectric materials

The study addresses a long-standing bottleneck in thermoelectric (TE) materials research: the prevailing belief that top-performing TE materials must be heavily doped narrow-bandgap semiconductors (e.g., Bi2Te3, PbTe, GeTe, CoSb3) due to the need to balance Seebeck coefficient and electrical conductivity for optimal power factor and zT. Despite decades of research, commercial TE materials (notably Bi2Te3-based) achieve peak zT ~1, and reproducible zT ~2 remains rare and debated. This work challenges the semiconductor-centric paradigm by investigating metallic systems as potential high-performance TE materials. It poses the question whether non-Fermi-liquid (NFL) metallic compounds near quantum criticality can deliver large thermopower and competitive zT across wide temperature ranges. The authors focus on Heusler-like compounds TiFexCu2x−1Sb (x = 0.70, 0.75, 0.80) and TiFe1.33Sb, where excess Fe/Cu occupy nominally vacant half-Heusler lattice sites, to explore the interplay between unconventional metallic transport (quasi-linear resistivity, NFL behavior), magnetic fluctuations, and enhanced thermopower.

• Historical focus has shifted from metals—dismissed due to low Seebeck coefficients and zT—to heavily doped narrow-bandgap semiconductors which dominate current high performance (Bi2Te3, PbTe, GeTe, CoSb3). Commercial success remains limited to Bi2Te3-based materials with peak zT ~1 and reproducible zT near 2 still contentious.
• Non-semiconductor approaches: Spin entropy in layered cobalt oxides (e.g., NaxCo2O4) yields sizable thermopower (~100 µV/K at 300 K; ~200 µV/K at 800 K) but zT saturates around ~1 at 800 K due to spin entropy limits from d-band degeneracy.
• Heavy-fermion and 4f electron systems (e.g., YbAl3, CePd3) can show high thermopower near room temperature (|S| ~100 µV/K) but modest zT (~0.2–0.3 at 300 K), limited by Seebeck coefficients <120 µV/K.
• Spin fluctuation-enhanced thermopower observed in weak itinerant ferromagnets (Fe2V0.9Cr0.1Al0.9Si0.1, Fe2.2V0.8Al0.6Si0.4) produces only 15–20% enhancement near TC.
• NFL superconducting oxides (YBa2Cu4O8, La2−xSrxCuO4) exhibit intriguing TE behavior but negligibly small zT, far below semiconductor benchmarks.
• Overall, prior non-semiconductor strategies have not produced a conceptual breakthrough comparable to the best semiconductors, underscoring the need to explore new physics—such as NFL behavior and quantum criticality—in metallic systems for high TE performance.

Sample synthesis: Polycrystalline TiFexCu2−x−1Sb (x = 0.70, 0.75, 0.80) and TiFe1.33Sb were synthesized by high-energy ball milling (SPEX 8000M, 30 h) of Ti (99.6%), Fe (99.99%), Cu (99.99%), and Sb (99.999%) under Ar, followed by spark plasma sintering (SPS) at 973 K for 20 min under 60 MPa in a 12.7 mm graphite die. Relative densities were 94–98%.

Structure and microstructure characterization: High-resolution powder X-ray diffraction (Rigaku SmartLab-II, Cu Kα) for phase/structure analysis; high-resolution TEM (JEOL JEM-F200) and probe Cs-corrected TEM (Thermo Fisher Themis ETEM) for microstructure; energy-dispersive X-ray spectroscopy (EDS) for nanoscale elemental mapping; integrated differential phase contrast (iDPC) imaging; X-ray photoemission spectroscopy (XPS) for Fe valence state comparison.

Transport and thermophysical measurements: Electrical conductivity and Seebeck coefficient measured by four-probe (ULVAC-RIKO ZEM-3) above room temperature; low-T (5–350 K) σ, S, and κ by PPMS with TTO. High-T thermal conductivity via κ = λ ρa Cp with thermal diffusivity (NETZSCH LFA 467), density by Archimedes method, Cp estimated via Dulong–Petit. Sound velocity at room temperature by ultrasonic system (UMS-100). Low-temperature specific heat Cp measured by PPMS with dilution refrigerator (PPMS-DR). Low-T resistivity fitted to Bloch–Grüneisen model to extract Debye-like parameter.

Magnetism: Magnetic susceptibility measured (details in Supplementary) and analyzed via Curie–Weiss fitting and a local quantum criticality model χ(T) = 1/(θ + B T^α).

Electronic structure calculations: Density functional theory with SCAN meta-GGA implemented in VASP and FHI-aims (cross-checked). VASP: 500 eV cutoff, 2×2×2 k-mesh. Vacancy/disorder modeled in a 3×3×3 supercell (216 tetrahedral 4c/4d sites with quasi-random occupancy by 144 Fe to represent TiFe1.33Sb). Full structural relaxations. Spin-polarized calculations to probe magnetic instabilities, local moments, and AFM couplings. Constrained random phase approximation (cRPA) evaluated on-site U for Fe 3d e_g states. Analysis of density of states near EF and spatial distributions of spin and charge densities.

• Metallic transport with NFL signatures: TiFexCu2x−1Sb and TiFe1.33Sb exhibit quasi-linear resistivity ρ(T) from near 0 K up to at least 500–700 K; TiFe1.33Sb is nearly perfectly linear in 2–100 K. Resistivity magnitudes ~10^−6–10^−5 Ω·m, significantly higher than constantan, indicating bad-metal behavior.
• High thermopower in metals: Seebeck coefficient S rises with temperature, reaching 194 µV/K at 700 K in TiFe0.75Cu0.4Sb, surpassing known TE metals (e.g., constantan ~60 µV/K, YbAl3 ~−120 µV/K, CePd3 ~110 µV/K).
• Thermoelectric performance: TiFe0.75Cu0.4Sb achieves average z̄T = 0.75 at 973 K with a power factor up to 20.8 µW·cm^−1·K^−2; other compositions show z̄T > 0.3, comparable to state-of-the-art half-Heusler semiconductors optimized on transition-metal sites.
• Thermal transport: Very low thermal conductivity attributed to structural disorder supports high zT at elevated temperatures.
• Low-T specific heat: Electronic specific heat follows C_el/T ∝ −ln T at low temperatures in both TiFe0.7Cu0.4Sb and TiFe1.33Sb, coexisting with linear ρ(T), a hallmark of NFL and quantum critical behavior. Electronic specific heat coefficients are ≥ one order of magnitude larger than in pure metals and approach heavy-fermion systems.
• Bloch–Grüneisen fitting yields a Debye-like parameter ~40 K, far below the phonon Debye temperature (~389 K) estimated from sound velocity, indicating unconventional scattering.
• Mean free path estimates: As low as 0.47 nm (TiFe0.75Cu0.4Sb) and 0.73 nm (TiFe1.33Sb), approaching or below lattice constants, consistent with bad metallicity.
• XPS: Fe exhibits valence near zero; Fe 2p spectra resemble metallic Fe/FeSe/FeTe, distinct from oxides, supporting metallic Fe-like states.
• Microstructure: HAADF-STEM/EDS/iDPC show uniform composition and near-random occupancy of 4c and 4d sites by Fe/Cu in a single-phase Heusler-like F43m structure; polycrystalline grains several hundred nm; density affects TE slightly; no texture observed.
• DFT insights: Metallic electronic structure with mixed Fe-3d, Ti-3d, and Sb-5p near EF. Narrow Fe 3d e_g bandwidth (~1.5 eV) with cRPA U ~1.7 eV indicates strong correlations. Spin polarization lowers energy by >40 meV/Fe; local Fe moments vary from ~0 to ≥1 µB, with small induced Ti moments (≈0 to ±0.4 µB). Two AFM interactions identified: nearest-neighbor Fe4c–Fe4d AFM (checkerboard-like tendency disrupted by vacancies) and Fe–Ti AFM (effective exchange ≳30 meV). Dual itinerant carriers (Ti-3d, Sb-5p) coexist.
• Kondo physics and quantum criticality: Symmetry-enforced two-fold degenerate Fe e_g states and dual itinerant channels suggest multi-channel (two-channel) Kondo effect; competition between AFM ordering and Kondo-like spin compensation underlies NFL behavior and quantum criticality.
• Magnetism: Magnetic susceptibility of TiFe1.33Sb indicates AFM coupling with Curie–Weiss temperature θ_CW = −56 K. Deviations from Curie–Weiss below 100 K. Susceptibility fits χ(T) = 1/(θ + B T^α) with α = 0.79 over 2–100 K and 2–300 K, consistent with local quantum criticality theory (α ≈ 0.75).

The results demonstrate that NFL metallic compounds near quantum criticality can yield exceptionally large thermopower and competitive zT, challenging the prevailing semiconductor paradigm in thermoelectrics. The quasi-linear ρ(T) and logarithmic-in-T electronic specific heat establish NFL behavior, while high S and respectable electrical conductivity persist across a wide temperature range. DFT reveals a microscopic origin: narrow, strongly correlated Fe 3d e_g states with fluctuating local moments embedded in a Ti–Sb matrix hosting dual itinerant electrons (Ti-3d and Sb-5p). Random occupancy of Fe/Cu at 4c/4d sites creates strong disorder, enhancing local moment fluctuations and promoting a competition between Fe–Fe (4c–4d) AFM order and Fe–Ti AFM-mediated Kondo-like spin compensation. The presence of two-fold degenerate e_g states and multiple itinerant channels supports a multi-channel Kondo effect, a known route to non-Fermi-liquid behavior and quantum criticality. This intertwined magnetic fluctuation/Kondo physics provides a consistent framework for the observed transport anomalies and enhanced thermopower. Practically, the combination of high S, moderate σ, and low κ from structural disorder produces z̄T up to 0.75 at 973 K in TiFe0.75Cu0.4Sb, rivaling optimized half-Heuslers. These findings suggest that tuning correlated electron phenomena and magnetic fluctuations in disordered Heusler-like metals is a viable pathway to high-performance thermoelectrics.

This work identifies TiFexCu2x−1Sb and TiFe1.33Sb as high-performance metallic thermoelectrics exhibiting non-Fermi-liquid transport and quantum critical signatures. Key achievements include record-high thermopower for a metal (S = 194 µV/K at 700 K in TiFe0.75Cu0.4Sb) and competitive z̄T (0.75 at 973 K), enabled by bad-metal transport, strong electron correlations, magnetic fluctuations, and low thermal conductivity from structural disorder. Microscopic analysis links the performance to narrow, correlated Fe 3d e_g states, AFM interactions (Fe–Fe and Fe–Ti), and multi-channel Kondo physics arising from random 4c/4d occupancy. These results broaden the design space beyond narrow-bandgap semiconductors and point to NFL quantum critical metals as promising TE candidates. Potential future directions include: (i) compositional tuning of Fe/Cu occupancy and disorder to optimize the balance between Kondo screening, AFM interactions, and carrier transport; (ii) exploring related Heusler/half-Heusler matrices and other transition-metal substitutions to generalize the NFL–TE linkage; (iii) detailed mapping of structural transitions at high temperature and their impact on transport; (iv) advanced spectroscopic and scattering studies to quantify localization and spin fluctuations; and (v) efforts toward single-crystal growth to disentangle intrinsic from microstructural effects.

• The high-temperature turnover in S(T) above ~600 K is attributed to a possible structural transition, but its nature and full impact on transport are not fully resolved.
• The degree of electronic localization associated with NFL behavior and disorder is inferred but not quantitatively determined (“hardly quantified for now”).
• Magnetic analysis shows deviations from Curie–Weiss behavior below 100 K, indicating complex spin fluctuations beyond simple models.
• Some thermophysical parameters (e.g., high-T Cp via Dulong–Petit) rely on approximations; Debye-like parameter from Bloch–Grüneisen fitting (~40 K) strongly deviates from phonon Debye temperature (~389 K), reflecting unconventional scattering not fully captured by standard models.
• Polycrystalline samples with 94–98% density were studied; while density effects were minor, potential grain-boundary contributions and the absence of single-crystal data may limit precise separation of intrinsic vs microstructural effects.
• Not all author-listed affiliations (indices 6 and 7) and associated institutional details were available in the provided text, which may limit contextual attribution but does not affect scientific conclusions.