Evidence for ground state coherence in a two-dimensional Kondo lattice

The study contrasts the well-understood single-impurity Kondo effect with the more complex Kondo lattice, where below a coherence scale T* the competition between Kondo screening and RKKY interactions yields distinct ground states (Kondo paramagnet/insulator or magnetically ordered phases per the Doniach phase diagram). Traditional heavy-fermion systems (Yb-, Ce-based) are complex and lack tunability, hampering microscopic determination of the coherent ground state and associated quantum critical behavior. Recently, 2D TMD heterobilayers combining 1T (hosting Star-of-David charge density wave clusters with local moments) and metallic 1H layers have enabled observation of single-impurity Kondo resonances (T_K ~ 18–57 K), but coherence and the ground state of the Kondo lattice at low temperature remained unknown. This work aims to determine the coherent ground state in 1T/1H-TaSe2 by STM/STS at 340 mK and magnetic fields, testing whether the low-energy spectrum is consistent with a Kondo insulator or magnetically ordered coherent lattice, aided by ab initio parameter extraction and mean-field modeling.

- Doniach’s framework predicts a competition between Kondo screening and RKKY interactions leading to Kondo paramagnetic/insulating or magnetically ordered ground states, with possible coexistence scenarios and quantum critical points. - f-electron heavy-fermion compounds (e.g., YbRh2Si2, Ce-based materials) have shown emergent heavy fermions and quantum criticality but are structurally complex and less tunable. - In TMD heterobilayers (1T/1H stacks of TaSe2, TaS2, NbSe2), a √13 × √13 Star-of-David CDW in 1T generates a flat band with one unpaired electron, forming local moments and a Mott insulating state that hybridizes with the metallic 1H layer to yield Kondo resonances. Prior studies reported narrow Kondo peaks with T_K ~ 18–57 K, confirming local moment formation, but lacked sub-Kelvin evidence of lattice coherence or ground state identification. - Theoretical tools include periodic Anderson and Kondo lattice models, mean-field auxiliary-fermion descriptions, and QMC studies that predict distinct field dependencies for Kondo-insulating vs magnetically ordered coherent states.

- Sample growth: 1T-TaSe2/1H-TaSe2 heterobilayers grown on bilayer graphene on SiC(0001) via UHV-MBE in a two-step process. BLG prepared by annealing 4H-SiC(0001) at ~1400 °C; 1H-TaSe2 grown at ~550 °C by co-evaporation of Ta and Se (flux ~1:30, growth rate ~2.5 h/ML); 1T-TaSe2 formed by increasing substrate temperature to 640 °C. Post-growth Se anneal, Se capping (~10 nm) for transfer, decapped in UHV by annealing at ~300 °C. Growth monitored by RHEED. - STM/STS: Conducted in UHV at T = 0.34–4.2 K (Unisoku USM-1300) with out-of-plane magnetic fields up to 11 T using Pt/Ir tips. Tips calibrated on Cu(111); functionalized tips avoided by DOS inspection. Lock-in modulation: 20–50 µV for low-bias and ~1–2 mV for large-bias STS at 833 Hz. Energy resolution validated on Pb(111). dI/dV spectra and grids acquired to map low-energy features; constant-height conductance maps recorded at ±1 mV bias. - Structural/electronic characterization: STM images to identify √13 × √13 SoD CDW in 1T-TaSe2. dI/dV spectroscopy at 4.2 K and 0.34 K to resolve Kondo-related features and low-energy splitting. Spatially resolved 40×40 dI/dV grids used to extract Δ (peak separation) maps and histograms. - Magnetic-field dependence: Sequential dI/dV spectra acquired as Bz swept between 0 and ±11 T. Peak positions tracked; Δ(B) analyzed for linear and non-linear regimes; Landé g-factor extracted from high-field slope. High-resolution spectra around peak maxima (−30 µV/point) checked for additional features. - Control experiment: Kondo resonance of CoPC on 1H-TaSe2 measured at 340 mK to test for intrinsic magnetism of the 1H substrate (no splitting observed). - Theory and parameter extraction: DFT (Quantum ESPRESSO, PBE) calculations for 1H, 1T (CDW), and 1T/1H heterostructure band structures. Extracted parameters: 1H bandwidth W ≈ 1.2 eV, DOS at EF ρ ≈ 2.5 eV−1; 1T flat band width ~25 meV within ~0.55 eV CDW gap with central SoD localization. Periodic Anderson model fit (U=0) to heterostructure bands to estimate hybridization V ≈ 15–20 meV; combined with experimental Hubbard U = 208 ± 4 meV to estimate Kondo coupling J_K = 8V^2/U ≈ 8–15 meV and dimensionless J_Kρ ~ 0.037–0.1. Auxiliary-fermion mean-field framework used to compare field-dependent splitting patterns for Kondo insulator vs magnetic order (FM/AFM, in-plane vs out-of-plane), and to model non-linear Δ(B) via field-induced reorientation of moments.

- At 4.2 K, dI/dV spectra on 1T/1H-TaSe2 show a prominent peak at EF flanked by Hubbard bands, with Hubbard U = 208 ± 4 meV. - At 0.34 K, the EF peak resolves into two symmetric peaks around EF; spatial conductance maps at ±1 mV show localization on Se atoms bonded to the central Ta of each SoD cluster, consistent with the localized moment site. - Spatial mapping of peak separation Δ across SoD clusters reveals intra-cluster uniformity with inter-cluster variations; histogram mean Δ = 1.2 ± 0.2 mV at zero field. - Magnetic field dependence (Bz up to 11 T): Δ increases with B, exhibiting two regimes: (i) non-linear low-field regime below Bt ≈ 0.45 ± 0.07 T with zero-field deviation from linearity δ ≈ 0.15 ± 0.02 mV; (ii) linear high-field Zeeman regime with Landé g-factor g = 3.1 ± 0.2. The behavior is symmetric in field polarity (no hysteresis). Peak intensities decrease and LDOS near EF depletes with B, with no additional low-energy peaks resolved at 0.34 K. - The observed two-peak spectrum and its field evolution are incompatible with a fully Kondo-screened paramagnetic insulator (which would yield four peaks and gap closing under Zeeman field). Instead, modeling supports a coherent Kondo lattice with magnetic order, most consistent with in-plane order (FM or AFM cannot be distinguished by local spectroscopy without dispersion). - Ab initio–informed parameters: 1H W ≈ 1.2 eV, ρ ≈ 2.5 eV−1; hybridization V ≈ 15–20 meV; U ≈ 208 meV; estimated J_K ≈ 8–15 meV, placing J_Kρ ≈ 0.037–0.1 on the magnetic side of the Doniach diagram. - Control measurements on CoPC/1H-TaSe2 at 340 mK show an unsplit Kondo resonance, ruling out intrinsic magnetism in 1H-TaSe2 as the cause of splitting and reinforcing lattice coherence as the origin.

The emergence of a split Kondo peak at zero field signifies the onset of lattice coherence in the 2D Kondo lattice, going beyond single-impurity physics. The detailed B-dependent evolution of Δ, with symmetric non-linear behavior at low fields and linear Zeeman splitting at higher fields, aligns with a magnetically ordered coherent ground state rather than a Kondo insulator. Mean-field auxiliary-fermion analysis indicates that in-plane magnetic order yields symmetric Δ(B) with polarity and naturally explains the non-linear low-field behavior via field-induced moment reorientation and growth. Parameter estimates from DFT and experiment (V, U, J_K, ρ) place the system on the magnetic side of the Doniach phase diagram, consistent with the observed spectra. The absence of splitting for CoPC on 1H-TaSe2 excludes substrate ferromagnetism, indicating that the split originates from the coherent Kondo lattice in the 1T/1H heterostructure. These findings clarify the ground state of the 2D Kondo lattice platform and connect it to proximate magnetic fluctuations in isolated 1H-TMD metals (e.g., predicted in-plane AFM/spin-spiral instabilities), suggesting the 1H layer can influence the selection and field-driven reorientation of magnetic order.

This work provides experimental evidence of ground-state coherence in a 2D Kondo lattice realized in 1T/1H-TaSe2, revealed by a zero-field split Kondo resonance localized at SoD centers and a characteristic, symmetric non-linear-to-linear magnetic-field evolution. Combined with ab initio–guided parameter extraction and mean-field modeling, the results support a coherent, magnetically ordered ground state on the magnetic side of the Doniach diagram and are incompatible with a fully Kondo-screened insulator. The platform’s accessibility and tunability enable exploration of magnetic quantum criticality, Kondo breakdown, and potentially unconventional superconductivity. Future directions include spin-sensitive probes (spin susceptibility, spin-resolved STS) to resolve the exact magnetic order (FM vs AFM), and tuning J·ρ via electrostatic/chemical doping and displacement fields to approach quantum critical points.

- The magnetic order (FM vs AFM, detailed texture) is inferred from spectral signatures and mean-field modeling; direct spin-sensitive measurements were not performed. - Local spectroscopy lacks dispersion information of the f-band, limiting the ability to distinguish FM from AFM purely from LDOS. - Parameter estimates (V, J_K) rely on DFT fits with simplifying assumptions (e.g., neglecting the 3×3 CDW in the 1H layer and assuming commensurate lattices), and mean-field treatments may not capture all correlations. - Spatial variability of Δ across SoD clusters indicates local heterogeneity; the origin (e.g., strain, local environment) is not fully resolved. - Energy resolution and temperature, while sub-Kelvin, could still mask very fine structures; only out-of-plane magnetic fields were explored.