The Kondo lattice, a periodic array of magnetic impurities interacting with conduction electrons, presents a complex problem in condensed matter physics. Understanding its ground state is crucial, especially given the possible emergence of phases like Kondo paramagnets or magnetically ordered states depending on the interplay between Kondo exchange and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. This interplay is often visualized using the Doniach phase diagram. While traditionally studied in complex bulk f-electron systems, transition metal dichalcogenide (TMD) heterobilayers offer a simpler, tunable platform for studying 2D Kondo lattices. Previous research has demonstrated the Kondo effect in TMD heterobilayers, but evidence of lattice coherence and the nature of the ground state remain elusive. This study addresses this gap by investigating the 1T/1H-TaSe₂ heterobilayer, a prototypical 2D Kondo lattice system. The 1T phase exhibits a √13 × √13 charge density wave (CDW) known as the Star-of-David (SoD) pattern, which creates localized magnetic moments. The hybridization of these moments with the conduction electrons in the underlying 1H metallic layer gives rise to the Kondo effect. By performing high-resolution STM/STS measurements at ultralow temperatures and in the presence of magnetic fields, the researchers aim to determine the ground state of this system and its position within the Doniach phase diagram.

The single-impurity Kondo problem, where a magnetic impurity is embedded in a metallic host, is relatively well understood. Below the Kondo temperature (TK), the impurity forms singlet correlations with conduction electrons, leading to complete screening at T=0K. In contrast, the Kondo lattice problem, involving a periodic array of such impurities, is far more intricate due to the competition between Kondo screening and the RKKY interaction between magnetic moments. Doniach's seminal work proposed that the ground state could be either a Kondo insulator (fully screened) or a magnetically ordered state, depending on the relative strength of these interactions. However, more complex scenarios, including the coexistence of Kondo screening and magnetic order, are also possible. The experimental investigation of these states has been historically limited by the complexity and lack of tunability of traditional f-electron-based Kondo lattice materials. The recent emergence of TMD heterobilayers as a platform for 2D Kondo lattices has provided a new avenue for studying these systems, offering tunability and accessibility. Previous studies have reported the Kondo effect in TMD heterobilayers such as TaSe₂, TaS₂, and NbSe₂, but lower-temperature investigations to elucidate the coherent behavior and ground state have been lacking.

High-quality 1T/1H-TaSe₂ heterobilayers were grown on epitaxial bilayer graphene (BLG) on 6H-SiC(0001) substrates using molecular beam epitaxy (MBE). The heterostructure naturally forms during growth due to the similar formation energies of the 1T and 1H polytypes. STM/STS measurements were performed at temperatures ranging from 340 mK to 4.2 K using a commercial UHV-STM system equipped with a perpendicular magnetic field up to 11 T. Pt/Ir tips were used, and careful tip calibration was performed using a Cu(111) reference surface to avoid artifacts. Low-bias STS (20-50 µV) and large-bias STS (1-2 mV) measurements were carried out with lock-in a.c. modulation. Spatially resolved measurements of the differential conductance (dI/dV) were performed to map the electronic structure. The effect of an external magnetic field (B) on the electronic structure was thoroughly investigated. Ab initio calculations based on density functional theory (DFT) using the Quantum Espresso package were performed to obtain the electronic band structure for 1H, 1T, and 1H/1T-TaSe₂ structures. These calculations were used to extract model parameters for theoretical analysis. A periodic Anderson model, which in the large U limit maps onto a Kondo lattice model, was employed to interpret the experimental findings, with parameters extracted from both the DFT calculations and experimental measurements. Mean-field and auxiliary fermion calculations were used to understand the behavior of the system under a magnetic field.

High-resolution STM/STS measurements at 340 mK revealed the presence of two symmetric electronic resonances around the Fermi energy (EF) in the 1T/1H-TaSe₂ heterobilayer. This double-peak feature is significantly different from observations in related systems and points towards the emergence of coherence in the Kondo lattice at ultralow temperatures. Spatial mapping of the energy separation (Δ) between these peaks showed variations between different Star-of-David (SoD) clusters but consistent behavior within individual clusters. Atomically resolved conductance maps revealed that the intensity of the peaks is largely localized on the Se atoms directly bonded to the central Ta atom of the SoD, consistent with the expected location of the unpaired electron responsible for the magnetic moment. Applying an external magnetic field (Bz) perpendicular to the plane of the heterobilayer caused a gradual shift of both peaks away from EF, resulting in a non-linear increase of Δ with Bz. This behavior comprises two distinct regimes: a non-linear low-field regime (Bz < 0.5 T) followed by a linear high-field regime (Bz ≥ 0.5 T). The linear regime is attributed to Zeeman splitting, providing an experimental g-factor. The non-linear behavior could not be explained by isolated magnetic moments interacting with an external field and supports a coherent ground state. The data is consistent with an in-plane magnetic order. The non-linear dependence of Δ on Bz at low magnetic fields is interpreted as a transition from in-plane to out-of-plane magnetic order. Analysis using a periodic Anderson model and auxiliary fermion mean-field calculations supports the conclusion that the observed behavior is inconsistent with a fully screened Kondo lattice (Kondo insulator) and suggests a magnetically ordered ground state. Comparing the results to measurements on isolated CoPC impurities on 1H-TaSe₂ demonstrates that the observed behavior cannot be attributed to magnetic order in the 1H-TaSe₂ layer alone. The ab initio calculations and the Kondo lattice modeling corroborate this finding by providing estimated values of relevant parameters that place the system clearly in the magnetically ordered region of the Doniach phase diagram. The measured g-factor of 4.3 is high compared to that of the free electron, 2, providing further evidence for strong many-body interactions

The observation of a split Kondo peak at zero magnetic field, along with its non-linear magnetic field dependence, provides strong evidence for the emergence of coherence in the 2D Kondo lattice of the 1T/1H-TaSe₂ heterostructure. The results strongly indicate that this system resides on the magnetically ordered side of the Doniach phase diagram, a scenario supported by ab initio calculations and a periodic Anderson model. The non-linear field dependence is explained by a Zeeman-induced transition from in-plane to out-of-plane magnetic order. The observed magnetic coherence in this 2D Kondo lattice system offers a unique platform to study fundamental phenomena like quantum criticality, Kondo breakdown transitions, and the potential for unconventional superconductivity in the strict two-dimensional limit. The findings demonstrate the possibility of realizing and manipulating complex quantum phenomena in artificially designed 2D materials.

This work presents compelling evidence for a coherent magnetic ground state in a 2D Kondo lattice realized in a 1T/1H-TaSe₂ heterobilayer. The observed splitting of the Kondo resonance and its field dependence strongly support a magnetically ordered state, contrasting with a fully screened Kondo insulator. This opens new avenues for investigating fundamental many-body phenomena in 2D systems, including quantum criticality and unconventional superconductivity. Future studies could utilize spin-resolved STM/STS or other magnetically sensitive probes to fully characterize the magnetic ground state and investigate tunability through doping or electric fields.

The analysis relies on a simplified model (periodic Anderson model) to interpret the experimental findings, neglecting certain complexities of the system. The use of mean-field approximation in the theoretical analysis may limit the accuracy of the quantitative predictions. Further studies using more sophisticated theoretical techniques could provide a deeper understanding of the system's behavior. The observed phenomena might be impacted by subtle variations in the heterostructure morphology, potentially influencing the degree of coherence.