Mott-Derived Local Moments and Kondo Hybridization in a d-electron Kagome lattice

Abstract: Unlike canonical Kondo lattices in f-electron systems, where localized f orbitalsnaturally provide local moments, d-electron Kondo lattices require a distinct mechanism for local-moment formation. However, the study of d-electron Kondo lattices in bulk materials remains far from settled, particularly with regard to the microscopic origin of the local moments. Here, we report a microscopic mechanism for this process in the bilayer kagome metal CsCr6Sb6, where strong correlations drive a Mott splitting of the kagome flat band to supply the requisite local moments. By combining STM/STS and ARPES, we resolve a spectroscopic hierarchy between high-energy correlation effects and low temperature hybridization. Low-temperature STS reveals a robust asymmetric suppression of the density of states near EF that is well captured phenomenologically by a Fano-type lineshape, while ARPES detects a sharp quasiparticlepeak near EF. These low-energy signatures evolveon the same temperature scale and disappear upon warming, consistent with the onset of Kondo hybridization. At the same time, STS resolves symmetric humps at approximately +-50 mV and ARPES identifies a weakly dispersive feature around 50 meV below EF; unlike the near-EF hybridization signatures, these features persist to substantially higher temperatures. This separation of energy and temperature scales supports a two-stage picture in which a kagome flat band first undergoes correlation-driven splitting into lower and upper Hubbard bands, and the occupied lower Hubbard band supplies the local moments that later hybridize with itinerant electrons at lower temperature. Our results therefore move beyond the phenomenology of a kagome Kondo lattice candidate and instead provide a microscopic spectroscopic picture linking Mottness to Kondo hybridization in a frustrated d-electron system.

• The paper demonstrates that Mott splitting of a flat kagome band produces local moments which then hybridize with itinerant electrons via a Kondo mechanism.
• Integrated STM/STS and ARPES measurements resolve distinct energy scales and momentum-dependent features that confirm the two-stage electronic hierarchy.
• The findings highlight implications for low-carrier density Kondo lattices and potential novel quantum states in frustrated d-electron systems.

Mott-Derived Local Moments and Kondo Hybridization in a $d$-Electron Kagome Lattice

Introduction and Context

The paper "Mott-Derived Local Moments and Kondo Hybridization in a d-electron Kagome lattice" (2604.02922) addresses a fundamental outstanding question in the physics of Kondo lattice systems: the microscopic origin of local moments in $d$-electron compounds, specifically within geometrically frustrated kagome lattices. While conventional Kondo physics is anchored in the presence of robust $f$-electron local moments, realization of analogous phenomena in $d$-electron systems is substantially more challenging due to the increased itinerancy and broader bandwidths of $d$-electrons. Here, the focus is on CsCr$_6$Sb$_6$, a bilayer kagome metal, wherein the confluence of strong correlation effects and lattice geometry induces a two-step mechanism: Mott splitting of a kagome flat band yields local moments, which subsequently undergo Kondo hybridization with itinerant electrons.

This work integrates scanning tunneling microscopy/spectroscopy (STM/STS) and angle-resolved photoemission spectroscopy (ARPES) to resolve both the spectroscopic hierarchy and the temperature and energy scales associated with Mott and Kondo phenomena. The results provide a direct spectroscopic link between Mottness and Kondo hybridization in a $d$-electron system—invoking a qualitatively distinct mechanism from canonical $f$-electron Kondo lattices.

Structural and Transport Properties

CsCr$_6$Sb$d$0 crystallizes in a double kagome bilayer structure (space group $d$1), with the Cr sites forming the essential kagome motif. STM topography reveals high-quality, atomically resolved surfaces, either Cs- or Sb$d$2-terminated, with the latter being optimal for spectroscopy of the underlying electronic structure. Transport measurements exhibit a low-temperature upturn in resistivity, and $d$3 reveals a kink near $d$4 K, consistent with frustrated short-range magnetic ordering.

Figure 1: Crystal structure of CsCr$d$5Sb$d$6 and temperature-dependent resistivity, showcasing key features of the double kagome bilayer and the emergence of transport anomalies connected to magnetism and hybridization.

STM/STS Evidence for Kondo and Mott Physics

Low-temperature STS spectra on both terminations reveal two robust features: (i) a pronounced, asymmetric suppression of DOS near $d$7, which is well modeled by a Fano profile and (ii) symmetric, temperature-insensitive humps centered at approximately $d$8 mV. The Fano lineshape, a hallmark of Kondo hybridization due to interference between localized and itinerant electronic tunneling channels, yields a resonance width $d$9 corresponding to $f$0 K. Upon warming above this temperature, the asymmetric gap rapidly fills, in clear excess to simple thermal broadening, indicating the loss of Kondo-derived coherence.

Crucially, the $f$1 mV humps persist to temperatures far exceeding the Kondo scale, indicating their independence from hybridization physics. These humps are interpreted as Hubbard bands arising from strong correlation-driven Mott splitting of a flat kagome band, with the lower Hubbard band (LHB) being observed directly in both STM and ARPES spectra.

Figure 2: STM/STS topographies and spectra on Sb$f$2- and Cs-terminated surfaces, temperature evolution of the Kondo hybridization gap, and fitting of the DOS suppression by a Fano+Gaussian model.

Momentum-Resolved ARPES and the Two-Stage Electronic Hierarchy

ARPES measurements directly resolve the band structure across key regions of the Brillouin zone. Near $f$3, four low-energy bands of predominantly Cr 3$f$4 character ($f$5, $f$6, $f$7, $f$8) dominate the electronic landscape. The $f$9 band, weakly dispersive and located $d$0 meV below $d$1, is assigned as the LHB, corroborated by its energy alignment with the STS humps.

At low temperature and primarily at high-symmetry points M and K, a sharp, coherent quasiparticle peak is detected right at $d$2, which is strongly suppressed as temperature increases through $d$3. In contrast, at the $d$4 point, the spectral weight and band coherence remain unaffected by temperature, aligning with observations of persistent features in STS. This dichotomy directly links Kondo hybridization in momentum space to selected Fermi surface regions.

Figure 3: ARPES mapping of the Fermi surface, detailed band dispersions along high-symmetry directions, temperature evolution of quasiparticle peaks, and quantitative spectral weight extraction as a function of temperature at key momenta.

Microscopic Mechanism: From Mott Flat Band to Kondo Lattice

The integrated STM/STS and ARPES data reveal a clear separation of energy and temperature scales: (1) high-energy Hubbard features—robust against temperature and originating from correlation-induced splitting of the flat band, and (2) low-energy, thermally sensitive Kondo hybridization peaks at specific $d$5 points. This substantiates a two-stage scenario unique to kagome $d$6-electron systems:

1. Mott Splitting of Flat Band: Kagome geometry produces a half-filled, narrow flat band near $d$7, highly susceptible to on-site Coulomb repulsion. This drives Mott splitting into UHB/LHB, with the occupied LHB serving as the source of localized moments.
2. Kondo Hybridization: At lower temperature, these Mott-localized moments hybridize with itinerant conduction electrons, producing a Fano-profiled gap in STM and a coherent quasiparticle peak in ARPES.

   Figure 4: Schematic summary of the two-stage scenario—(a) initial flat band, (b) Mott-split flat band into UHB/LHB, (c) onset of hybridization with Kondo resonance, (d)-(e) momentum-selective band hybridization as mapped by experiment and modeled by the periodic Anderson framework.

Implications, Contrasts, and Future Directions

The demonstrated two-stage hierarchy—first Mottness in a non-$d$8 multiorbital context, followed by Kondo hybridization—establishes a general microscopic mechanism for Kondo lattice behavior in $d$9-electron kagome metals. This stands in contrast to both $d$0-electron Kondo systems and scenarios where pure atomic orbital localization is invoked. Alternative explanations via impurity Kondo scattering or magnetic order are systematically excluded based on a lack of substantial impurity content, the absence of long-range magnetic signatures below $d$1, and the persistence of the spectroscopic features across surface reconstructions and sample preparations.

The incomplete screening, inferred from residual low-temperature DOS at $d$2 and anomalous transport signatures, suggests that CsCr$d$3Sb$d$4 realizes a low-carrier density Kondo lattice where not all moments are fully screened. This could have broader implications for exotic non-Fermi liquid states and unconventional ordering phenomena in related materials.

The findings position CsCr$d$5Sb$d$6 as a platform for exploring the interplay of flat-band physics, Mottness, and Kondo lattice phenomena in non-$d$7-electron materials, directly relevant for quantum criticality, novel heavy-fermion states, and the emergence of unconventional superconductivity in kagome systems. Possible future directions include direct measurement of dynamic correlations via inelastic probes, mapping of the spin fluctuation spectrum, and studies under varying dimensional confinement or external tuning (e.g., pressure, doping).

Conclusion

The authors establish, via high-resolution STM/STS and ARPES, that CsCr$d$8Sb$d$9 embodies a unique $_6$0-electron kagome Kondo lattice where strong correlations induce Mott localization within a flat band, subsequently enabling Kondo hybridization at low temperatures. The two-stage evolution—Mott splitting followed by momentum-selective hybridization—diverges from canonical $_6$1-electron Kondo systems and sets a new paradigm for local moment formation in frustrated $_6$2-electron materials. This work opens controlled spectroscopic access to the intertwined physics of Mottness and emergent heavy-fermion behavior in geometrically frustrated lattices, providing a template for future theoretical and experimental inquiries in correlated quantum materials.