Survival of the metallic state in a single-hole multiband $p$-orbital molecular system

Abstract: Strong correlations and ferromagnetic Hund's coupling lead to diverse electronic phenomena in transition-metal oxides that sensitively depend on the $d$-orbital electron filling. Fullerides, their $p$-electron counterparts, exhibit effective antiferromagnetic Hund's coupling in a different energy range. At half-filling ($n=3$, three electrons in triply degenerate orbitals), both $d-$ and $p$-electron systems are Mott insulators due to strong correlations and Hund's coupling. Away from half-filling, in single-electron/hole ($n=1,5$) $d$-orbital systems, Hund's coupling opposes the correlations, reducing the Mott gap and allowing survival of metallicity. Here we report a single-hole multiorbital correlated $p$-electron system, orthorhombic-structured Yb$<em>2$CsC$</em>{60}$ comprising pentavalent C$<em>{60}<sup>{5-}$ anions, which also exhibits a robust metallic state with no Mott transition, just like in the metastable single-electron cubic-structured CsC$</em>{60}$. We assert that particle-hole symmetry holds well in ($n=1,5$) fullerides and that their $p$-electron-derived states are analogous to those in $d$-orbital solids, providing impetus for further study of these correlated systems.

• The paper demonstrates that Yb₂CsC₆₀ retains a metallic state at single-hole occupancy, validating multiband Hubbard model predictions.
• Using X-ray, neutron diffraction, NMR, and Raman spectroscopy, the study quantifies a low density of states (≈5 states/eV/C60) and confirms particle-hole symmetry.
• First-principles DFT calculations corroborate experimental bandwidth and metal behavior, paving the way for exploration of correlated molecular solids.

Survival of Metallic State in Single-Hole Multiband $p$-Orbital Fulleride: Yb$_2$CsC$_{60}$

Context and Theoretical Background

This study addresses the interplay between electronic correlations, crystal-field effects, and band filling in multiband, $p$-orbital molecular solids built from C$_{60}$ fullerenes. Historically, much of the physics of strongly correlated systems has been explored within the Hubbard model framework, which encapsulates the competition between electronic kinetic energy and on-site Coulomb repulsion ($U$), extended to include orbital multiplicity and Hund's coupling ($J_H$) in multiband materials. While this model has been extensively validated for $d$-orbital oxide systems, where Hund's coupling effects are well-understood to alternate between promoting Mott insulating states at half-filling and favoring metallicity at single-electron or hole doping, analogous investigations for $p$-orbital molecular solids have been severely limited by synthesis challenges.

Alkali-doped fullerides, where the triply degenerate $t_{1u}$ molecular orbitals of C$_2$0 host correlated electrons or holes, provide a prototypical $_2$1-orbital Hubbard system. Previous decades have focused on half-filled ($_2$2) trivalent states (A$_2$3C$_2$4, A: alkali metal), exhibiting Mott insulating ground states and pressure-induced superconductivity. However, systematic exploration away from half-filling, particularly the single-hole ($_2$5) regime—necessary for direct tests of particle-hole symmetry and the role of effective Hund's exchange in $_2$6-band systems—has been largely absent due to the scarcity of suitable model compounds.

Synthesis, Structure, and Characterization of Yb$_2$7CsC$_2$8

This work reports the reproducible synthesis, crystallographic analysis, and spectroscopic characterization of Yb$_2$9CsC$_{60}$0: a pentavalent (C$_{60}$1 anion-based), orthorhombic structure with formal single-hole occupancy of the $_{60}$2 molecular bands. The Yb cation is shown (via X-ray absorption spectroscopy and $_{60}$3Yb NMR) to adopt a pure divalent ($_{60}$4) state. This ensures charge balance and unambiguously identifies the C$_{60}$5 site as the $_{60}$6 charged species, making Yb$_{60}$7CsC$_{60}$8 the first experimentally tractable realization of a single-hole, multiband, strongly correlated $_{60}$9-orbital molecular material.

Neutron and synchrotron X-ray diffraction reveal an anisotropically contracted orthorhombic (Pmnn) structure with coordination environments and cation placements distinct from prior Ba$p$0CsC$p$1 analogues. The lower structural symmetry is accompanied by weak, static, prolate distortion of the C$p$2 cages (to $p$3 symmetry) induced by the anisotropic crystal field rather than by dynamic Jahn-Teller effects. NMR and Raman data confirm valence and symmetry assignments, while variable temperature diffraction and displacement parameter analysis show no structural or magnetic instabilities—crystalline order and orbital-distortion remain robust across the full measured range.

Electronic Ground State and Experimental Evidence for Metallicity

Temperature-dependent $p$4C NMR, $p$5Yb NMR, and $p$6Cs NMR, alongside Raman and L$p$7-edge XAS, unambiguously demonstrate a low-carrier-density metallic ground state in Yb$p$8CsC$p$9. The $_{60}$0C Knight shift is weakly temperature dependent, and the spin-lattice relaxation rate ($_{60}$1) assumes a temperature-independent Korringa form below 200 K, signaling a dominantly Pauli-like susceptibility and Fermi-liquid metallicity. Notably, the derived density of states at $_{60}$2, $_{60}$3 states/eV/C$_{60}$4, is significantly lower (by a factor of $_{60}$53) than canonical A$_{60}$6C$_{60}$7 materials, but quantitatively agrees with DFT predictions and values for single-electron quenched-cubic CsC$_{60}$8.

Comparisons with Ba$_{60}$9CsC$U$0 indicate stronger crystal field effects (and possible charge localization via Jahn-Teller-coupled double occupancy) in the latter, whereas Yb$U$1CsC$U$2 stabilizes a fully metallic state without detectable charge or orbital ordering or Mott transition signatures—a critical demonstration of the survival of metallicity in a strongly correlated, multiband $U$3-orbital system at the single-hole boundary.

First-Principles Calculations and Phase Diagram Placement

DFT calculations, employing both experimentally measured Pmnn and geometry-relaxed higher symmetry Immm structures, confirm the dominance of $U$4-derived conduction bands. The $U$5-band crossing $U$6 substantiates the metallic ground state and yields a total electronic bandwidth $U$7 eV. The calculated density of states matches experiment, and both the energy separation of $U$8 from other bands and the small magnitude of crystal field splitting validate the spectroscopic conclusions.

With an estimated $U$9 (for $J_H$0 eV), the system resides far from the critical value $J_H$1 for Mott localization in fullerides. This is entirely consistent with the absence of a Mott transition in the observed phase diagram for Yb$J_H$2CsC$J_H$3, directly paralleling $J_H$4-orbital systems at single-carrier doping. Importantly, the results empirically demonstrate that, in $J_H$5-orbital molecular solids as in their $J_H$6-orbital counterparts, Hund's coupling at $J_H$7 acts to suppress correlation-induced localization and enables the persistence of metallicity even with strong $J_H$8.

Particle-Hole Symmetry and Implications

The key empirical finding is that particle-hole symmetry holds remarkably well for $J_H$9-band fullerides: both single-electron (e.g., cubic CsC$d$0, $d$1) and single-hole (Yb$d$2CsC$d$3, $d$4) systems exhibit essentially identical signatures of metallicity, $d$5C spin-lattice relaxation, and density of states. This is in stark contrast to half-filled and two-carrier regimes, where insulating or "bad metal" behavior dominates due to enhanced correlations. Thus, the band-filling dependence of correlation physics in molecular fullerides mirrors the canonical behavior of multiband $d$6-electron oxides.

This work establishes that multiband $d$7-orbital fullerides can be regarded as legitimate analogues of $d$8-orbital transition metal systems in the context of strong correlations, Hund's physics, and Mott criticality. The survival of metallicity at $d$9 further allows meaningful exploration of the correlated molecular solid phase diagram well away from half-filling.

Outlook and Prospects for Future Research

The synthetic breakthrough enabling access to stable, single-hole multiband $p$0-orbital systems (here, Yb$p$1CsC$p$2) paves the way for systematic studies of the M$p$3AC$p$4 ($p$5 = Ba, Sr, Ca, Sm, Eu, Yb; $p$6 = Cs, Rb, K, Na) family. This provides unique opportunities to probe the interplay of orbital degeneracy, static and dynamic lattice effects, and interaction-driven instabilities across a range of fillings, bandwidths, and structural symmetries. In particular, the robust metallicity—combined with the absence of disorder and instabilities—renders these systems ideal for pressure-tuned experiments, targeted doping, and potential realization of high-$p$7 superconductivity predicted for quarter- and three-quarter-filled $p$8 bands. The role of effective Hund's exchange (notably negative in these $p$9-orbital systems) and structural field effects in tuning emergent magnetic and superconducting orders remains an explicit target for future theoretical and experimental efforts.

Conclusion

Yb$t_{1u}$0CsC$t_{1u}$1 represents the first experimental realization of a single-hole, multiband $t_{1u}$2-orbital molecular metal, exhibiting a robust metallic ground state in full agreement with multiband Hubbard model expectations for strong Hund's coupling away from half-filling. The findings validate the analogy between $t_{1u}$3-orbital fullerides and $t_{1u}$4-orbital oxides, confirm particle-hole symmetry at $t_{1u}$5 and $t_{1u}$6, and significantly extend the accessible phase space for systematic exploration of correlated molecular electron systems. This sets the stage for further investigation of superconductivity, quantum criticality, and emergent phenomena in molecular solids with controlled orbital, band-filling, and interaction degrees of freedom.

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Reference: "Survival of the metallic state in a single-hole multiband $t_{1u}$7-orbital molecular system" (2606.28836)