Unified understanding of superconductivity and Mott transition in alkali-doped fullerides from first principles

Fulleride superconductivity tuned by elastic strain due to cation compositional disorder

Dynamical fluctuations of the elastic strain in strongly correlated systems are known to affect the onset of metal-to-insulator or superconducting transitions. Here we report their effect on the properties of a family of bandwidth-controlled alkali-intercalated fullerene superconductors. We introduce elastic strain through static local structural disorder in a systematic and controllable way in the fcc-structured K x Cs3-x C60 (with potassium content, 0.22 ≤ x K ≤ 2) series of compositions by utilizing the difference in size between the K+ and Cs+ co-dopants. The occurrence of the crossover from the Mott-Jahn-Teller insulating (MJTI) state into the strongly correlated Jahn-Teller metal (JTM) on cooling is evidenced for the compositions with x K < 1.28 by both synchrotron X-ray powder diffraction (SXRPD) - anomalous reduction of the unit cell volume - and 133Cs NMR spectroscopy - sudden suppression in the 133Cs spin-lattice relaxation rates. The emerging superconducting state with a maximum critical temperature, T c = 30.9 K shows a characteristic dome-like dependence on the unit-cell volume or equivalently, on the ratio between the on-site Coulomb repulsion, U, and the bandwidth, W. However, compared to the parent Cs3C60 composition in which cation disorder effects are completely absent, the maximum T c is lower by ∼12%. The reduction in T c displays a linear dependence on the variance of the tetrahedral-site cation size, σ T 2, thus establishing a clear link between structural-disorder-induced attenuation of critical elastic strain fluctuations and the electronic ground state.

Evidence for Band Renormalizations in Strong-Coupling Superconducting Alkali-Fulleride Films

There has been a long-standing debate about the mechanism of the unusual superconductivity in alkali-intercalated fullerides. In this Letter, using high-resolution angle-resolved photoemission spectroscopy, we systematically investigate the electronic structures of superconducting K_{3}C_{60} thin films. We observe a dispersive energy band crossing the Fermi level with the occupied bandwidth of about 130 meV. The measured band structure shows prominent quasiparticle kinks and a replica band involving the Jahn-Teller active phonon modes, which reflects strong electron-phonon coupling in the system. The electron-phonon coupling constant is estimated to be about 1.2, which dominates the quasiparticle mass renormalization. Moreover, we observe an isotropic nodeless superconducting gap beyond the mean-field estimation (2Δ/k_{B}T_{c}≈5). Both the large electron-phonon coupling constant and large reduced superconducting gap suggest a strong-coupling superconductivity in K_{3}C_{60}, while the electronic correlation effect is suggested by the observation of a waterfall-like band dispersion and the small bandwidth compared with the effective Coulomb interaction. Our results not only directly visualize the crucial band structure but also provide important insights into the mechanism of the unusual superconductivity of fulleride compounds.

Doping Asymmetry and Layer-Selective Metal-Insulator Transition in Trilayer K_{3+x}C_{60}

Thin films provide a versatile platform to tune electron correlations and explore new physics in strongly correlated materials. Epitaxially grown thin films of the alkali-doped fulleride K_{3+x}C_{60}, for example, exhibit intriguing phenomena, including Mott transitions and superconductivity, depending on dimensionality and doping. Surprisingly, in the trilayer case, a strong electron-hole doping asymmetry has been observed in the superconducting phase, which is absent in the three-dimensional bulk limit. Using density-functional theory plus dynamical mean-field theory, we show that this doping asymmetry results from a substantial charge reshuffling from the top layer to the middle layer. While the nominal filling per fullerene is close to n=3, the top layer rapidly switches to an n=2 insulating state upon hole doping, which implies a doping asymmetry of the superconducting gap. The interlayer charge transfer and layer-selective metal-insulator transition result from the interplay between crystal field splittings, strong Coulomb interactions, and an effectively negative Hund coupling. This peculiar charge reshuffling is absent in the monolayer system, which is an n=3 Mott insulator, as expected from the nominal filling.

Utilizing the coffee-ring effect to synthesize tin tetraiodide intercalated fullerene (C60) microcrystals by evaporative-driven self-assembly with enhanced photoluminescence

Exodo-metallofullerene microcrystals of C₆₀(SnI₄)₂ were produced by utilizing the “coffee-ring” effect during a simple drop-drying process.

Synergy between Hund-Driven Correlations and Boson-Mediated Superconductivity

Multiorbital systems such as the iron-based superconductors provide a new avenue to attack the long-standing problem of superconductivity in strongly correlated systems. In this work we study the superconductivity driven by a generic bosonic mechanism in a multiorbital model including the full dynamical electronic correlations induced by the Hubbard U and the Hund's coupling. We show that superconductivity survives much more in a Hund's metal than in an ordinary correlated metal with the same degree of correlation. The redistribution of spectral weight characteristic of the Hund's metal reflects also in the enhancement of the orbital-selective character of the superconducting gaps, in agreement with experiments in iron-based superconductors.

Direct Observation of Full-Gap Superconductivity and Pseudogap in Two-Dimensional Fullerides

Alkali-fulleride superconductors with a maximum critical temperature T_{c}∼40  K exhibit a similar electronic phase diagram to that of unconventional high-T_{c} superconductors. Here we employ cryogenic scanning tunneling microscopy to show that trilayer K_{3}C_{60} displays fully gapped strong coupling s-wave superconductivity, accompanied by a pseudogap above T_{c}∼22  K and within vortices. A precise control of the electronic correlations and potassium doping enables us to reveal that superconductivity occurs near a superconductor-Mott-insulator transition and reaches maximum at half-filling. The s-wave symmetry retains over the entire phase diagram, which, in conjunction with an abrupt decline of the superconductivity below half-filling, indicates that alkali fullerides are predominantly phonon-mediated superconductors, although the electronic correlations also come into play.

Realization of Lieb lattice in covalent-organic frameworks with tunable topology and magnetism

Lieb lattice has been predicted to host various exotic electronic properties due to its unusual Dirac-flat band structure. However, the realization of a Lieb lattice in a real material is still unachievable. Based on tight-binding modeling, we find that the lattice distortion can significantly determine the electronic and topological properties of a Lieb lattice. Importantly, based on first-principles calculations, we predict that the two existing covalent organic frameworks (COFs), i.e., sp2C-COF and sp2N-COF, are actually the first two material realizations of organic-ligand-based Lieb lattice. Interestingly, the sp2C-COF can experience the phase transitions from a paramagnetic state to a ferromagnetic one and then to a Néel antiferromagnetic one, as the carrier doping concentration increases. Our findings not only confirm the first material realization of Lieb lattice in COFs, but also offer a possible way to achieve tunable topology and magnetism in organic lattices.

Ultrafast and large optical nonlinearity of a TiSe2 saturable absorber in the 2 μm wavelength region

The non-equilibrium state of correlated electron materials is crucial for both scientific research and practical applications in optoelectronic and photonic devices. Because of the weak optical nonlinearity of most materials even under a dense optical excitation, it is desirable to achieve a significant nonlinear optical response with ultrafast and large optical nonlinearity utilizing a common material. Here, an ultrafast response and large optical nonlinearity induced by non-equilibrium electrons in typical transition metal dichalcogenides, TiSe2, are investigated in the 1.55-2.0 μm wavelength region. Significantly, we observe an ultrafast transient dynamics of 491 femtoseconds as well as a large optical nonlinearity with a saturable coefficient of -0.17 cm GW-1 (1.55 μm) and -0.10 cm GW-1 (2.0 μm). Upon increasing pump fluence, TiSe2 exhibits an enhanced bleaching response amplitude up to 563%. Furthermore, a stable Q-switched fiber laser in the 2.0 μm wavelength region is achieved by employing the TiSe2-saturable absorber. The findings offer the potential design to enhance the optical nonlinearity via non-equilibrium electrons for advanced photonic devices.

Charge Disproportionation, Mixed Valence, and Janus Effect in Multiorbital Systems: A Tale of Two Insulators

Multiorbital Hubbard models host strongly correlated "Hund's metals" even for interactions much stronger than the bandwidth. We characterize this interaction-resilient metal as a mixed-valence state. In particular, it can be pictured as a bridge between two strongly correlated insulators: a high-spin Mott insulator and a charge-disproportionated insulator which is stabilized by a very large Hund's coupling. This picture is confirmed comparing models with negative and positive Hund's coupling for different fillings. Our results provide a characterization of the Hund's metal state and connect its presence with charge disproportionation, which has indeed been observed in chromates and proposed to play a role in iron-based superconductors.

Pressure tuning of light-induced superconductivity in K3C60

Optical excitation at terahertz frequencies has emerged as an effective means to dynamically manipulate complex materials. In the molecular solid K₃C₆₀, short mid-infrared pulses transform the high-temperature metal into a non-equilibrium state with the optical properties of a superconductor. Here we tune this effect with hydrostatic pressure and find that the superconducting-like features gradually disappear at around 0.3 GPa. Reduction with pressure underscores the similarity with the equilibrium superconducting phase of K₃C₆₀, in which a larger electronic bandwidth induced by pressure is also detrimental for pairing. Crucially, our observation excludes alternative interpretations based on a high-mobility metallic phase. The pressure dependence also suggests that transient, incipient superconductivity occurs far above the 150 K hypothesised previously, and rather extends all the way to room temperature.

Competition among Superconducting, Antiferromagnetic, and Charge Orders with Intervention by Phase Separation in the 2D Holstein-Hubbard Model

Using a variational Monte Carlo method, we study the competition of strong electron-electron and electron-phonon interactions in the ground state of the Holstein-Hubbard model on a square lattice. At half filling, an extended intermediate metallic or weakly superconducting (SC) phase emerges, sandwiched between antiferromagnetic and charge order (CO) insulating phases. By carrier doping into the CO insulator, the SC order dramatically increases for strong electron-phonon couplings, but is largely hampered by wide phase separation (PS) regions. Superconductivity is optimized at the border to the PS.

Nonempirical Calculation of Superconducting Transition Temperatures in Light-Element Superconductors

Recent progress in the fully nonempirical calculation of the superconducting transition temperature (T_c ) is reviewed. Especially, this study focuses on three representative light-element high-T_c superconductors, i.e., elemental Li, sulfur hydrides, and alkali-doped fullerides. Here, it is discussed how crucial it is to develop the beyond Migdal-Eliashberg (ME) methods. For Li, a scheme of superconducting density functional theory for the plasmon mechanism is formulated and it is found that T_c is dramatically enhanced by considering the frequency dependence of the screened Coulomb interaction. For sulfur hydrides, it is essential to go beyond not only the static approximation for the screened Coulomb interaction, but also the constant density-of-states approximation for electrons, the harmonic approximation for phonons, and the Migdal approximation for the electron-phonon vertex, all of which have been employed in the standard ME calculation. It is also shown that the feedback effect in the self-consistent calculation of the self-energy and the zero point motion considerably affect the calculation of T_c . For alkali-doped fullerides, the interplay between electron-phonon coupling and electron correlations becomes more nontrivial. It has been demonstrated that the combination of density functional theory and dynamical mean field theory with the ab initio downfolding scheme for electron-phonon coupled systems works successfully. This study not only reproduces the experimental phase diagram but also obtains a unified view of the high-T_c superconductivity and the Mott-Hubbard transition in the fullerides. The results for these high-T_c superconductors will provide a firm ground for future materials design of new superconductors.

Can CF3-Functionalized La@C60 Be Isolated Experimentally and Become Superconducting?

Superconducting behavior even under harsh ambient conditions is expected to occur in La@C₆₀ if it could be isolated from the primary metallofullerene soot when functionalized by CF₃ radicals. We use ab initio density functional theory calculations to compare the stability and electronic structure of C₆₀ and the La@C₆₀ endohedral metallofullerene to their counterparts functionalized by CF₃. We found that CF₃ radicals favor binding to C₆₀ and La@C₆₀ and have identified the most stable isomers. Structures with an even number m of radicals are energetically preferred for C₆₀ and structures with odd m for La@C₆₀ due to the extra charge on the fullerene. This is consistent with a wide HOMO-LUMO gap in La@C₆₀(CF₃)_m with odd m, causing extra stabilization in the closed-shell electronic configuration. CF₃ radicals are both stabilizing agents and molecular separators in a metallic crystal, which could increase the critical temperature for superconductivity.

Spontaneous Orbital-Selective Mott Transitions and the Jahn-Teller Metal of A_{3}C_{60}

The alkali-doped fullerides A_{3}C_{60} are half-filled three-orbital Hubbard systems which exhibit an unconventional superconducting phase next to a Mott insulator. While the pairing is understood to arise from an effectively negative Hund coupling, the highly unusual Jahn-Teller metal near the Mott transition, featuring both localized and itinerant electrons, has not been understood. This property is consistently explained by a previously unrecognized phenomenon: the spontaneous transition of multiorbital systems with negative Hund coupling into an orbital-selective Mott state. This symmetry-broken state, which has no ordinary orbital moment, is characterized by an orbital-dependent two-body operator (the double occupancy) or an orbital-dependent kinetic energy and may be regarded as a diagonal-order version of odd-frequency superconductivity. We propose that the recently discovered Jahn-Teller metal phase of Rb_{x}Cs_{3-x}C_{60} is an experimental realization of this novel state of matter.

High-T C superconductivity in Cs3C60 compounds governed by local Cs-C60 Coulomb interactions

Unique among alkali-doped A ₃C₆₀ fullerene compounds, the A15 and fcc forms of Cs₃C₆₀ exhibit superconducting states varying under hydrostatic pressure with highest transition temperatures at [Formula: see text]  =  38.3 and 35.2 K, respectively. Herein it is argued that these two compounds under pressure represent the optimal materials of the A ₃C₆₀ family, and that the C₆₀-associated superconductivity is mediated through Coulombic interactions with charges on the alkalis. A derivation of the interlayer Coulombic pairing model of high-T _C superconductivity employing non-planar geometry is introduced, generalizing the picture of two interacting layers to an interaction between charge reservoirs located on the C₆₀ and alkali ions. The optimal transition temperature follows the algebraic expression, T _C0  =  (12.474 nm² K)/ℓζ, where ℓ relates to the mean spacing between interacting surface charges on the C₆₀ and ζ is the average radial distance between the C₆₀ surface and the neighboring Cs ions. Values of T _C0 for the measured cation stoichiometries of Cs_3-x C₆₀ with x  ≈  0 are found to be 38.19 and 36.88 K for the A15 and fcc forms, respectively, with the dichotomy in transition temperature reflecting the larger ζ and structural disorder in the fcc form. In the A15 form, modeled interacting charges and Coulomb potential e²/ζ are shown to agree quantitatively with findings from nuclear-spin relaxation and mid-infrared optical conductivity. In the fcc form, suppression of [Formula: see text] below T _C0 is ascribed to native structural disorder. Phononic effects in conjunction with Coulombic pairing are discussed.

Upper critical field reaches 90 tesla near the Mott transition in fulleride superconductors

Controlled access to the border of the Mott insulating state by variation of control parameters offers exotic electronic states such as anomalous and possibly high-transition-temperature (T_c) superconductivity. The alkali-doped fullerides show a transition from a Mott insulator to a superconductor for the first time in three-dimensional materials, but the impact of dimensionality and electron correlation on superconducting properties has remained unclear. Here we show that, near the Mott insulating phase, the upper critical field H_c2 of the fulleride superconductors reaches values as high as ∼90 T—the highest among cubic crystals. This is accompanied by a crossover from weak- to strong-coupling superconductivity and appears upon entering the metallic state with the dynamical Jahn–Teller effect as the Mott transition is approached. These results suggest that the cooperative interplay between molecular electronic structure and strong electron correlations plays a key role in realizing robust superconductivity with high-T_c and high-H_c2.

Alkali-doped fullerides are superconductors but the impact of dimensionality and electron correlation remains unclear. Here, Kasahara et al. report an upper critical field about 90 T, suggesting cooperative interplay between molecular electronic structure and strong electron correlations.

Unconventional high-Tc superconductivity in fullerides

A3C60 molecular superconductors share a common electronic phase diagram with unconventional high-temperature superconductors such as the cuprates: superconductivity emerges from an antiferromagnetic strongly correlated Mott-insulating state upon tuning a parameter such as pressure (bandwidth control) accompanied by a dome-shaped dependence of the critical temperature, Tc However, unlike atom-based superconductors, the parent state from which superconductivity emerges solely by changing an electronic parameter-the overlap between the outer wave functions of the constituent molecules-is controlled by the C60 (3-) molecular electronic structure via the on-molecule Jahn-Teller effect influence of molecular geometry and spin state. Destruction of the parent Mott-Jahn-Teller state through chemical or physical pressurization yields an unconventional Jahn-Teller metal, where quasi-localized and itinerant electron behaviours coexist. Localized features gradually disappear with lattice contraction and conventional Fermi liquid behaviour is recovered. The nature of the underlying (correlated versus weak-coupling Bardeen-Cooper-Schrieffer theory) s-wave superconducting states mirrors the unconventional/conventional metal dichotomy: the highest superconducting critical temperature occurs at the crossover between Jahn-Teller and Fermi liquid metal when the Jahn-Teller distortion melts.This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'.

Exotic s-wave superconductivity in alkali-doped fullerides

Alkali-doped fullerides (A3C60 with A = K, Rb, Cs) show a surprising phase diagram, in which a high transition-temperature (Tc) s-wave superconducting state emerges next to a Mott insulating phase as a function of the lattice spacing. This is in contrast with the common belief that Mott physics and phonon-driven s-wave superconductivity are incompatible, raising a fundamental question on the mechanism of the high-Tc superconductivity. This article reviews recent ab initio calculations, which have succeeded in reproducing comprehensively the experimental phase diagram with high accuracy and elucidated an unusual cooperation between the electron-phonon coupling and the electron-electron interactions leading to Mott localization to realize an unconventional s-wave superconductivity in the alkali-doped fullerides. A driving force behind the exotic physics is unusual intramolecular interactions, characterized by the coexistence of a strongly repulsive Coulomb interaction and a small effectively negative exchange interaction. This is realized by a subtle energy balance between the coupling with the Jahn-Teller phonons and Hund's coupling within the C60 molecule. The unusual form of the interaction leads to a formation of pairs of up- and down-spin electrons on the molecules, which enables the s-wave pairing. The emergent superconductivity crucially relies on the presence of the Jahn-Teller phonons, but surprisingly benefits from the strong correlations because the correlations suppress the kinetic energy of the electrons and help the formation of the electron pairs, in agreement with previous model calculations. This confirms that the alkali-doped fullerides are a new type of unconventional superconductors, where the unusual synergy between the phonons and Coulomb interactions drives the high-Tc superconductivity.