NMR study of the superconducting gap variation near the Mott transition in Cs₃C₆₀

Synthesis and structural analysis of nonstoichiometric ternary fulleride K 1.5 Ba 0.25 CsC 60

The existence of cation-vacancy sites in fullerides might lead to long-range ordering and generate a new vacancy-ordered superstructure. The purpose of this work is to search whether or not long-range ordering of vacant tetrahedral sites, namely superstructure emerges in nonstoichiometric K 1.5 Ba 0.25 CsC 60 fulleride. Therefore, K 1.5 Ba 0.25 CsC 60 with cation-vacancy sites is synthesized using a precursor method to avoid inadequate stoichiometry control and formation of impurity phases within the target composition. For this purpose, first, phase-pure K 6 C 60 , Ba 6 C 60 and Cs 6 C 60 precursors are synthesized. Stoichiometric quantities of these precursors are used for further reaction with C 60 to afford K 1.5 Ba 0.25 CsC 60 . Rietveld analysis of the high-resolution synchrotron X-ray powder diffraction data of the precursors and K 1.5 Ba 0.25 CsC 60 confirms that K 6 C 60 , Ba 6 C 60 and Cs 6 C 60 are single-phase and they crystallize in a body-centered-cubic structure ( Im 3) as reported in the literature. The analysis also shows that K 1.5 Ba 0.25 CsC 60 phase can be perfectly modeled using a face-centered cubic structure. No new peaks appear which could have implied the appearance of a superstructure. This suggests that there is no long-range ordered arrangement of vacant tetrahedral sites in K 1.5 Ba 0.25 CsC 60 .

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.

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.

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.

Nanoscale orbital excitations and the infrared spectrum of a molecular Mott insulator: A15-Cs3C60

The quantum physics of ions and electrons behind low-energy spectra of strongly correlated molecular conductors, superconductors and Mott insulators is poorly known, yet fascinating especially in orbitally degenerate cases. The fulleride insulator Cs₃C₆₀ (A15), one such system, exhibits infrared (IR) spectra with low temperature peak features and splittings suggestive of static Jahn-Teller distortions with a breakdown of orbital symmetry in the molecular site. That is puzzling, since there is no detectable static distortion, and because the features and splittings disappear upon modest heating, which they should not. Taking advantage of the Mott-induced collapse of electronic wavefunctions from lattice-extended to nanoscale localized inside a caged molecular site, we show that the unbroken spin and orbital symmetry of the ion multiplets explains the IR spectrum without adjustable parameters. This demonstrates the importance of a fully quantum treatment of nuclear positions and orbital momenta in the Mott insulator sites, dynamically but not statically distorted. The observed demise of these features with temperature is explained by the thermal population of a multiplet term whose nuclear positions are essentially undistorted, but whose energy is very low-lying. That term is in fact a scaled-down orbital excitation analogous to that of other Mott insulators, with the same spin 1/2 as the ground state, but with a larger orbital momentum of two instead of one.

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.

The strength of electron electron correlation in Cs3C60

Cs3C60 is an antiferromagnetic insulator that under pressure (P) becomes metallic and superconducting below Tc = 38 K. The superconducting dome present in the T - P phase diagram close to a magnetic state reminds what found in superconducting cuprates and pnictides, strongly suggesting that superconductivity is not of the conventional Bardeen-Cooper-Schrieffer (BCS) type We investigate the insulator to metal transition induced by pressure in Cs3C60 by means of infrared spectroscopy supplemented by Dynamical Mean-Field Theory calculations. The insulating compound is driven towards a metallic-like behaviour, while strong correlations survive in the investigated pressure range. The metallization process is accompanied by an enhancement of the Jahn-Teller effect. This shows that electronic correlations are crucial in determining the insulating behaviour at ambient pressure and the bad metallic nature for increasing pressure. On the other hand, the relevance of the Jahn-Teller coupling in the metallic state confirms that phonon coupling survives in the presence of strong correlations.

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

Alkali-doped fullerides A 3C60 (A = K, Rb, Cs) are surprising materials where conventional phonon-mediated superconductivity and unconventional Mott physics meet, leading to a remarkable phase diagram as a function of volume per C60 molecule. We address these materials with a state-of-the-art calculation, where we construct a realistic low-energy model from first principles without using a priori information other than the crystal structure and solve it with an accurate many-body theory. Remarkably, our scheme comprehensively reproduces the experimental phase diagram including the low-spin Mott-insulating phase next to the superconducting phase. More remarkably, the critical temperatures T c's calculated from first principles quantitatively reproduce the experimental values. The driving force behind the surprising phase diagram of A 3C60 is a subtle competition between Hund's coupling and Jahn-Teller phonons, which leads to an effectively inverted Hund's coupling. Our results establish that the fullerides are the first members of a novel class of molecular superconductors in which the multiorbital electronic correlations and phonons cooperate to reach high T c s-wave superconductivity.

Optimized unconventional superconductivity in a molecular Jahn-Teller metal

Understanding the relationship between the superconducting, the neighboring insulating, and the normal metallic state above T c is a major challenge for all unconventional superconductors. The molecular A3C60 fulleride superconductors have a parent antiferromagnetic insulator in common with the atom-based cuprates, but here, the C60 (3-) electronic structure controls the geometry and spin state of the structural building unit via the on-molecule Jahn-Teller effect. We identify the Jahn-Teller metal as a fluctuating microscopically heterogeneous coexistence of both localized Jahn-Teller-active and itinerant electrons that connects the insulating and superconducting states of fullerides. The balance between these molecular and extended lattice features of the electrons at the Fermi level gives a dome-shaped variation of T c with interfulleride separation, demonstrating molecular electronic structure control of superconductivity.

Size and symmetry of the superconducting gap in the f.c.c. Cs3C60 polymorph close to the metal-Mott insulator boundary

The alkali fullerides, A(3)C(60) (A = alkali metal) are molecular superconductors that undergo a transition to a magnetic Mott-insulating state at large lattice parameters. However, although the size and the symmetry of the superconducting gap, Δ, are both crucial for the understanding of the pairing mechanism, they are currently unknown for superconducting fullerides close to the correlation-driven magnetic insulator. Here we report a comprehensive nuclear magnetic resonance (NMR) study of face-centred-cubic (f.c.c.) Cs(3)C(60) polymorph, which can be tuned continuously through the bandwidth-controlled Mott insulator-metal/superconductor transition by pressure. When superconductivity emerges from the insulating state at large interfullerene separations upon compression, we observe an isotropic (s-wave) Δ with a large gap-to-superconducting transition temperature ratio, 2Δ0/k(B)T(c) = 5.3(2) [Δ0 = Δ(0 K)]. 2Δ0/k(B)T(c) decreases continuously upon pressurization until it approaches a value of ~3.5, characteristic of weak-coupling BCS theory of superconductivity despite the dome-shaped dependence of Tc on interfullerene separation. The results indicate the importance of the electronic correlations for the pairing interaction as the metal/superconductor-insulator boundary is approached.

Jahn–Teller orbital glass state in the expanded fcc Cs3C60 fulleride

Magic-angle-spinning NMR measurements on fcc Cs₃C₆₀ to cryogenic temperatures reveal freezing-out of the C₆₀^3¬ Jahn–Teller dynamics and emergence of an electronic orbital glass state guided by the C₆₀^3¬ merohedral disorder.