Alkali-doped Fullerides Research Articles

Variation of the critical temperature with the lattice parameter in K3C60

Alkali-doped fullerides are a fascinating system exhibiting the convergence of s-wave superconductivity and Mott physics. A direct relationship between the critical temperature Tc and lattice constant established by applying physical or chemical pressure in these compounds is generally believed to be the foundation for the identification of the microscopic electron pairing(s). Here the evolution of Tc with lattice compression for the first fulleride K3C60 is systematically studied via the high-pressure electrical transport and synchrotron x-ray diffraction measurements on the same well-characterized sample. The combination of the theoretically calculated density of states at the Fermi level, the electron-phonon coupling and mean phonon-frequency determined from high-pressure Raman spectra yields the Coulomb pseudopotential ranging from 0.15 to 0.32 with increasing pressure in terms of the McMillan formula. This indicates that the conventional phonon-mediated mechanism cannot account for the high-pressure evolution of Tc solely. However, the obtained pressure derivative of Tc and bulk modulus are used to reproduce well the experimentally observed isotope exponent in this superconductor within the theoretical framework of the non-phononic theory. These results and findings together demonstrate the important role of the study of the lattice effect on Tc played in determining the mechanisms of superconductivity in fullerides.

Superconductivity and Magnetism in the A15 Phase of Alkali-Doped Fullerides

Superconductivity and Magnetism in the A15 Phase of Alkali-Doped Fullerides

Visualizing molecular orientational ordering and electronic structure in CsnC60 fulleride films

Alkali-doped fullerides exhibit a wealth of unusual phases that remain controversial by nature. Here we report a cryogenic scanning tunneling microscopy study of the sub-molecular structural and electronic properties of expanded fullerene C60 films with various cesium (Cs) doping. By varying the discrete charge states and film thicknesses, we reveal a large tunability of orientational ordering of C60 anions, yet the tunneling conductance spectra are all robustly characteristic of energy gaps, hallmarks of Jahn-Teller instability and electronic correlations. The Fermi level lies halfway within the insulating gap for stoichiometric Cs doping level of n = 1, 2, 3 and 4, apart from which it moves toward band edges with concomitant electronic states within the energy gap. Our findings establish the universality of Jahn-Teller instability, and clarify the relationship among the doping, structural and electronic structures in CsnC60 fullerides.

Superconductivity in alkali-doped fullerides with wood’s metal and heterofullerides with two different alkali metals A(1)A(2)MC60

Here we report our experimental data on the synthesis and investigation of superconductivity in fullerides and heterofullerides synthesized by different methods and also doped by alloys with low melting temperature Tm: Wood’s metal (W – Sn,Pb,Bi,Cd; Tm = 65°С), alloy Y (Y - Bi,Sn.Pb,In,Cd,Tl; Тm = 41.5°С) and Tl doped heterofullerides with two different alkali metals – ACsTlC60 (A = K, Rb). We found superconductivity in heterofullerides K2W1C60 (Tc = 16 K), Rb2W1C60 (Tc = 8 K) and K2Y1C60 (Tc = 8 K). Also synthesized heterofullerides with Cesium KCsTlC60 (Тс = 21.7 K) and RbCsTlC60 (Тс = 26.4 K) are superconductors.

Theoretical phase diagram of unconventional alkali-doped fullerides

By constructing an effective model based on recently calculated \emph{ab }initio bare interaction parameters, we study the phase diagram of alkali doped fullerides as a function of temperature and internal pressure. We use a slave-rotor mean-field approach at the weak and intermediate coupling limits and a variational mean-field approach at the strong coupling limit, and find a good agreement with experimental phase diagram. We explain the unified description of the phase diagram including the proximity of s-wave superconducting state and the Mott-insulating state, and the existence of Jahn-Teller distorted metallic state using orbital selective physics. We ague that the double electronic occupation of two degenerate orbitals triggers both s-wave superconductivity and Jahn-Teller distortion. While the orbital ordering of two electrons causes the distortion, the remaining single electron in the third orbital causes the metal-insulator transition.

The role of electron–vibron interaction and local pairing in conductivity and superconductivity of alkali-doped fullerides

We investigate the competition between the electron–vibron interaction (interaction with the Jahn–Teller phonons) and the Coulomb repulsion in a system with the local pairing of electrons on the 3-fold degenerate lowest unoccupied molecular orbital (LUMO). The el.–vib. interaction and the local pairing radically change conductivity and magnetic properties of alkali-doped fullerides AnC60, which would have to be antiferromagnetic Mott insulators: we have shown that materials with n=1,5 and A=K,Rb are conductors but not superconductors; n=3 and A=K,Rb are conductors and superconductors at low temperatures, but with A=Cs they are Mott–Jahn–Teller insulators at normal pressure; n=2,4 are nonmagnetic Mott insulators. Thus superconductivity, conductivity and insulation of these materials have common nature. Using this approach we obtain the phase diagram of A3C60 analytically, which is the result of interplay between the local pairing, the el.–vib. interaction, Coulomb correlations, and formation of small radius polarons.

Spontaneously orbital-selective superconductivity in a three-orbital Hubbard model

We study a three-orbital Hubbard model with negative Hund coupling in infinite dimensions, combining dynamical mean-field theory with continuous time quantum Monte Carlo simulations. This model, which is relevant for the description of alkali-doped fullerides, has previously been shown to exhibit a spontaneous orbital selective Mott phase in the vicinity of the superconducting phase. Calculating the pair potential and double occupancy in each orbital, we study the competition between different homogeneous ordered states and determine the corresponding finite temperature phase diagram of the model. We identify two distinct types of spontaneous orbital-selective Mott states and show that an orbital-selective $s$-wave superconducting state with one superconducting and two metallic orbitals is spontaneously realized between the conventional $s$-wave superconducting phase and these two kinds of spontaneously orbital-selective Mott states.

Chemical effects of alkali atoms on critical temperature in superconducting alkali-doped fullerides

Alkali metal doped fullerides (A3C60) are superconductors with critical temperatures, Tc, extending up to 38 K. Tc is known to depend strongly on the lattice parameter a, which can be adjusted by physical or chemical pressure. In the latter case an alkali atom is replaced by a different sized one, which changes a. We have collected an extensive data base of experimental data for Tc from very early up to recent measurements. We disentangle alkali atom chemical effects on Tc, beyond the well-known consequences of changing a. It is found that Tc, for a fixed a, is typically increased as smaller alkali atoms are replaced by larger ones, except for very large a. Possible reasons for these results are discussed. Although smaller in size than the lattice parameter contribution, the chemical effect is not negligible and should be considered in future physical model developments.

Nonequilibrium superconductivity in driven alkali-doped fullerides

We investigate the formation of non-equilibrium superconducting states in driven alkali-doped fullerides A$_3$C$_{60}$. Within a minimal three-orbital model for the superconductivity of these materials, it was recently demonstrated theoretically that an orbital-dependent imbalance of the interactions leads to an enhancement of superconductivity at equilibrium [M. Kim et al. Phys. Rev. B 94, 155152 (2016)]. We investigate the dynamical response to a time periodic modulation of this interaction imbalance, and show that it leads to the formation of a transient superconducting state which survives much beyond the equilibrium critical temperature $T_c$. For a specific range of modulation frequencies, we find that the driving reduces superconductivity when applied to a superconducting state below $T_c$, while still inducing a superconducting state when the initial temperature is larger than $T_c$. These findings reinforce the relevance of the interaction-imbalance mechanism as a possible explanation of the recent experimental observation of light-induced superconductivity in alkali-doped fullerenes.

Enhancement of superexchange pairing in the periodically driven Hubbard model

Recent experiments performed on cuprates and alkali-doped fullerides have demonstated that key signatures of superconductivity can be induced above the equilibrium critical temperature by optical modulation. These observations in disparate physical systems may indicate a general underlying mechanism. Multiple theories have been proposed, but these either consider specific features, such as competing instabilities, or focus on conventional BCS-type superconductivity. Here we show that periodic driving can enhance electron pairing in strongly-correlated systems. Focusing on the strongly-repulsive limit of the doped Hubbard model, we investigate in-gap, spatially inhomogeneous, on-site modulations. We demonstrate that such modulations substantially reduce electronic hopping, while simultaneously sustaining super-exchange interactions and pair hopping via driving-induced virtual charge excitations. We calculate real-time dynamics for the one-dimensional case, starting from zero and finite temperature initial states, and show that enhanced singlet--pair correlations emerge quickly and robustly in the out-of-equilibrium many-body state. Our results reveal a fundamental pairing mechanism that might underpin optically induced superconductivity in some strongly correlated quantum materials.

Ultrafast switching of composite order in A3C60

We study the controlled manipulation of the Jahn-Teller metal state of fulleride compounds using nonequilibrium dynamical mean field theory. This anomalous metallic state is a spontaneous orbital-selective Mott phase, which is characterized by one metallic and two insulating orbitals. Using protocols based on transiently reduced hopping amplitudes or periodic electric fields, we demonstrate the possibility to switch orbitals between Mott insulating and metallic on a sub-picosecond timescale, and to rotate the order parameter between three equivalent states that can be distinguished by their anisotropic conductance. The Jahn-Teller metal phase of alkali-doped fullerides thus provides a promising platform for ultrafast persistent memory devices.

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.

Upper critical field reaches 90\u2009tesla 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 (Tc) 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 Hc2 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-Tc and high-Hc2.

Nonempirical Calculation of Superconducting Transition Temperatures in Light-Element Superconductors.

Recent progress in the fully nonempirical calculation of the superconducting transition temperature (Tc ) is reviewed. Especially, this study focuses on three representative light-element high-Tc 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 Tc 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 Tc . 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-Tc superconductivity and the Mott-Hubbard transition in the fullerides. The results for these high-Tc superconductors will provide a firm ground for future materials design of new superconductors.

Orbital disproportionation of electronic density is a universal feature of alkali-doped fullerides.

Alkali-doped fullerides show a wide range of electronic phases in function of alkali atoms and the degree of doping. Although the presence of strong electron correlations is well established, recent investigations also give evidence for dynamical Jahn–Teller instability in the insulating and the metallic trivalent fullerides. In this work, to reveal the interplay of these interactions in fullerides with even electrons, we address the electronic phase of tetravalent fulleride with accurate many-body calculations within a realistic electronic model including all basic interactions extracted from first principles. We find that the Jahn–Teller instability is always realized in these materials too. In sharp contrast to the correlated metals, tetravalent system displays uncorrelated band-insulating state despite similar interactions present in both fullerides. Our results show that the Jahn–Teller instability and the accompanying orbital disproportionation of electronic density in the degenerate lowest unoccupied molecular orbital band is a universal feature of fullerides.

Electronic orders in multiorbital Hubbard models with lifted orbital degeneracy

We study the symmetry-broken phases in two- and three-orbital Hubbard models with lifted orbital degeneracy using dynamical mean field theory. On the technical level, we explain how symmetry relations can be exploited to measure the four-point correlation functions needed for the calculation of the lattice susceptibilities. In the half-filled two-orbital model with crystal field splitting, we find an instability of the metallic phase to spin-orbital order with neither spin nor orbital moment. This ordered phase is shown to be related to the recently discovered fluctuating-moment induced spin-triplet superconducting state in the orbitally degenerate model with shifted chemical potential. In the three-orbital case, we consider the effect of a crystal field splitting on the spin-triplet superconducting state in the model with positive Hund coupling, and the spin-singlet superconducting state in the case of negative Hund coupling. It is demonstrated that for certain crystal field splittings the higher energy orbitals instead of the lower ones are relevant for superconductivity, and that $T_c$ can be enhanced by the crystal field effect. We comment on the implications of our results for the superconductivity in strontium ruthenates, and for the recently reported light-enhanced superconducting state in alkali-doped fullerides.

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.

Nonempirical study of superconductivity in alkali-doped fullerides based on density functional theory for superconductors

We apply the density functional theory for superconductors (SCDFT) based on the local-density approximation (LDA) to alkali-doped fullerides A3C60 with the face-centered cubic structure. We evaluate the superconducting transition temperature (Tc) from first principles considering energy dependence of electron-phonon coupling, the mass renormalization, and the retardation effect. The calculated Tc=7.5, 9.0 and 15.7 K for A=K, Rb, Cs are approximately 60 % smaller than the experimentally observed values. Our results strongly suggest necessity to go beyond the framework of the Migdal-Eliashberg theory based on the LDA.

Rotationally invariant slave bosons for strongly correlated superconductors

We extend the rotationally invariant formulation of the slave-boson method to superconducting states. This generalization, building on the recent work by Lechermann et al. [Phys. Rev. B 76, 155102 (2007)], allows to study superconductivity in strongly correlated systems. We apply the formalism to a specific case of strongly correlated superconductivity, as that found in a multiorbital Hubbard model for alkali-doped fullerides, where the superconducting pairing has phonic origin, yet it has been shown to be favored by strong correlation owing to the symmetry of the interaction. The method allows to treat on the same footing the strong correlation effects and the interorbital interactions driving superconductivity, and to capture the physics of strongly correlated superconductivity, in which the proximity to a Mott transition favors the superconducting phenomenon.

Competition fix

The complex electronic properties of alkali-doped fullerides derive from the interplay between competing interactions. Fine control of the doping levels and thickness of fulleride films makes it possible to tune relevant parameters.