There continues to be enormous interest in the BCS to BEC transition as there still is no exact theory. We recently reported a revealing reinterpretation of the condensed phase Boson-Fermion Model (BFM) by comparing it to a cold atom formulation [1]. While the ground and singly excited states appear to remain continuous in all models we have examined, the collective modes contain a singularity due to a Feshbach resonance (tuned by doping) causing a breakdown of the Migdal theorem. As a result of vertex corrections, there is a fundamental change in the nature of the superconductivity due to the formation of preformed pairs as the previously suggested location [1] of a quantum critical point in the fulleride phase diagram is passed. The result is a quantum phase transition (QPT) between BCS and BEC-like (or Feshbach resonance) superconductivity (SC).
We discuss features of the resonance and the role of the experimentally observed preformed pair formation in fullerides, essential to the Boson-Fermion Model (BFM), and often speculated since the work of Nozieres and Schmitt-Rink [17]. Here, we present arguments to establish a model of the preformed pair which can be favorably compared to a circular charge density wave (CDW) isolated on a fulleride molecule. The binding is much larger than a Cooper pair. The CDW seems to be stabalized by splitting of the Jahn-Teller active vibrational modes to reduce Coulomb repulsions. Our conclusions are: 1) the doping of two electrons into triply degenerate orbitals results in the experimentally observed singlet state (CDW); and 2) this CDW (preformed pair) has a dual role as doping is varied: suppression of BCS SC and enabling a Feshbach resonance form of SC.
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…
A repulsive interaction model of superconductivity (SC) is studied for tight-binding models with three-fold degenerate molecular orbitals. Taking a weak-coupling approach, we derive dimensionless coupling constants for various symmetries of SC pairs. In addition to anisotropic SC pairs, the s-wave pairing ($A_g$) can also be formed. With the purely repulsive interaction, however, the $A_g$ pair is not the most stable in both bcc and fcc lattices. The most stable SC pair for the bcc lattice has the $T_g$ symmetry, which is favored by a strongly nesting Fermi surface. In the fcc lattice, various…
Alkali-doped fullerides A3C60 (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 the volume per C60 molecule. Here 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-spi…
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 eluci…
Alkali-fulleride superconductors with a maximum critical temperature Tc of 40 K exhibit similar electronic phase diagram with unconventional high-Tc superconductors where the superconductivity resides proximate to a magnetic Mott-insulating state. However, distinct from cuprate compounds, which superconduct through two-dimensional (2D) CuO2 planes, alkali fullerides are attributed to the three-dimensional (3D) members of high-Tc family. Here, we employ scanning tunneling microscopy to show that trilayer K3C60 displays fully gapped strong coupling s-wave superconductivity that coexists spatiall…
The successful preparation of superconducting alkali fulleride (A$_x$C$_{60}$, A = K, Rb, Cs) films using state-of-the-art molecular beam epitaxy overcomes the disadvantages of the air-sensitivity and phase separation in bulk A$_x$C$_{60}$, enabling for the first time a direct investigation of the superconductivity in alkali fullerides on the molecular scale. In this paper, we briefly review recent cryogenic scanning tunneling microscopy results of the structural, electronic, and superconducting properties of the fcc A$_x$C$_{60}$ films grown on graphitized SiC substrates. Robust $s$-wave supe…
Motivated by the recent experimental report of a possible light-induced superconductivity in A3C60 at high temperature [Mitrano et al., Nature 530, 451 (2016)], we investigate theoretical mechanisms for enhanced superconductivity in A3C60 fullerenes. We find that an `interaction imbalance' corresponding to a smaller value of the Coulomb matrix element for two of the molecular orbitals in comparison to the third one, efficiently enhances superconductivity. Furthermore, we perform first-principle calculations of the changes in the electronic structure and in the screened Coulomb matrix elements …
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 t…
We investigate the competition between the electron-vibron interaction (interaction with the Jahn-Teller phonons) and the Coulomb repulsion in a system with local pairing of electrons on the triply degenerate lowest unoccupied molecular orbital (LUMO). The electron-vibron interaction radically changes conductivity and magnetic properties of alkali-doped fullerides AnC60, which should be antiferromagnetic Mott insulators: we have found that materials with n=1,2 and A=K,Rb are conductors but not superconductors; n=3 and A=K,Rb are conductors (superconductors at low temperatures), but with A=Cs a…
Over the past 20 years, fullerides have been studied as the source of high-transition-temperature (Tc) superconductivity except for copper oxides. The recent finding of the Mott insulating state right beside superconductivity in Cs3C60 has suggested that magnetism helps raise Tc even in fullerides as in heavy-fermion compounds, high-Tc copper oxides, two-dimensional organic conductors, and iron pnictides. Namely, one tends to think that the link between Mott insulator and superconductivity takes place in fullerides, which can give rise to the mechanism beyond the Bardeen-Cooper-Schrieffer fram…
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 $\texttt{A}_{n}\texttt{C}_{60}$, which would have to be antiferromagnetic Mott insulators: we have shown that materials with $n=1,5$ and $\texttt{A}=\texttt{K},\texttt{Rb}$ are conductors but not superconductors; $n…
We present a theory of superconductivity in magic-angle twisted bilayer graphene and analyze the superconducting phase diagram in presence of the magnetic field. Namely, we consider a model of a granular array hosting localized states, which are hybridized via the delocalized fermions in the inter-grain regions. We study a strong coupling situation when the interactions lead to an incoherent state with preformed Cooper pairs inside the grains. The Andreev scattering among different grains manifests itself through the global phase-coherent superconducting state at lower temperatures. We demonst…
This paper addresses the long standing and controversial issue of the origin of superconductivity in cuprates. Their superconductivity can be attributed to amphoteric defects associated with vacancy sites in copper oxide planes. A local defect lattice relaxation results in a negative-$U$ energy binding two holes on amphoteric defects in the donor configuration that act as preformed boson pair. Thermodynamic equilibrium between defects in the donor and acceptor configurations stabilizes Fermi energy at the amphoteric defect charge transition state assuring resonant coupling between free holes a…
Egorov and March plotted the product of resistivity and the copper spin-lattice relaxation time vs. temperature for yttrium barium copper oxide finding a minimum at temperature T greater than the superconducting temperature, heralding an electronic phase change which can be interpreted as the formation of a "preformed" pair. In this context we propose a superconducting mechanism based on the notion that the preformed pair is a "soft" boson (a localized, different type of Cooper pair) which dissociates above the classical BKT transition temperature, resulting in two circular charge density wave…
We report an NMR and magnetometry study on the expanded intercalated fulleride Cs_3C_60 in both its A15 and face centered cubic structures. NMR allowed us to evidence that both exhibit a first-order Mott transition to a superconducting (SC) state, occuring at distinct critical pressures p_c and temperatures T_c. Though the ground state magnetism of the Mott phases differs, their high $T$ paramagnetic and SC properties are found similar, and the phase diagrams versus unit volume per C_60 are superimposed. Thus, as expected for a strongly correlated system, the inter-ball distance is the relveva…
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 {\bf 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 multi-orbital 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 metho…
We study conditions for the emergence of the preformed Cooper pairs in materials hosting flat bands. As a particular example, we consider a semimetal, with a pair of three-band crossing points at which a flat band intersects with a Dirac cone, and focus on the s-wave intervalley pairing channel. The nearly dispersionless nature of the flat band at strong attraction between electrons promotes local Cooper pair formation so that the system may be modeled as an array of superconducting grains. Due to dispersive bands, Andreev scattering between the grains gives rise to the global phase-coherent s…
A weird electronic state accompanied with an anomalous superconducting precursor and/or exotic orders, called the pseudogap state, arises prior to a superconducting condensate in underdoped cuprates that are situated near Mott transition. Another way to make the system approach the Mott transition is the variation of bandwidth or correlation strength, which gives a new dimension to exploring this exotic state. Here we report nuclear magnetic resonance (NMR) studies on layered organic superconductors with half-filled bands whose widths are pressure-tuned near the Mott transition. The system sit…
Observation of Andreev reflection in the c-axis transport of Bi_2Sr_2CaCu_2O_{8+x} single crystals near T_c and search for the preformed-pair state
我们观察到Au $/$ Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+x}$（Bi 2212）结在超导转变温度$T_c$附近的$c$轴微分电导在零偏压附近的增强。我们将电导增强归因于表面Cu-O双层与相邻的超导内双层之间的Andreev反射。随着温度从下方接近$T_c$，零偏压微分电导从降低到增强的连续演化指向相邻Cu-O双层之间的非超导层的势垒强度的减弱。我们观察到，电导增强持续到几度以上$T_c$在轻微过掺杂的Bi 2212晶体上制备的结。然而，没有观察到电导增强以上$T_c$在欠掺杂晶体，虽然最近提出的理论考虑表明，甚至更宽的温度范围内增强零偏置电导。这似乎为赝能隙态中存在相位不相干的预成对提供了一个消极的观点。
Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while the electron pairing occurs at higher temperature than the long-range phase coherence in the underdoped high-Tc cuprate superconductors. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO3 substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudoga…
The discovery in 1991 of high temperature superconductivity (SC) in A3C60 compounds, where A is an alkali ion, has been initially ascribed to a BCS mechanism, with a weak incidence of electron correlations. However various experimental evidences taken for compounds with distinct alkali content established the interplay of strong correlations and Jahn Teller distortions of the C60 ball. The importance of electronic correlations even in A3C60 has been highlighted by the recent discovery of two expanded fulleride Cs3C60 isomeric phases that are Mott insulators at ambient pressure. Both phases und…
The physical properties and structural evolution of the MX$_2$-type solid solution Au$_{1-x}$Pd$_x$Te$_2$ are reported. The end member AuTe$_2$ is a normal metal with a monoclinic distorted CdI$_2$-type structure with preformed Te-Te dimers. A monoclinic--trigonal structural phase transition at a finite temperature occurs upon Pd substitution and is suppressed to zero temperature near $x$ = 0.55, and a superconducting phase with a maximum $T_{\rm c}$ = 4.65 K emerges. A clear indication of strong coupling superconductivity is observed near the composition of the structural instability. The com…
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 mo…
The remarkable universality of the cuprate $T_c$ dome suggests a very fundamental unifying principle. Moreover, the superconducting gap is known to persist above $T_c$ in the pseudogap phase of all cuprates. So, contrary to BCS, the gap cannot be the order parameter of the transition. In this work, we show that both the $T_c$-dome and the pseudogap line $T^*(p)$ arise from a unique and identifiable principle: the interaction of localized `pairons' on an antiferromagnetic square lattice. The topological constraints on such preformed pairons give rise to both the $T_c$ dome and the pairing energ…
Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Mueller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of antiferromagnetic fluctuations, and the presence of a mysterious pseudogap phase close to the Mott state, one can conclude that high-Tc superconductors are clearly distinguishable from the well-understood BCS superconductors. The d-wave superconducting state can be understood through a Gutzwiller-type projected BCS wave-function. In this review article, we revisit the Hub…
To establish the doping-dependent phase diagram in alkali-metal doped C$_{60}$, we synthesize Rb-doped C$_{60}$ samples with different stoichiometries by using the improved wet-chemistry technique. The doping levels determined from the Raman scattering spectra often show the appearance of three electrons corresponding to the band filling of three for the synthesized compounds no matter matter what dopants are used. The multiple phase coexistence with the unique Rb$_{3}$C$_{60}$ is identified from the refined x-ray diffraction patterns. The phase fraction of Rb$_{3}$C$_{60}$ is found to behave …
In conventional superconductors, phonons glue two electrons with opposite spins to form Cooper pairs and condensation of these pairs leads to the superconductivity. Identifying the underlying mechanism of the high temperature superconductivity in cuprates is among the most important problems in physics. Even quarter of a century after the first report of high temperature superconductor by Bednorz and Muller in 1986, there is still no general consensus on the pairing mechanism of superconductivity in these materials. So far, many theories have been developed to explain the exotic properties of …
We analyze the interplay between superconductivity and the formation of bound pairs of fermions (BCS-BEC crossover) in 2D models of interacting fermions with small Fermi energy EF and weak attractive interaction, which extends to energies well above EF. The 2D case is special because one has to distinguish between bound state formation and superconductivity already at weak coupling. We briefly review the situation in the one-band model and then consider two different two-band models: the one with a hole and an electron band, and the one with two electron bands. In each case we obtain the bound…
The mutual interaction between Cooper pairs is proposed as a mechanism for the superconducting state. Above $T_c$, pre-existing but fluctuating Cooper pairs give rise to the unconventional {\it pseudogap} (PG) state, well-characterized by experiment. At the critical temperature, the pair-pair interaction induces a Bose-like condensation of these preformed pairs leading to the superconducting (SC) state. Below $T_c$, both the condensation energy and the pair-pair interaction $β$ are proportional to the condensate density $N_{oc}(T)$, whereas the usual Fermi-level spectral gap $Δ_p$ is independe…
Recent experiments have reported the emergence of high temperature superconductivity with critical temperature $T_c$ between 43K and 123K in a potassium doped aromatic hydrocarbon para-Terphenyl or p-Terphenyl. This achievement provides the record for the highest Tc in an organic superconductor overcoming the previous record of Tc=38 K in Cs3C60 fulleride. Here we propose that the driving mechanism is the quantum resonance between superconducting gaps near a Lifshitz transition which belongs to the class of Fano resonances called shape resonances. For the case of p-Terphenyl our numerical solu…
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 symmet…
By using the gauge-invariant kinetic equation approach [Yang and Wu, Phys. Rev. B {\bf 98}, 094507 (2018); {\bf 100}, 104513 (2019)], we construct the coupled dual dynamics of macroscopic phase coherence and microscopic electronic fluids in cuprate superconductors. We prove that the developed dual dynamics provides an efficient and simplified approach to formulate the dephasing process of macroscopic superconducting phase coherence, as well as its influence on microscopic electronic fluids (including gap, densities of superfluid and normal fluid, and in particular, the transport property to de…
In this paper, the sixth in series, we continue our analysis of the interplay between non-Fermi liquid and pairing in the effective low-energy model of fermions with singular dynamical interaction $V(Ω_m) = {\bar g}^γ/|Ω_m|^γ$ (the $γ$ model). The model describes low-energy physics of various quantum-critical metallic systems at the verge of an instability towards density or spin order, pairing of fermions at the half-filled Landau level, color superconductivity, and pairing in SYK-type models. In previous Papers I-V we analyzed the $γ$ model for $γ\leq 2$ and argued that the ground state is a…
The pseudogap phase of high-$T_c$ cuprates is controversially attributed to preformed pairs or to a phase which coexists and competes with superconductivity. One of the challenges is to develop theoretical and experimental studies in order to distinguish between both proposals. Very recently, researchers at Stanford have reported [M. Hashimoto {\it et al.}, Nat. Phys. {\bf 6}, 414 (2010); R.-H. He {\it et al.}, Science {\bf 331}, 1579 (2011)] angle-resolved photoemission spectroscopy experiments on Pb-Bi2201 supporting the point of view that the pseudogap is distinct from superconductivity and…
