Abstract
Local quasiparticle states around impurities provide essential insight into the mechanism of unconventional superconductivity, especially when the candidate materials are proximate to an antiferromagnetic Mott-insulating phase. While such states have been reported in atom-based cuprates and iron-based compounds, they are unexplored in organic superconductors which feature tunable molecular orientation. Here we employ scanning tunneling microscopy and spectroscopy to reveal multiple forms of robustness of an exotic s-wave superconductivity in epitaxial Rb3C60 films against merohedral disorder, non-magnetic single impurities and step edges at the atomic scale. Yu-Shiba-Rusinov (YSR) states, induced by deliberately incurred Fe adatoms that act as magnetic scatterers, have also been observed. The YSR bound states show abrupt spatial decay and vary in energy with the Fe adatom registry. These results and a doping-dependent study of superconductivity point towards local electron pairing in which the multiorbital electronic correlations and intramolecular phonons together drive the high-temperature superconductivity of doped fullerenes.
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Introduction
Disorders, impurities in an otherwise homogeneous or granular superconductor, are often undesired aliens because they may hinder observations of intrinsic properties of the host material1,2,3,4. Yet, dopant impurities could also be a double-edged sword by leading not only to emergent high-temperature (Tc) superconductivity in cuprates and iron pnictides5,6 but also to uncovering the underlying mechanism of unconventional superconductivity7,8,9,10,11,12,13, especially as multiple unusual states are complexly intertwined in these materials14,15. Whereas it has been well documented that non-magnetic impurities little affect Cooper pairs in conventional superconductors16,17, they induce local bound states in the superconducting gap (Δ) and suppress superconductivity via pair breaking for unconventional pairing symmetries, for example, in a d-wave or s± wave superconductor8,17,18,19,20. Recently, anomalous enhancement of superconductivity by disorder is another example of impurities revealing their fundamental significance for low-dimensional superconductors21,22,23,24. It is therefore tempting to consider impurities as a blessing in disguise to unveil the physics of candidate superconductors4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, to strive for optimal superconductivity with Tc and Δ reaching their respective maxima25, and to create exotic electronic states that never emerge from pure superconducting systems26.
Unlike atom-based superconductors, an organic superconductor is a synthetic molecule-based compound that uniquely exhibits additional degrees of freedom related to its molecular orientation. Consequently, inequivalent molecular orientations take place. Such orientational (merohedral) disorder has been seen early in pure and doped fullerenes27,28, but its impact, either harmful29,30 or irrelevant31,32, to superconductivity of fullerenes, is highly controversial. In addition, the fullerides represent an unusual category of organic superconductors in which the multiorbital electronic correlations and electron–phonon interactions are both suggested to be significant to reach high-Tc superconductivity33,34. Under this context, a systematic study of impurity effects on superconductivity of doped fullerenes would provide justification of the previously advocated s-wave pairing symmetry35,36,37, as well as advance the understanding of the superconducting state. However, such an experiment is unexplored and the roles played by magnetic and non-magnetic impurities remain unknown in fulleride superconductors.
In this work, we use a molecular beam epitaxy (MBE) technique to grow epitaxial films of rubidium (Rb)-doped fullerenes with thickness and filling tunability, and probe the local quasiparticle states in the vicinity of various impurities at the atomic scale by means of cryogenic scanning tunneling microscopy (STM) and spectroscopy (STS). Distinct from the superconducting K3C60 films without merohedral disorder37 and the insulating Cs3C60 ones with great merohedral disorder38, merohedrally disordered Rb3C60 films are superconducting. This allows for atomic-scale visualization of merohedral disorder impact on superconductivity of fullerenes, which, together with a detailed STS study of magnetic and non-magnetic impurities, shows that superconductivity of fullerenes is entirely consistent with local s-wave pairing. By studying the thickness and electron-filling dependence of superconducting gap Δ in RbxC60, we further establish a unified phase diagram of fullerenes in which the optimal superconductivity always develops at half-filling (x = 3).
Results
Merohedral disorder and its impact on superconductivity
Figure 1a depicts a representative STM topography of nine monolayer (ML) Rb3C60 thin films epitaxially grown on graphitized SiC(0001) substrates. Evidently, not all C60 molecules have the same orientation, although one threefold symmetry axis for every C60 is perpendicular to the surface. Specifically, nanoscale domains with two distinct C60 orientations, related by 44.48° rotation about the [111] axis (Fig. 1b), develop and are partially opacified in red and orange, respectively. This is reminiscent of the two standard orientations of C60 that randomly occur and cause merohedral disorder in face-centered cubic-structured trivalent fullerides28,29,30. The C60 orientations are more disordered in regions between adjacent merohedral domains. In order to quantify the merohedral disorder, the averaged orientational correlation functions <cos(θij)>39, in which θij = θi −θj denotes the angle between nearest-neighbor C60 molecules (i.e., i and j), are calculated and summarized in Fig. 1c. The orientational correlation decreases with alkali metal radius, indicating increasing merohedral disorder. This most probably arises from a weakening of Coulomb repulsion between adjacent trivalent C60 ions associated with the lattice expansion40, which otherwise stabilizes a long-ranged merohedral order in the K3C60 films37, to wit <cos(θij)> = 1. For a specific K3C60 or Rb3C60 compound, it turns out that the orientational correlation and thus merohedral disorder change little with the film thickness (Supplementary Figure 1).
Tunneling spectroscopy of fullerides probes the local density of quasiparticle states (DOS) and measures the superconducting energy gap at the Fermi level (EF). In Fig. 1d, we compare tunneling dI/dV spectra on various trivalent fulleride films A3C60 (A = K, Rb, Cs) with the same thickness of 9 ML. Although two sharp DOS peaks develop ~−0.4 eV and 0.1 eV in the merohedrally ordered K3C60 films37, they are largely smoothed out in both Rb3C60 and RbCs2C60 with the great merohedral disorder. This observation is consistent with the theoretical calculation that the merohedral disorder would blur t1u-derived DOS peaks in A3C6041. It is, however, worth noting that the low-lying DOS width estimated as the spacing between the two conductance minima below and above EF (>1.2 eV, see the two dashed lines in Fig. 1d) is significantly larger than the commonly argued t1u bandwidth of ∼0.5 eV41,42. Such a discrepancy might originate from the Jahn-Teller (JT) instabilities and Coulomb interactions omitted by three-band first-principles calculations41,42. In consideration of JT-induced subband splitting and electronic correlations, the t1u bandwidth could be substantially increased34,43,44 and accords with our observation. A further enhancement of electronic correlations U in the most expanded Cs3C60 films pushes the t1u-derived DOS toward higher energy and opens a Mott-insulating gap38, in contrast to the superconducting ground state in K3C60 and Rb3C60 (Fig. 1d).
Despite nanoscale merohedral disorder, superconductivity develops well in Rb3C60 films. We unambiguously reveal this by measuring the spatial dependence of superconducting gaps at the atomic scale via STS, as exemplified in Fig. 1e. Even on the boundaries between adjacent merohedral domains, the superconducting gaps exhibit clear coherence peaks (blue curves) and are immune to the local merohedral disorder (Fig. 1a). This is further confirmed in Cs and Rb co-doped RbCs2C60 films, which imprint a comparably large merohedral disorder but exhibit a superconducting transition temperature up to Tc = 23 K (Supplementary Figure 2). Nevertheless, the superconducting spectra present some spatial electronic inhomogeneities, especially for the coherence peaks. A careful examination of Rb3C60 films at varied thicknesses and spatial locations reveals that the coherence peak amplitude scales inversely with Δ (Supplementary Figure 3). This is unexpected by the conventional wisdom of Bardeen-Cooper-Schrieffer (BCS) picture, and we ascribe to coexistence of competing order, e.g., the ubiquitous pseudogap phase (Supplementary Figure 4)37. Similar behavior and pseudogap phenomenology have been documented in cuprate superconductors45.
Thickness and filling dependence of superconductivity
Having established the merohedral disorder-independent superconductivity in fullerides, we then explore its dependence on thickness and electron filling. Elaborated in Fig. 2a–c is the temperature dependence of spatially averaged dI/dV spectra measured on 3 ML, 6 ML, and 9 ML Rb3C60, respectively. Again, the fully gapped superconductivity with an isotropic s-wave pairing is consistently confirmed in Rb3C60 and gets smeared out at elevated temperatures. By examining the temperature dependence of the gap depth in Fig. 2d, the critical temperature Tc is determined and increases from 23 K for 3 ML, to 26 K for 6 ML, and 28 K for 9 ML Rb3C60. Such a Tc evolution with film thickness stands in marked contrast to K3C60, where the maximum Tc occurs in 3 ML films37. This hints at other factor, possibly linking with alkali metal-dependent electronic correlations (U)36, to consider for a unified understanding of superconductivity of A3C60 films at varied thicknesses. Note that due to the significantly increased U monolayer and bilayer Rb3C60 films are non-superconducting at all (Supplementary Figure 5), in analogy to the K3C60 counterparts37. A residual DOS depletion around EF, hence pseudogap, is also observed in all superconducting Rb3C60 films above Tc (see the red curves in Fig. 2a–c) and within vortices (Supplementary Figure 4b).
In what follows, we explore the superconductivity of RbxC60 by tuning the stoichiometry and thus electron filling x. Figure 2e summarizes the superconducting gap Δ (top panel) and averaged orientational correlation (bottom panel) as a function of Rb doping level x. Clearly, Δ increases with the film thickness, in good accordance with Tc (Fig. 2d). The extracted reduced gap ratio 2Δ/kBTc = 6.0 ± 0.4 is comparable to that of KxC60 films37, but appreciably exceeds the canonical BCS value of 3.53. Interestingly, Δ reaches its peak at half-filling irrespective of film thickness, and declines more quickly below half-filling for thin Rb3C60 films. Notwithstanding a dome-shaped variation of Δ, the merohedral disorder remains unchanged with electron filling x and film thickness (bottom panel of Fig. 1e). This not only corroborates the above claim that superconductivity is little influenced by merohedral disorder31,46, but also hints that the dome-shaped superconducting phase diagram does not correlate from any x-dependent merohedral disorder effects.
Robust superconductivity against non-magnetic impurities
As the electron doping of RbxC60 deviates slightly from half-filling, subsurface tetragonal Rb vacancies emerge as dark windmills as x < 3, whereas excess K adatoms appear and occupy the octahedral sites as x > 3. Analogous to KxC60 (Supplementary Figure 6a, b)37, they do not alter profoundly the orientation of nearby fullerene molecules and thus serve as intrinsically non-magnetic impurities to test the fully gapped superconductivity in fullerides. Figure 3a–d shows the STM topographies of a single Rb vacancy and an excess Rb adatom, as well as linecut dI/dV spectra taken across both impurities. No in-gap bound state is revealed (red curves), although Δ shrinks by ∼25% on Rb excess impurity (Supplementary Figure 7a, b). Similar responses of the superconducting gap to K impurities have been observed in KxC60 as well (Supplementary Figure 6c). Here the Δ reduction possibly arises from a local doping variation, namely a deviation of x from 3. The vacancies are located beneath the top C60 molecules, rendering the local Δ reduction invisible for surface-sensitive STS.
On the other hand, step edges could be seen as one-dimensional perturbations and bring about Andreev bound states as they are normal to the possible sign-changing direction in Δ45,47. The spectroscopic signature of these bound states, e.g., a zero-bias conductance peak (ZBCP), has been observed experimentally in a few cuprate and iron-pnictide superconductors45,48,49. Figure 3e depicts a topographic STM image of one monomolecular step edge separating Rb3C60 epitaxial films between 8 ML (lower terrace) and 9 ML (upper terrace). Note that all step edges run along the close-packed directions of C60 molecules. Figure 3f shows dI/dV spectra taken along a trajectory approaching the step edge (solid line in Fig. 3e). The superconducting gap remains undisturbed at the step edge and nearby, and no evidence of Andreev bound states is found (Supplementary Figure 7c). Some random variations in the coherence peak, including strong coherence peaks near Rb excess impurity in Fig. 3d, might be related to the slight electronic inhomogeneity of superconducting Rb3C60 films (Fig. 1e).
Local probe of Yu-Shiba-Rusinov states
To fully understand the impurity impact on fulleride superconductivity, we intentionally deposited Fe atoms on Rb3C60 surface at low temperature (∼100 K). Single Fe adatoms formed (bright protrusions) and occupied top or hollow sites of the surface C60 lattice, dubbed as Fe(I) and Fe(II) in Fig. 4a. Figure 4b represents the dI/dV spectra on both Fe impurities and defect-free regions. Note that multiple Fe(I) and Fe(II) impurities have been measured and averaged to eliminate the spatial inhomogeneity effects on dI/dV spectra. Evidently, both Fe(I) and Fe(II) adatoms act as magnetic scatterers and significantly suppress the superconducting coherence peaks, whereas a prominent ZBCP is clearly observed on Fe(I). They are hallmarks of the Yu-Shiba-Rusinov (YSR) states induced by coupling of magnetic impurity to an s-wave superconductor10,12,16,17,26,50,51,52,53. Figure 4c shows a series of tunneling spectra across an isolated Fe(I) impurity. The ZBCP intensity decreases quite abruptly and gets barely visible at a spatial distance of 1.4 nm from the impurity site. Here the distinct behaviors of YSR states on Fe(I) and Fe(II) may be caused by the varied coupling strength between them and the Rb3C60 films54. In other words, the exchange coupling of Fe(II) adsorbed at the hollow sites to Copper pairs might be so significantly weak that the YSR states nearly merge into the superconducting gap edges and are little discernible. Further theoretical analysis is needed to comprehensively understand the Fe registry site-dependent YSR bound states in fulleride superconductors.
Discussion
Our atomic-scale observations of short-range YSR bound states on magnetic Fe adatoms, robust superconductivity against non-magnetic merohedral disorder and impurities compellingly confirm a sign-unchanged s-wave pairing state in fulleride superconductors17. Distinct from a conventional superconductor, however, in charged fullerenes the t1u-derived conduction band of ∼0.5 eV is narrow and comparable to the electron–vibron interactions, thereby causing a breakdown of the Migdal’s theorem55,56,57. As a result, superconductivity with local nonretarded attractive interactions33,34 is less sensitive to the distribution of the electronic DOS in conduction band58, and instead determined by some ensemble-averaged DOS59. This differs from the classic BCS superconductors where Tc is essentially governed by the DOS at EF, and happens to match our finding, i.e., the merohedral disorder considerably modifies the t1u-derived DOS distribution but never affect superconductivity (Fig. 1d, e). Such local electron pairing33,34, mediated by intramolecular JT phonons60,61, has also been reinforced by a short coherence length in fullerides. As estimated from the vortex core radius (Supplementary Figure 4a,c), the coherence length of a Cooper pair is 1.5 ± 0.2 nm in Rb3C60 and 2.6 ± 0.5 nm in K3C6037, respectively, which are only about twice the separation between nearest-neighbor fullerene molecules.
In the local pairing mechanism, the key ingredients for high-Tc superconductivity are the strong coupling of the t1u electrons to intramolecular JT phonons in trivalent fullerides59,60,61. The phonon-mediated unusual multiorbital (attractive) interactions lead to an effectively inverted Hund’s coupling (S = 1/2)36 and a local spin-singlet s-wave pairing on the same orbital34, further enhanced via coherent tunneling of pairs between orbitals (the Suhl-Kondo mechanism)62,63. On the other hand, the multiorbital electronic correlations suppress electron hopping-induced charge fluctuations and effectively bind electrons into intraorbital pairs33. In this sense, the Coulomb interactions actually help the local pairing, until they are strong enough to drive a transition from the superconductivity to Mott-insulating phase37. Such a local pairing scenario naturally accounts for the dome-shaped dependence of Tc on C60 packing density-controlled U31,36,46 as well as the conflicting variation of superconductivity with film thickness in K3C60 and Rb3C60. In K3C60, U is relatively small and its enhancement at reduced film thicknesses stabilizes the local pairing and thus enhances superconductivity37, whereas the opposite holds true owing to the already large U in Rb3C60. A further enhancement of U pushes thin Rb3C60 films closer to a Mott transition and suppresses superconductivity, as observed. In Fig. 5, we show the phase diagram of charged fullerides and discover universal optimal superconductivity at half-filling, no matter how the electronic correlations U change with the alkali metal and film thickness. This finding is unusual and probably stems from a decrease in the dynamical JT-related pair binding energy (Ux, negative) away from half-filling61,62, until the superconductivity vanishes as the Ux changes its sign. For the evenly charged fullerenes, U2 and U4 are positive and the JT coupling instead stabilizes two correlated insulating ground states61,62. It is also important to note that an asymmetry of Δ versus x phase diagram relative to half-filling (x = 3) occurs as U becomes strong. This is related to a monotone shrinkage of U with the doping x in view of the enhanced Coulomb screening from itinerant electron carriers37. In strongly correlated regimes, a small increase of U below half-filling can suppress superconductivity significantly and leads to the observed dome asymmetry.
Finally, we note that the large ratio of energy gap Δ to critical temperature (e.g., 2Δ/kBTc > 6.0) seems to be a generic trait of high-Tc superconductivity in narrow-band systems10,20,35,37,49, including the copper-oxide superconductors45. Such a large deviation from the canonical BCS value of 3.53 could be straightforward to understand theoretically in the framework of local nonretarded superconductivity58. Experimentally, a similar local pairing mechanism, assisted cooperatively by a dynamic interfacial polaron, has been recently proposed to be responsible for the high-Tc superconductivity in monolayer FeSe epitaxial films grown on SrTiO3 substrate64. A question naturally arises as to whether the local pairing mechanism is applicable to other narrow-band cuprates and multi-band iron pnictides65. Another interesting issue is to unravel the nature of pseudogap that ubiquitously emerges from the doped fullerene films with no spatially modulated electronic charge density (Fig. 2a–c). This excludes a possible origin of the pseudogap from charge orders. Whether the pseudogap shares the same mechanism as that of cuprates and how it interplays with high-Tc superconductivity remain unsolved issues that merit further investigations. In any case, our experimental results of fulleride superconductors shed important light on the electron pairing in narrow-band high-Tc superconductors.
Methods
Sample preparations
Our experiments were conducted in a commercial Unisoku 1500 ultra-high vacuum STM facility, connected to an MBE chamber for in situ film preparation. The base pressure of both chambers is lower than 2.0 × 10−10 Torr. C60 molecules were evaporated from a standard Knudsen diffusion cell and grew layer-by-layer on nitrogen-doped SiC(0001) wafers (0.1 Ω cm) at 473 K, which were pre-graphitized by thermal heating (up to 1600 K) to form bilayer graphene. Desired alkali metal atoms (Rb or Cs) were then deposited from thoroughly outgassed SAES getters on C60 films at a low temperature of ∼200 K step by step, followed by >3 h of post-annealing at room temperature. The layer index n of RbxC60 multilayers (n ≤ 3) is determined from the step height, STM topographies and tunneling dI/dV spectra, which varies significantly with n. The flux rate of C60 is therefore calculated by dividing the coverage of fulleride films by growth time, and is used as a reference for the determination of the nominal thickness for thicker fullerides, e.g., n = 6 and 9 in the main text.
Away from half-filling, the electron doping x is calculated directly from the areal density of Rb vacancies (Fig. 3a) or excess Rb dopants (Fig. 3c). For x ∼ 3, there exist little defect that leads to trivalent fulleride films (Fig. 1a). A single Rb vacancy (excess) is reasonably considered as one missing (additional) Rb dopant relative to Rb3C60. For higher doping, x is estimated from the coverage of Rb clusters, since the excess Rb dopants are individually undistinguishable. By this method, the estimated x has a statistical error of <0.5%.
STM measurements
After the sample growth, the fulleride epitaxial films were immediately transferred into our STM chamber for all STM and STS data collections at 4.6 K. A bias voltage was applied to the samples. To accurately characterize the superconductivity and electronic structure of fulleride films, special measures such as grounding and shielding were taken to optimize the stability and spectroscopic resolution of our STM facility. Polycrystalline PtIr tips were used after careful calibration on Ag films grown on Si(111). All STM topographic images were taken in a constant current mode. Tunneling dI/dV spectra and electronic DOS maps were acquired using a standard lock-in technique with modulation frequency f = 975 Hz, while the modulation amplitudes were 0.2 meV and 20 meV for measuring the superconducting gaps and wider-energy-range (±1.0 eV) dI/dV spectra, respectively.
Data availability
All data are available from the corresponding author on reasonable request.
References
Sacépé, B. et al. Localization of preformed Cooper pairs in disordered superconductors. Nat. Phys. 7, 239–244 (2011).
Mao, Z. Q., Mori, Y. & Maeno, Y. Suppression of superconductivity in Sr2RuO4 caused by defects. Phys. Rev. B 60, 610–614 (1999).
Song, C. L. et al. Direct observation of nodes and twofold symmetry in FeSe superconductor. Science 332, 1410–1413 (2011).
Zhang, G. et al. Bosonic confinement and coherence in disordered Nano diamond arrays. ACS Nano 11, 11746–11754 (2017).
Lee, P. A., Nagaosa, N. & Wen, X. G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Kamihara, Y., Watanabe, T., Hirano, M. & Hosono, H. Iron-based layered superconductor La(O1-xFx)FeAs (x = 0.5 - 0.12) with Tc = 26 K. J. Am. Chem. Soc. 130, 3296–3297 (2008).
Liu, B. Nonmagnetic impurity resonance states as a test of superconducting pairing symmetry in CeCoIn5. Phys. Rev. B 88, 245127 (2013).
Li, J. et al. Local destruction of superconductivity by non-magnetic impurities in mesoscopic iron-based superconductors. Nat. Commun. 6, 7614 (2015).
Fan, Q. et al. Plain s-wave superconductivity in single-layer FeSe on SrTiO3 probed by scanning tunneling microscopy. Nat. Phys. 11, 946–952 (2015).
Yamashita, T. et al. Fully gapped superconductivity with no sign change in the prototypical heavy-fermion CeCu2Si2. Sci. Adv. 3, e1601667 (2017).
Choi, D. J. et al. Mapping the orbital structure of impurity bound states in a superconductor. Nat. Commun. 8, 15175 (2017).
Zhang, G. F. et al. Global and local superconductivity in boron-doped granular diamond. Adv. Mater. 26, 2034–2040 (2014).
Zhang, G. F. et al. Yu-Shiba-Rusinov bands in ferromagnetic superconducting diamond. Sci. Adv. 6, eaaz2536 (2020).
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).
Fernandes, R. M., Chubukov, A. V. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97–104 (2014).
Yazdani, A., Jones, B. A., Lutz, C. P., Crommie, M. F. & Eigler, D. M. Probing the local effects of magnetic impurities on superconductivity. Science 275, 1767–1770 (1977).
Balatsky, A. V., Vekhter, I. & Zhu, J. X. Impurity-induced states in conventional and unconventional superconductors. Rev. Mod. Phys. 78, 373–433 (2006).
Pan, S. H. et al. Imaging the effects of individual zinc impurity atoms on superconductivity in Bi2Sr2CaCu2O8+δ. Nature 403, 746–750 (2000).
Grothe, S. et al. Bound states of defects in superconducting LiFeAs studied by scanning tunneling spectroscopy. Phys. Rev. B 86, 174503 (2012).
Yang, H. et al. In-gap quasiparticle excitations induced by non-magnetic Cu impurities in Na(Fe0.96Co0.03Cu0.01)As revealed by scanning tunneling spectroscopy. Nat. Commun. 4, 2749 (2013).
Petrovic, A. P. et al. A disorder-enhanced quasi-one-dimensional superconductor. Nat. Commun. 7, 12262 (2016).
Peng, J. et al. Disorder enhanced superconductivity toward TaS2 monolayer. ACS Nano 12, 9461–9466 (2018).
Zhao, K. et al. Disorder-induced multifractal superconductivity in monolayer niobium dichalcogenides. Nat. Phys. 15, 904–910 (2019).
An, C. et al. Long-range ordered amorphous atomic chains as building blocks of a superconducting quasi-one-dimensional crystal. Adv. Mater. 32, 2002352 (2020).
Poccia, N. et al. Evolution and control of oxygen order in a cuprate superconductor. Nat. Mater. 10, 733–736 (2011).
Heinrich, B. W., Pascual, J. I. & Franke, K. J. Single magnetic adsorbates on s-wave superconductors. Prog. Surf. Sci. 93, 1–19 (2018).
David, W., Ibberson, R. M., Dennis, T. J. S., Hare, J. P. & Prassides, K. Structural phase-transition in the fullerene C60. Europhys. Lett. 18, 219–225 (1992).
Stephens, P. W. et al. Structure of single-phase superconducting K3C60. Nature 351, 632–634 (1991).
Hirosawa, I. et al. Orientational disordering of C60 in Na2RbC60 superconductor. Solid State Commun. 87, 945–949 (1993).
Prassides, K. et al. Crystal structure, bonding, and phase transition of the superconducting Na2CsC60 fulleride. Science 263, 950–954 (1994).
Takabayashi, Y. et al. The disorder-free non-BCS superconductor Cs3C60 emerges from an antiferromagnetic insulator parent state. Science 323, 1585–1590 (2009).
Potočnik, A. et al. Jahn-Teller orbital glass state in the expanded fcc Cs3C60 fulleride. Chem. Sci. 5, 3008–3017 (2014).
Han, J. E., Gunnarsson, O. & Crespi, V. H. Strong superconductivity with local Jahn-Teller phonons in C60 solids. Phys. Rev. Lett. 90, 167006 (2003).
Nomura, Y., Sakai, S., Capone, M. & Arita, R. Unified understanding of superconductivity and Mott transition in alkali-doped fullerides from first principles. Sci. Adv. 1, e1500568 (2015).
Koller, D. et al. Energy gap in superconducting fullerides: optical and tunneling studies. Phys. Rev. Lett. 77, 4082–4085 (1996).
Capone, M., Fabrizio, M., Castellani, C. & Tosatti, E. Colloquium: Modeling the unconventional superconducting properties of expanded A3C60 fullerides. Rev. Mod. Phys. 81, 943–958 (2009).
Ren, M. Q. et al. Direct observation of full-gap superconductivity and pseudogap in two-dimensional fullerides. Phys. Rev. Lett. 124, 187001 (2020).
Han, S. et al. Visualizing molecular orientational ordering and electronic structure in CsnC60 fulleride films. Phys. Rev. B 101, 085413 (2020).
Kämmerer, S., Kob, W. & Schilling, R. Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules. Phys. Rev. E 56, 5450–5461 (1997).
Yildirim, T., Hong, S., Harris, A. B. & Mele, E. J. Orientational phases for M3C60. Phys. Rev. B 48, 12262–12277 (1993).
Gelfand, M. P. & Lu, J. P. Orientational disorder and electronic states in C60 and A3C60, where A is an alkali metal. Phys. Rev. Lett. 68, 1050–1053 (1992).
Normura, Y., Nakamura, K. & Arita, R. Ab initio derivation of electronic low-energy models for C60 and aromatic compounds. Phys. Rev. B 85, 155452 (2012).
Ceulemans, A., Chibotaru, L. F. & Cimpoesu, F. Intramolecular charge disproportionation and the band structure of A3C60 superconductors. Phys. Rev. Lett. 78, 3725–3728 (1997).
Suzuki, S. & Nakao, K. Electron-electron and electron-phonon interactions in alkali-metal-doped C60. Phys. Rev. B 52, 14206–14218 (1995).
Fischer, Ø., Kugler, M., Maggio-Aprile, I., Berthod, C. & Renner, C. Scanning tunneling spectroscopy of high-temperature superconductors. Rev. Mod. Phys. 79, 353–419 (2007).
Gasuhiro, A. Y. et al. Polymorphism control of superconductivity and magnetism in Cs3C60 close to the Mott transition. Nature 466, 221–225 (2010).
Satoshi, K. & Yukio, T. Tunneling effects on surface bound states in unconventional superconductors. Rep. Prog. Phys. 63, 1641–1724 (2000).
Yeh, N. C. et al. Evidence of doing-dependent pairing symmetry in cuprate superconductors. Phys. Rev. Lett. 87, 087003 (2001).
Liu, X. et al. Evidence of nematic order and nodal superconducting gap along [110] direction in RbFe2As2. Nat. Commun. 10, 1039 (2019).
Luh, Y. Bound state in superconductors with paramagnetic impurities. Acta Phys. Sin. 21, 75 (1965).
Shiba, H. Classical spins in superconductors. Prog. Theor. Phys. 40, 435–451 (1968).
Rusinov, A. I. On the theory of gapless superconductivity in alloys containing paramagnetic impurities. Sov. JETP 29, 1101 (1969).
Yang, X. et al. Observation of short-range Yu-Shiba-Rusinov states with threefold symmetry in layered superconductor 2H-NbSe2. Nanoscale 12, 8174–8179 (2020).
Farinacci, L. et al. Tuning the coupling of an individual magnetic impurity to a superconductor: quantum phase transition and transport. Phys. Rev. Lett. 121, 196803 (2018).
Migdal, A. B. et al. Interaction between electrons and lattice vibrations in a normal metal. Sov. Phys. JEPT 34, 996–1001 (1958).
Pietronero, L., Strässler, S. & Grimaldi, C. Nonadiabatic superconductivity. I. Vertex correlations for the electron-phonon interactions. Phys. Rev. B 52, 10516–10529 (1995).
Grimaldi, C., Pietronero, L. & Strässler, S. Nonadiabatic superconductivity. II. Generalized Eliashberg equation beyond Migdal’s theorem. Phys. Rev. B 52, 10530–10546 (1995).
Micnas, R., Ranninger, J. & Robaszkiewicz, S. Superconductivity in narrow-band systems with local nonretarded attractive interactions. Rev. Mod. Phys. 62, 113–171 (1990).
Grigorishin, K. V. The role of electron-vibron interaction and local pairing in conductivity and superconductivity of alkali-doped fullerides. Phys. C. 562, 56–69 (2019).
Auerbach, A., Manini, N. & Tosatti, E. Electron-vibron interactions in charged fullerenes. I. Berry phases. Phys. Rev. B 49, 12998–13007 (1994).
Manini, N., Tosatti, E. & Auerbach, A. Electron-vibron interactions in charged fullerenes. II. Pair energies and spectra. Phys. Rev. B 49, 13008–13016 (1994).
Suhl, H., Matthias, B. T. & Walker, L. R. Bardeen-Cooper-Schrieffer theory of superconductivity in the case of overlapping bands. Phys. Rev. Lett. 3, 552–554 (1959).
Kondo, J. Superconductivity in transition metals. Prog. Theor. Phys. 29, 1–9 (1963).
Zhang, S. Y. et al. Enhanced superconducting state in FeSe/SrTiO3 by a dynamic interfacial polaron mechanism. Phys. Rev. Lett. 122, 066802 (2019).
Keller, H., Bussmann-Holder, A. & Muller, K. A. Jahn-Teller physics and high-Tc superconductivity. Mater. Today 11, 38–46 (2008).
Acknowledgements
We thank H.Y. and H.W.L. for fruitful discussions. The work was financially supported by the Natural Science Foundation of China (grants no. 51788104, no. 11634007, and no. 11774192), the Ministry of Science and Technology of China (2017YFA0304600, 2016YFA0301004, 2018YFA0305603), and in part by the Beijing Advanced Innovation Center for Future Chip.
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C.L.S., X.C.M., and Q.K.X. conceived and designed the experiments. S.Z.W., S.H., and M.Q.R. carried out the MBE growth and STM measurements. M.Q.R., S.Z.W., F.J.C., and C.L.S. analyzed the data and wrote the manuscript with comments from all authors.
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Wang, SZ., Ren, MQ., Han, S. et al. Merohedral disorder and impurity impacts on superconductivity of fullerenes. Commun Phys 4, 114 (2021). https://doi.org/10.1038/s42005-021-00619-y
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DOI: https://doi.org/10.1038/s42005-021-00619-y
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