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).

Fig. 1: Merohedral disorder and superconductivity in Rb3C60.
figure 1

a Scanning tunneling microscopy (STM) topography (20 nm × 20 nm, V = 1.0 V, I = 30 pA) on nine monolayer (ML) Rb3C60 films. The V and I represent the applied sample bias and tunneling current, respectively. Two standard orientations of C60 related by 44.48o rotation about the [111] axis are partially opacified in red and orange, respectively. b Schematic view of the two standard orientations of C60 molecules along the [111] direction. c Alkali metal ion dependence of the orientational correlation of C60 molecules (i.e., merohedral disorder). The statistical errors indicate the standard derivations of the merohedral disorder measured in various regions. Inset: definition of the angle θi of C60 orientation with respect to the horizontal axis. d Spatially averaged differential conductance dI/dV spectra on 9 ML A3C60 (A = K, Rb, Cs) films. The spectra have been vertically offset for clarity, with their zero conductance positions marked by correspondingly colored horizontal lines. Setpoint: V = 1.0 V and I = 200 pA. e Conductance dI/dV spectra (V = 30 mV and I = 200 pA) taken at equal separation (2.8 nm) along the diagonal line from top left to the bottom right and color-coded to match the C60 domains in a.

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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).

Fig. 2: Thickness dependence of superconductivity.
figure 2

a–c Spatially averaged and normalized conductance dI/dV spectra as a function of temperature and thickness of Rb3C60 films as indicated. The normalization was performed by dividing the raw tunneling spectrum by its background, which was extracted from a cubic fit the conductance for |V | > 10 mV. Setpoint: V = 30 mV and I = 200 pA. The red curves denote the residual pseudogap justly above the superconducting transition temperature (Tc). d Dependence of the superconducting gap depth on temperature, yielding a gradual increase of Tc with film thickness (see the guided solid lines and arrows). Here the gap depth denotes the difference between unity and the normalized zero-energy conductance. e Electronic phase diagram showing the evolution of superconducting energy gap Δ (empty circles) and averaged orientational correlation (diamonds) as a function of Rb doping x. Note that the orientational correlation function <cos(θij)> is only averaged over the trivalent C60 molecules to minimize any disruption by Rb impurities and excess atoms away from half-filling.

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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.

Fig. 3: Immunity of fulleride superconductivity to non-magnetic impurities.
figure 3

a, b High-resolution STM topography (7 nm × 7 nm, V = 1.0 V, I = 20 pA) of a single Rb vacancy (red dot) and tunneling spectra acquired 0.5 nm apart along the colored line in a. c, d STM topography (7 nm × 7 nm, V = 1.0 V, I = 20 pA) of a single Rb excess impurity (red dot) and tunneling spectra acquired 0.5 nm apart along the colored line in c. e, f STM topography (30 nm × 30 nm, V = 1.0 V, I = 20 pA) of Rb3C60 films with a monomolecular step edge and tunneling spectra acquired 1.3 nm apart along the colored line in e. The tunneling spectra are color-coded to match the probed positions near (red) and away from impurities (black). The tunneling gap is set at V = 30 mV and I = 200 pA. Note that two different color gradients are used in a, c, and e.

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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.

Fig. 4: Magnetic impurity (Fe)-induced bound states.
figure 4

a STM topography (28 nm × 18 nm, V = 2.0 V, I = 30 pA) of superconducting Rb3C60 films upon intentional post-deposition of tiny Fe adatoms. The yellow dots indicate the topmost C60 molecules. b Comparison of tunneling conductance dI/dV spectra averaged over single Fe(I), Fe(II) impurities, and locations far from any impurities. Black vertical dashes denote the energy positions of the superconducting gap. c Linecut dI/dV spectra taken at equal separations (0.7 nm) across an isolated Fe(I) impurity. The red curve is measured justly on the impurity site. Setpoint: V = 30 mV and I = 200 pA.

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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.

Fig. 5: Unified phase diagram of Δ variation with electronic correlations U and doping.
figure 5

The empty circles and squares distinctively mark the experimental Δ measured in K3C60 and Rb3C60 films, respectively. Contour plots of Δ with a separation of 2 meV are shown in gray dashes. Note that the fulleride superconductivity is always peaked at half-filling at any specific U/W, with W denoting the t1u bandwidth.

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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.