1 Introduction

Alkali fullerides (A3C60, A = K, Rb, Cs) have been intensively studied since the first discovery of superconductivity in K3C60 in 1991 [1]. They exhibit a maximum superconducting transition temperature Tc of ∼ 40 K, which is the highest among the molecular superconductors and only gets surpassed by cuprates and iron-based superconductors [1,2,3,4,5,6]. Early studies found that the Tc in A3C60 increases monotonically with increasing molecular spacing as A+ cation size enlarges [5, 7,8,9,10,11]. The superconductivity in alkali fullerides seemly falls into the conventional Bardeen-Cooper-Schrieffer (BCS) regime where the intramolecular phonon plays a decisive role and the Tc is mainly controlled by the density of states (DOS) at the Fermi level (EF) [12, 13]. The full gap expected from a phonon mechanism scenario has been evidenced by various experimental techniques, such as scanning tunneling microscopy (STM) [14, 15] and nuclear magnetic resonance (NMR) [16].

From the view point of electronic structures, the superconductivity in A3C60 originates from the half-filled t1u band which possesses a narrow bandwidth (W ~ 0.5 eV) because of the negligible charge transfers between C60 molecules [7,8,9]. Though the on-site Coulomb repulsion (U ~ 1.5 eV) significantly exceeds the t1u bandwidth [17, 18], metallicity is commonly observed in K3C60 and Rb3C60. The absence of a Mott localization was explained in terms of the t1u orbital degeneracy, which would strongly enhance the critical value (U/W)c of the Mott transition [19, 20].

Recent experiments on expanded Cs3C60 polymorphs reveal a dome-shaped phase diagram as a function of the C603− packing volume where superconductivity resides in proximity to a magnetic Mott-insulating state, highlighting the importance of electronic correlation in fulleride superconductors [21,22,23,24,25,26]. The measured Néel temperature TN is about 46 K in Cs3C60 with an orientational ordered A15 structure [22, 23], and is suppressed to 2.2 K in face-centered cubic (fcc) structured Cs3C60 due to the geometrical frustration [27,28,29].

In contrast to the atom-based cuprates high-Tc superconductors, dynamic Jahn–Teller (JT) effect (JJT) arising from the coupling of electrons to the on-molecule vibrations lifts the degeneracy of t1u orbital (see Fig. 1) and competes with the local exchange coupling (JH) in fulleride superconductors [30, 31]. The larger energy of JT effect (JJT > JH) renders a low-spin state (S = 1/2) of Cs3C60 and an orbital disproportionation of filled electrons in fullerides [22, 24, 27, 32,33,34,35]. From this point of view, Cs3C60 (fcc and A15) polymorphs have been classified as magnetic Mott–Jahn–Teller insulators (MJTIs) [8, 10, 21,22,23,24,25,26]. The cooperation between strong correlation (U/W) and JT distortion stabilizes the magnetism. With increasing pressure or bandwidth W, Cs3C60 involves from an MJTI phase into a JT metal (metallic phase with JT effect), accompanied with a dome-shaped superconductivity upon cooling [24]. The superconductivity in A3C60 is expected to be modulated by these diversified phases. For example, recent studies found that the optimized Tc in fcc RbxCs3-xC60 occurs at the boundary between a JT metal and a conventional metal [24], and the reduced gap ratio 2Δ/kBTc increases dramatically in the expanded regime where JT effect matters [24, 36].

Fig. 1
figure 1

Sketches of molecular orbital energy of C603− anions and simplified electronic structure of solid A3C60 (a) with and (b) without JT effect. The JT distortion splits the triple degenerated t1u orbital into b1u, b2u, and b3u orbitals

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As discussed above, the competition/cooperation between bandwidth, on-molecule electron-phonon coupling, and electronic correlation rises much complexity in A3C60 and obstacles a comprehensive understanding on the electronic structure and superconductivity. In particular, the complexity arising from the air sensitivity and phase separation of A3C60 polymorphs, limits the experimental techniques primarily to NMR and magnetization measurements [10, 21,22,23,24,25,26,27,28]. Local measuring probes, such as STM, may circumvent the above issues but thus far have been limited to several mechanically cleaved A3C60 crystals under the atmospheric or argon environment [14, 15, 37,38,39] and a few non-superconducting KxC60 films on metal substrates [40,41,42]. Preceding STM experiments on cleaved K3C60, Rb3C60, and Rb2CsC60 reveal a highly inhomogeneous superconducting gap, because of the strongly varied stoichiometry. The poor quality of the cleaved A3C60 surfaces hinders the atomically resolved imaging and further measurements [14, 15, 37,38,39].

Until now, there remains a couple of important issues in A3C60 superconductors. First, the microscopic mechanism of fulleride superconductivity, with the conventional phonon-mediated pairing or unconventional electronic pairing or a synergy between them, remains controversial [17, 24, 32, 43]. Besides, the interplay between electronic correlation and molecular JT instability might reduce the dimensionality of low-lying states from 3D to 2D [30, 34]. A fundamental question thus arises as to how the reduced dimensionality affects the superconductivity in fullerides. What is more, the phase diagram in A3C60 is commonly documented as a function of pressure or C603− packing volume, in contrast to the doping-controlled phase diagram in cuprates. Therefore, the successful preparation of high-quality superconducting A3C60 films with precisely controlled film thickness and electron doping is crucial to clarify these issues [44,45,46].

This article aims to give a brief introduction to recent STM results on the fcc AxC60 superconducting films and is organized as follows. First, we describe the diversified orientational orderings of C60x− in AxC60 films. Then, we proceed to discuss the s-wave superconductivity and its response to impurities or merohedral disorders. After this, we turn to the tunability of electronic structure and superconductivity in AxC60 films via controlling the electron doping x and the film thickness. Finally, a doping-controlled phase diagram of AxC60 is summed up, which gives strong restrictions on the superconducting mechanism in alkali fullerides.

2 State-of-the-art MBE growth

Bulk AxC60 crystalizes into either a fcc structure (see Fig. 2a) or an orientational ordered A15 structure (Cs3C60) in which C60 locates on the body-centered-cubic (bcc) lattice [21, 23, 27, 47, 48]. The preparation of AxC60 films (see Fig. 2b) using molecular beam epitaxy (MBE) includes two steps [44,45,46]. Firstly, C60 molecules were evaporated onto the bilayer-graphene dominated SiC surfaces with well-controlled film thickness. Secondly, alkali-metal atoms were deposited onto the pristine C60 films followed by a moderate annealing. The as-grown AxC60 films crystallize into a (111)-orientated fcc structure, as depicted in Fig. 2c. It is clear that the C60 molecules assemble into a hexagonal lattice. Notably, C60 molecules in n ML and (n + 2) ML occupy two symmetry-inequivalent sites in the unit cell of the middle layer, suggesting an ABC stacking as expected from the fcc structure [45]. On the other hand, the in-plane and inter-layer spacings of C60 molecules in K3C60 films is measured to be 8.1 ± 0.1 Å and 10.0 ± 0.1 Å, consistent well with that of the fcc-structured bulk K3C60 crystals.

Fig. 2
figure 2

(a) Crystal structure of fcc K3C60. (b) Schematic side view of K3C60(111) films on graphitized SiC substrate. (c) STM topography (V = 3.0 V, I = 10 pA) showing three consecutive K3C60 layers. Taken from ref. [45]

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3 Orientational orderings

Unlike the atom-based superconductors, molecule-based alkali fullerides exhibit additional degrees of freedom related to the molecular orientation. The merohedral disorder, one typical arrangement of C60 orientations, has been confirmed in A3C60 [47, 48]. However, the role of the merohedral disorder has been neglected in most theoretical calculations, though some calculations show that it would significantly alter the low-energy electronic structures [49, 50]. On the other hand, experimental evidences for its impact on superconductivity and the electronic structures are even rarer. Thus, it becomes increasingly important to visualize and quantify the merohedral disorder and C60 orientational orderings in A3C60.

3.1 Undoped C60 films

STM topographies of C60 films on graphene/SiC reveal five distinct C60 orientations, namely, C60 molecules orientate a hexagon (H), a pentagon (P), a 6:6 bond (H:H), a 6:5 bond (H:P), or a carbon apex (CA) pointing up (see Fig. 3a, b) [44]. It is worth mentioning that the H-orientated C60 molecules exhibit a tri-star-like topography. This is because that C-C bonds connecting a pentagon (P) and a hexagon (H) have relatively lower electron density and thus the C60 pentagons would brighten in the empty-states, as colored in red in Fig. 3c. Besides, the C60 orientations in both monolayer and bilayer films arrange into a quasi-(2 × 2) superstructure with a short-range correlation (white rhombus in Fig. 3a, b). The submolecular structures and the 2 × 2 superstructure have been routinely observed in C60 films grown on either the graphene substrate or metal substrates, and will not be discussed here [52,53,54,55].

Fig. 3
figure 3

C60 orientations in undoped C60 films. (a, b) Empty-state STM images (10 × 10 nm2) of monolayer and bilayer C60 films. The white rhombuses mark the unit cells of the quasi-(2 × 2) superstructures. (c) Sketch maps for five orientations (as labeled) of C60 molecules viewed from [51]. Taken from Ref. [44]

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3.2 Merohedral disorder in A3C60 films

With alkali-metal atoms intercalated into the tetrahedral and octahedral sites in fcc A3C60, the repulsive A-C60 interaction strongly favors two standard orientations (see Fig. 4a), which are related by 90° rotation about [56] direction or 44.48° rotation about [51, 57]. Both of them are H-orientated when viewed from [51]. The merohedral disorder thus refers to the random occupation of the two standard orientations by C60 molecules at low temperature.

Fig. 4
figure 4

Orientational orderings in A3C60 films. (a) Two standard C60 orientations viewed along the [51] direction. (b) Orientational correlation in 9 ML A3C60 films. Inset shows the definition of θi. (c) Averaged orientational correlation in 9 ML RbxC60 films as a function of doping x. (d-f) STM topographies of 9 ML A3C60 films. (g, h) STM topographies of monolayer K3C60 and Cs3C60 films revealing a √3 × √3 superstructure. Taken from ref. [44,45,46]

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Experimentally, the C60 molecules in A3C60 films grown on graphene/SiC are universally H-orientated, but their orderings are strongly fluctuated by the film thickness and alkali-metal species [44,45,46]. The STM topographies of A3C60 thick films (~ 9 ML) are shown in Fig. 4d-f. The H-orientated C60 molecules with a tri-star-like feature assemble into an hexagonal 1 × 1 lattice. Notably, C60 molecules in K3C60 behave the same orientation with a long-range orientational correlation (no merohedral disorder). However, the long-range ordering melts in Rb3C60 and nanoscale patches occur as colored in Fig. 4d, indicating a moderate merohedral disorder. Finally, the orientational correlation completely disappears in Cs3C60 (strong merohedral disorder). In order to quantify the merohedral disorder, we calculated the averaged orientational correlation function <cos(θij)> [58], in which θij = θi - θj denotes the angle between nearest neighbor C60 molecules. As shown in Fig. 4b, the value of <cos(θij)> equals to 1 in K3C60 films, as expected from the complete orientational ordering [44,45,46]. With increasing A+ cations size, <cos(θij)> decreases dramatically, indicating an enhanced merohedral disorder. This change is probably due to the weakening repulsions between neighboring C603− as a result of lattice expansion [59]. Despite of the significant change of <cos(θij)> with alkali-metal atoms, <cos(θij)> is found to be almost independent of the electron doping x, if the deviation x − 3 is not very large (see Fig. 4c), indicating an essentially unchanged merohedral disorder against x. The impact of merohedral disorder on the electronic structures and superconductivity will be discussed in section 4.3 and section 5, respectively.

Not only the A+ cations, C60 orientational orderings in A3C60 are also associated with the film thickness, which holds particularly true for monolayer films. Monolayer K3C60 and Cs3C60 exhibit a √3 × √3 superstructure of the H-orientated C60 (see Fig. 4g, h) [44, 45], suggesting a non-negligible graphene-C60 interaction. For Cs3C60, the √3 × √3 superstructure exists solely to the monolayer and is absent in thicker (> 2 ML) films [44]. For K3C60, a weak √3 × √3 superstructure persists in the bilayer but disappears completely in a trilayer film [45]. The same √3 × √3 superstructure has also been observed in monolayer K3C60 grown on Au (111), and is attributed to the K-induced reconstruction therein [40,41,42].

3.3 Orientational orderings in CsxC60 (x = 1, 2, 4) films

As discussed above, the C60 molecules in A3C60 are all H-orientated, which is stabilized by the repulsive A-C60 interaction. Thus, dramatic changes of C60 orientations are expected to occur in AxC60 (x = 1, 2, 4), since the occupation sites of alkali-metal atoms are different [60]. In A3C60, alkali-metal atoms occupy all the octahedral and tetrahedral sites. In A1C60 (A2C60), only the octahedral sites (two tetrahedral sites) are occupied. For A4C60 films, the fourth alkali-metal atom occupies the octahedral site for the topmost C60 layer [45]. This differs to that in Li4C60 bulk where the fourth Li occupies the 32f sites [61]. We have intensively studied the orientational orderings in CsxC60 (x = 1, 3 ,4) [44], and the results are summarized in Fig. 5. In bilayer CsxC60, which is weakly correlated with the graphene substrates, the C60 orientations change from CA, H:P, H to H:H with x = 1, 2, 3, 4, respectively. However, C60 molecules in monolayer Cs1C60 and Cs2C60 all become H-orientated, confirming again the role of substrate to C60 orientations. Besides, the periodicity of superstructures in the monolayer CsxC60 is found to strongly rely on the electron doping x.

Fig. 5
figure 5

STM topographies of 1 ML CsxC60 (x = 1, 2) and 2 ML CsxC60 (x = 1, 2, 4) as labeled. The C60 orientations and the unit cells are marked for clarity. Taken from ref. [44]

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In summary, AxC60 films grown on graphene/SiC exhibit diversified C60 orientations and their orderings, which are closely associated with the alkali-metal atoms (K, Rb, Cs), electron doping x, and film thickness, as listed in Table 1. Electron doping x dominates the C60 orientations in bilayer or thicker AxC60 films as well as the periodicity of superstructures in AxC60 monolayers. Film thickness dramatically impacts on the C60 orientations in monolayer films, because of the non-negligible graphene-C60 interaction. The alkali-metal atoms mainly control the merohedral disorder of the two standard H-orientated C60 molecules in A3C60.

Table 1 A brief summary of C60 orientations and their orderings in AxC60 films prepared on graphene. H, CA, H:P, H:H donate the C60 orientations. OD is short for merohedral disorder. Taken from ref. [44,45,46]
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4 Low-energy electronic states and superconductivity

4.1 Decoupling effect in undoped C60 films

Before starting the A3C60 films, it is necessary to introduce some important results on the undoped C60 films. Monolayer C60 grown on graphene is an insulator with a HOMO-LUMO gap of 3.5 eV, consistent fairly well with that in solid C60 [62], but is relatively larger than that grown on metal surfaces [63,64,65]. This indicates a minor charge transfer and substrate-induced screening from underlying graphene compared to metal substrates [52, 66]. This decoupling effect enables it readily to deduce the intrinsic electronic properties of C60 films and A3C60 overlayers [44], though graphene substrate plays a non-negligible role in determining the C60 orientations in monolayers. Notably, the triply degenerate t1u orbital has been lifted into two discrete peaks (see Fig. 6), indicating the presence of JT distortion in charged fullerenes [67, 68], even though the charge transfer is very small.

Fig. 6
figure 6

dI/dV spectrum of 1 ML C60 film grown on graphene. The inset shows the modified molecular orbitals (top) of C60x− anions by JT distortion (bottom). Taken from ref. [44]

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4.2 Insulating ground states in CsxC60

With alkali-metal intercalated, the transferred electrons will occupy the triply degenerate t1u orbital. The charge transfer between alkali-metal atoms and C60 molecules is considered to be essentially complete [69]; thus, x also indicates the electron doping for per C60x−. Considering a simple band theory, metallicity is expected in AxC60 if 0 < x < 6, since t1u orbital is partially filled. Experimentally, all measured Cs3C60 films (monolayer, bilayer, and 9 ML) grown on graphene substrates are insulating, characteristic of apparent energy gaps around EF [44, 46]. Moreover, monolayer and bilayer CsxC60 with other electron doping x = 1, 2, 4 are also insulators [44]. The case for Cs2C60 and Cs3C60 monolayers is depicted in Fig. 7a.

Fig. 7
figure 7

(a) dI/dV spectra of 1 ML Cs2C60 and Cs3C60. The triangles and up arrows donate the LHB/UHB or VB/CB and the satellite peaks from JT distortion, respectively. Taken from ref. [44]. (b) Schematic diagram of the universal insulating states in CsxC60

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The robust insulating behavior speaks highly of the role of both on-molecule Coulomb repulsion and JT instability in determining the electronic states in fulleride films [8, 24, 26]. The lift of the triply degenerate t1u orbitals via a JT coupling is evidenced by the accompanied satellite peaks (up arrows in Fig. 7a) beyond the gaps [44]. On the basis of JT coupling and correlation U, it is straightforward to explain the insulating ground states of CsxC60, as illustrated in Fig. 7b. For even x = 2 and 4, the strong JT effect splits the t1u orbital into sub-bands (b1u, b2u, b3u) and results in a charge-disproportionated insulator [33,34,35], whereas for odd x = 1 and 3, the strong correlation U further splits the partially filled sub-band into upper and lower Hubbard bands. Thus, the two nearest DOS peaks/kinks next to EF in the dI/dV spectra, as marked by the triangles in Fig. 7a, can be safely assigned to the JT sub-bands (x = 2, 4) or UHB/LHB (x = 1, 3).

4.3 Emergent superconductivity in K3C60 and Rb3C60

In A3C60 crystals, the cation size of alkali-metals controls the C603− packing volume and dramatically affects the bandwidth, and thus the superconductivity and low-energy electronics states. Similar phenomenon is also observed in the A3C60 films grown on graphene substrates, and the case for 9 ML films is shown in Fig. 8a. In the most expanded Cs3C60 films, the strong electronic correlation U/W and JT effect lead to the opening of a Mott insulating gap. Thus, 9 ML Cs3C60 film is a MJTI [44]. With reduced A+ cation size or lattice constant, electron delocalizes as U/W decreases, and metallicity as well as a superconductivity is realized in 9 ML K3C60 and Rb3C60 films. The evolution of the superconducting gap size ∆ and Tc with alkali-metal atoms is summarized in Fig. 8b, c. Similar to that in pressurized Cs3C60 [21, 22], a dome-shaped dependence of both the ∆ and Tc is clearly revealed, though only discrete values of lattice constant are accessible by controlling the alkali-metal atoms. Moreover, Tc of 9 ML K3C60 and Rb3C60 is almost identical to that of their bulk counterparts [1, 2], suggesting a similarity between 9 ML A3C60 films and the bulk crystals. The lower Tc in a RbCs2C60 films compared to its bulk form may result from an inhomogeneous distribution of Rb, Cs atoms, which may alter the actual chemical composition of the topmost layer.

Fig. 8
figure 8

Bandwidth control of 9 ML A3C60. (a) Low energy-scale dI/dV spectra. The triangles and up arrows donate the LHB/UHB and the satellite peaks from JT distortion, respectively. (b) Evolution of superconducting gap taken at 4.5 K. The spectra are color-coded to that in (a). (c) Electronic phase diagram of 9 ML A3C60 films. Taken from ref. [45, 46]

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Despite of the bandwidth-controlled superconductor-Mott-insulator transition (SMIT), the dI/dV spectra also reveal two important aspects. Firstly, 9 ML K3C60 exhibits two sharp peaks around −0.4 eV and 0.1 eV, following the calculated electronic structure of A3C60 assuming a fixed orientation [49, 70]. The ordered arrangement of C60 molecules in 9 ML K3C60 has been evidenced in Fig. 4d. However, the sharp peaks are erased in 9 ML Rb3C60 and RbCs2C60 with enhanced merohedral disorder, leading to a smooth variation of electronic DOS, as theoretically anticipated [49]. Secondly, the estimated bandwidth of t1u orbital, defined as the spacing between the two conductance minima (dashed lines in Fig. 8a) below and above EF, is significantly larger than the calculated value of ~ 0.5 eV [49, 70]. Such a discrepancy should originate from the JT instability and Coulomb interaction omitted by three-band first principle calculations [49, 70]. If the JT-induced sub-band splitting and electronic correlation are involved, calculations give a substantially increased t1u bandwidth, as observed here [26, 32, 71].

4.4 s-wave pairing

We declare that a fully gapped superconductivity as well as a pseudogap emerges robustly in K3C60 and Rb3C60 films (> 3 ML), whereas the monolayer and bilayer films are not superconducting. The superconducting gap in a K3C60 trilayer is exemplified in Fig. 9a, c. Despite some heterogeneity in the coherence peaks, the dI/dV spectra reveal completely vanished DOS near EF. At some positions, the gap exhibits pronounced coherence peaks and could be well fitted with a single BCS-type isotropic s-wave gap function [72]. The averaged Δ, defined as half the distance between the two coherence peaks, is estimated to be ~5.7 meV. Figure 9 plots the temperature dependence of the superconducting gap with elevated temperature. Apparently, the superconducting gap is gradually suppressed, but evolves continuously into a normal state quasiparticle gap rather than vanishes above Tc. This is reminiscent of the pseudogap phenomena in the underdoped cuprates [73, 74]. The enhanced Tc in K3C60 trilayer (~ 22 K) compared to 9 ML films may result from an increased correlation with reduced film thickness, as will discussed in section 5.

Fig. 9
figure 9

Superconductivity in 3 ML K3C60. (a) dI/dV spectrum taken at 2.5 K and its best fit to an isotropic s-wave superconducting gap. (b) Temperature dependence of the coherence peak (CP) amplitude and gap depth, revealing a Tc of 22 K. (c) Grid dI/dV spectra taken at 2.5 K in a field of view of 20 nm × 20 nm. (d) Spatially averaged dI/dV spectra as a function of temperature. Taken from ref. [45]

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The s-wave superconductivity is also confirmed by the observation of the isotropic vortices under magnetic fields (see Fig. 10a) [45, 46] By fitting the radial dependence of the normalized zero-energy conductance, we deduce the coherence length ξ and the angle dependence of ξ in the case of K3C60 trilayer is plotted in Fig. 10c. Apparently, ξ is angle independent, consistent with the isotropic s-wave symmetry, since ξ ∝ 1/Δ in BCS theory. Besides, ξ is measured to be 2.6 nm in K3C60 and 1.5 nm in Rb3C60 films, in accord with that in their bulk counterparts [45, 46, 75]. Such a small ξ agrees with a local pairing picture, where intramolecular JT phonons play an important role in the formation of cooper pairs [11, 26, 76]. Furthermore, the dI/dV spectra across the vortex (see Fig. 10e) reveal again the pseudogap feature. In contrast to cuprates, no spatial charge density modulation of the normal state quasiparticles is observed inside the vortex (see Fig. 10b), indicating that charge density wave (CDW) correlations are not responsible for the opening of the pseudogap [74]. A close examination reveals that the pseudogap is suppressed in 9 ML K3C60 than that in 3 ML K3C60 (see Fig. 10d). Previously, the pseudogap was not observed in bulk fullerides [15]. This implies that pseudogap might be a general phenomenology of 2D superconductors [77].

Fig. 10
figure 10

Vortex states in 3 ML K3C60. (a) Zero energy conductance map under a magnetic field of 8 T. (b) Enlarged images for a typical vortex at zero energy. (c) Azimuthal dependence of the fitted coherence length ξ. (d) Pseudogaps measured at 22 K and within vortices (measured at 4.6 K). (e) dI/dV spectra across a vortex core (T = 4.6 K and B = 2 T). Taken from ref. [45]

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In 9 ML Rb3C60 and 9 ML RbCs2C60, the superconducting gap shows a spatial inhomogeneity in both the coherence peak amplitude and the gap size ∆ [46]. Such inhomogeneity is proved to be irrelevant to the local merohedral disorder, since apparent coherence peaks can also exist on the regions between nearest neighbor merohedral domains [46]. Moreover, a careful examination of the superconducting Rb3C60 films reveals that the coherence peak amplitude scales inversely with the Δ [46]. This is unexpected by the conventional wisdom of BCS picture, and may be ascribed to a coexistence of competing order, such as the observed pseudogap phase.

To further examine the s-wave pairing, we probe the local quasiparticle states around impurities or disorders, which provide essential insight into the superconducting mechanism. This method has been routinely applied into cuprates and iron-based compounds, but remains unexplored in organic superconductors [74]. It is well documented that non-magnetic impurities little affect the pairing in conventional superconductors [78, 79], but scatter cooper pairs and induce localized in-gap bound states for unconventional pairing symmetry, such as the d-wave [79,80,81] or s ± wave superconductor [82,83,84,85].

If A3C60 films deviate slightly from stoichiometry, tetrahedral A+ vacancies and octahedra A+ adatoms will appear on the film surfaces, which behave as dark or bright windmills, respectively. They serve as non-magnetic impurities to test the pairing symmetry in fullerides [83]. Figure 11 shows the evolution of superconducting gap across a Rb vacancy (see Figs. 11a, d) and a Rb adatom (see Figs. 11b, e ). No evidence of any bound states is observed on both impurities. The robustness of the superconducting gap structure against alkali-metal atoms is also evidenced in K3C60 [45]. The shrinkage of Δ on Rb adatom arises probably from a local doping variation. Since the alkali metal vacancies are located below the topmost C603− anions, this renders the local Δ reduction invisible in surface-sensitive STS.

Fig. 11
figure 11

(a-c) STM topographies of a Rb vacancy, Rb excess, and step edge. (d-f) dI/dV spectra taken along the colored line in (a-c), respectively. Taken from ref. [46]

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In addition to point defects, step edges can be regarded as one-dimensional perturbations and would bring about Andreev bound states at zero-energy if they are normal to the possible pairing sign-changing direction [86]. These bound states have been observed in a few cuprate and iron-pniticide superconductors [87, 88]. In A3C60, the step edges always run along the close-packed directions of C60 molecules, as shown in Fig. 11c. The dI/dV spectra further reveal a robust superconducting gap near the step edge without any signature of the Andreev bound states (see Fig. 11f).

To further understand the impurity effect in fulleride superconductors, we deposited magnetic Fe atoms on Rb3C60 surface. Fe adatoms occupy the top (Fe-I) and hollow sites (Fe-II) of the C60 lattice (see Fig. 12a). The two types of Fe dopants exhibit distinct behaviors (see Fig. 12b). Particularly, a prominent zero-bias conductance peak (ZBCP) is observed on Fe-I. The ZBCP signatures a Yu-Shiba-Rusinov (YSR) state, which is expected from the exchange coupling between the magnetic impurity and an s-wave superconductor [78, 79, 81, 83, 89,90,91,92,93,94]. The coupling strength seems to be dependent on the Fe absorption sites. For Fe-II at the hollow sites, the coupling might be so weak that renders the YSR states nearly merge into the superconducting gap edges and thus are hardly distinguished. Further theoretical analysis is needed to comprehensively understand the Fe registry site-dependent YSR bound states in fulleride superconductors.

Fig. 12
figure 12

Fe-induced bound states. (a) STM topography of Rb3C60 films with diluted Fe adatoms. (b) Averaged dI/dV spectra on Fe-I, Fe-II impurities, and locations far from any impurities. Taken from ref. [46]

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To sum up, the robustness of superconductivity against non-magnetic disorder (alkali-metal atoms vacancies, dopants, and step edges) and emergent YSR bound states on magnetic Fe adatoms, unambiguously supports a sign-unchanged s-wave pairing in fulleride superconductors.

4.5 Tuning the electronic states and superconductivity via film thickness

For K3C60, the trilayer film processes a higher Tc (~ 22 K) compared to that of 9 ML film (~ 18.4 K) and its bulk counterpart [1, 47]. This indicates that thickness or dimensionality furnishes an alternatively way to tune the electronic properties and superconductivity in A3C60 films. With further reduced film thickness, the superconductivity eventually disappears in K3C60 bilayer and monolayer films. The dI/dV spectra on bilayer K3C60 reveal an asymmetric gap ~ 80 meV in the vicinity of EF (see Fig. 13b). Considering the large gap size, its insensitivity to magnetic field (see Fig. 13c) and the absence of vortices in the zero-energy conduction maps (see Fig. 13d), we conclude that bilayer K3C60 is not superconducting. The DOS hotspots in Fig. 13d, which strongly correlates to excess K dopants, should be assigned as K-induced impurity states. Besides, we find that the DOS intensity near gap edges varies simultaneous with the √3 × √3 superstructure (see Fig. 13b) and the DOS maps exhibit reversal intensity at occupied and empty states (see Fig. 13e, f), suggesting a possible CDW origin for the asymmetric gap in K3C60 bilayer. Moreover, the gap remains robustly in shape and size with elevated temperature up to 40 K (see Fig. 13g), indicating a very high phase transition temperature Ts.

Fig. 13
figure 13

Absence of superconductivity in bilayer K3C60 (a) STM topography of bilayer K3C60, interspersed with small amount of excess K dopants. (b) dI/dV spectra along the white dashed line in the inset. (c) Averaged dI/dV spectra at B = 0 and B = 8 T. (d-f) Electronic DOS maps with an energy of (d) 2 meV, (e) 38 meV, and (f) −40 meV, acquired simultaneously in the same field with (a) at B = 8 T. (g) Spatially averaged dI/dV spectra as a function of temperature. The red dashed line shows the convolution of electronic DOS measured at 4.6 K with a Fermi-Dirac function with T = 40 K. Taken from ref. [45]

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To reveal the enhanced Tc in trilayer K3C60 and the absence of superconductivity in bilayer films, we explore the layer-dependent structural and electronic properties of K3C60 and depict the dI/dV spectra in Fig. 14a. With reduced film thickness, a dip or insulating gap is noticeable near EF and increases in size, hallmarks of a thickness-controlled metal-insulator transition. The observed tunneling gaps (~ a few hundreds of meV) in monolayer and bilayer K3C60 are too large to be ascribed to CDW correlations. Alternatively, the gaps are suggested to arise from the enhanced electronic correlation U due to the poor screening of K3C60 at the 2D limit [42]. The strong U together with the JT effects splits the t1u orbital and leads to the opening of a Mott gap [44, 45]. Thus, the half-filled monolayer and bilayer K3C60 films become MJTIs at 2D limit. The extracted values of the Hubbard U (energy separation between UHB and LHB) and bandwidth in K3C60 are plotted in Fig. 14b. It is clear that U/W decreases dramatically with reduced film thickness, and the SMIT occurs when U/W ~ 1. The trilayer K3C60 exists on the verge of SMIT and a small enhancement of U renders the bilayer K3C60 not superconducting. In contrast to the SMIT observed in pressurized Cs3C60 and RbxCs3-xC60 (0.35 ≤ x < 2), which is achieved through a continuous control of W by tuning the interfullerene separation, the SMIT observed here is mainly governed by the thickness-controlled U.

Fig. 14
figure 14

(a) Thickness-dependent dI/dV spectra of K3C60. (b) Measured Hubbard U, W (upper panel), and U/W (lower panel) of K3C60 as a function of thickness. Taken from ref. [45]

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The thickness-controlled SMIT is also observed in Rb3C60 films [46], where trilayer Rb3C60 is superconducting, but the increased electronic correlation drives monolayer and bilayer Rb3C60 films into insulating phases. This further proves that the observed SMIT is dominated by thickness-controlled U. However, in contrast to the enhanced Tc in trilayer K3C60 film, superconductivity is suppressed in trilayer Rb3C60 (~ 23 K) compared to 9 ML Rb3C60 (~ 28 K) [46]. This is due to a larger molecular spacing in Rb3C60 and the preexisting strong electronic correlation. A further enhancement of U pushes thin Rb3C60 films closer to a Mott transitions and thus weakens superconductivity [46].

The enhanced correlation in K3C60 or Rb3C60 films with reduced thickness is distinct from that of the K3C60 films grown on Au (111) substrate [42]. This discrepancy can be reconciled in consideration of the combined screening effects from nearby polarized C603− anions (δUp) and the substrate (δUs). On Au (111) substrate, the δUs dominates the Coulomb reduction and results in a smaller effective U in the monolayer [42]. On graphene, the substrate screening is dramatically reduced because of the effective decoupling effect as discussed in section 4.1. Alternatively, the larger U in monolayer K3C60 or Rb3C60 supported by graphene is attributed to the reduced screening from nearby polarized C603− anions, whose number drops from nine in bilayer to six in monolayer.

Having discussed the electronic properties and superconductivity in stoichiometric A3C60 films, we summarize some of the key parameters, including the Coulomb repulsion (U), bandwidth (W), transition temperature (Tc), superconducting gap size (∆), reduced gap ratio (2∆/kBTc), and coherence length (ξ), of both K3C60 and Rb3C60 thin films in Table 2. The parameters for their bulk counterparts are also listed for comparison. Overall, A3C60 films at single layer limit are MJTIs and evolve into metallic state with reduced correlation or increased film thickness, followed by the emergence of the high-Tc superconductivity, which persists to at least 3 ML films. The Tc and ∆ in A3C60 films evolve gradually to that of their bulk counterparts with increased thickness, but deviate significantly in thinner films. Nevertheless, the short coherence length is universal in films and bulks, in accordance to a local pairing picture as will be discussed in section 5.

Table 2 A brief summary of some parameters of AxC60 films and bulks. Data of thin films are taken from ref. [44,45,46]
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4.6 Tuning the electronic states and superconductivity via electron doping

Electron doping provides another way to tune the electronic states of AxC60, because itinerant carriers can significantly screen the on-molecular electronic correlation U [42]. To reveal the doping-controlled U, we depict a series of dI/dV spectra of KxC60 in Fig. 15. The energy positions of UHB and LHB are marked by the red dashed lines. Apparently, U decreases smoothly with increasing x in all films. This is further evidenced by the fact that the Mott-induced DOS dip at EF gradually gets shallower with increasing x. Taken altogether, a fine control of electronic correlation U via electron doping and thickness has been realized in KxC60 films.

Fig. 15
figure 15

Spatially averaged dI/dV spectra as a function of electron doping x, measured on (a) 2 ML; (b) 3 ML; (c) 9 ML KxC60. The red dashed lines mark the doping evolution of UHB and LHB, with the black dashed ones signifying K-doping. Taken from ref. [45]

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Figure 15a also reveals that bilayer KxC60 undergoes a phase transition from a MJTI at half-filling into a metallic phase with finite DOS(EF) at x = 3.36. More interestingly, a low-energy gap of ~ 2.0 meV opens at EF in K3.36C60 bilayer (see Fig. 16c). The amplitude of coherence peaks and gap depth are significantly suppressed under external magnetic fields, confirming a superconductivity origin. Despite somewhat inhomogeneity in coherence peak amplitude, the superconducting gap exists ubiquitously both on and off excess K dopants (see Fig. 16). We therefore realize a doping-controlled SMIT in bilayer KxC60 just like that in cuprate superconductors [74].

Fig. 16
figure 16

Superconductivity in 2 ML K3.36C60. (a) STM topography of bilayer K3.36C60, with excess K dopants randomly distributed. (b) dI/dV spectra measured at T =2.5 K, color-coded to match the probe positions (empty circles) in (a). (c) Spatially averaged dI/dV spectra at B = 0 T (black curve) and B = 8 T (red curve). Taken from ref. [45]

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In contrast to the monotone shrinkage of U, ∆ in both 3 ML and 9 ML KxC60 exhibits a dome-shaped variation, with its maximum locked at x = 3 and decreases smoothly when x diverges from 3 (see Fig. 17). Nevertheless, all the dI/dV spectra show a fully gapped superconductivity with zero DOS and flat bottoms around EF [45]. The parabolic-shaped gap in 3 ML K2.928C60 results from a limited resolution of our equipment and the spatially averaged effect of the dI/dV spectra.

Fig. 17
figure 17

Evolution of the averaged superconducting gap (measured at 4.5 K) with K doping x in 3 ML and 9 ML KxC60. The coherence peaks are marked by the black triangles for eye guide. Taken from ref. [45]

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In KxC60 films, we can access a wide range of x (2.7 < × < 3.6) upon K doping. However, phase separation occurs if x derivates dramatically from 3. For x < 3, the K-doped films separate spatially into the superconducting KxC60 with vacancies and pristine C60 films. With further K depositing, the KxC60 region enlarges in size and the K vacancies decrease in density, until finally the film evolves into stoichiometric K3C60. The K1C60 and K2C60 do not show up in multilayer films during the entire growth process, indicating that they are less thermodynamically stable than K3C60 on graphene substrate. When x reaches a critical value of ~ 3.3, the K-doped films separate into the superconducting KxC60 (x > 3) and insulating K4C60 [45]. With further K depositing, the superconducting KxC60 gradually decreases in area and evolves into the tetravalent fulleride K4C60 eventually. We also note that the C60 molecules in superconducting KxC60 are all H-orientated as that in stoichiometric K3C60, despite of the K dopants or vacancies.

5 Phase diagram and superconducting mechanism

In the above section, we have shown the large tunability of the superconductivity and electronic states in A3C60 films by a combined control of alkali-metal atoms, film thickness, and electron doping. This enables us to track for the first time the variations of Δ and Tc over a wide range of electron doping x and thus to plot an unusual phase diagram (see Fig. 18). We note that T. Yildirim et al. have also reported a similar doping-dependent phase diagram of AxC60 crystals [106]. However, the evolution of Tc with doping in their study may be frustrated by the sample diversity and merohedral disorder, which is easily eliminated in our case. Figure 18 reveals several important aspects of the superconductivity in fullerides. (a) In either K3C60 (3 ML, 9 ML) or Rb3C60 (3 ML, 6 ML, and 9 ML), Δ(x) scales with Tc (lower panel) and exhibits dome-shaped variations with maxima locating at half-filling. (b) Δ declines more rapidly in 9 ML RbxC60 than in 9 ML KxC60 when x deviates from half-filling. (c) In contrast to 9 ML films, Δ(x) in trilayer fullerides exhibits great asymmetry with respect to x = 3. (d) Δ is enhanced in K3C60, but gets suppressed in Rb3C60 films when film thickness reduces from 9 ML to 3 ML.

Fig. 18
figure 18

Electronic phase diagram showing the evolution of Δ, and reduced gap 2Δ/kBTc of A3C60 films as a function of x. Taken from ref. [45]

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This unique phase diagram imposes strong restrictions on the superconducting mechanism in fullerides. Firstly, the Δ(x) peaks exactly at half-filling, excluding unambiguously the assumption that superconductivity in AxC60 comes from an accidental doping [17]. Secondly, it seems unlikely that the Δ shrinkage away from half-filling is due to some form of disorder effects, as the Δ(x) evolution is essentially thickness dependent and of great asymmetry in trilayer fullerides. Particularly, the dome-shaped phase diagram cannot be ascribed to the merohedral disorder effect, because the orientational correlation function remains essentially unchanged with x (see Fig. 4c). Thirdly, the superconducting dome also cannot be attributed solely to the x-dependent DOS variation at EF [32], because the electronic DOS of half-filled K3C60 shows a shoulder and even minimum at EF (see Fig. 7). Superconductivity would be enhanced with increasing DOS (EF) as x > 3, at odds with our observations. The breakdown of the conventional Migdal’s theorem might arise from the small retardation in fullerides, since the energy scale of molecular vibrations is comparable to the bare electron bandwidth W [76]. To overcome the weak retardation effects, local pairing is crucial in reducing the effects of Coulomb repulsion.

In the local pairing mechanism, the key ingredient for the high-Tc superconductivity in trivalent fullerides is the strong coupling of the t1u electrons to intramolecular JT phonons. The phonon-mediated multiorbital (attractive) interactions lead to an effectively inverted Hund’s coupling (S = 1/2) and the formation of a local spin-singlet s-wave electron pairs on the same orbital [11, 26, 76]. Superconductivity is further enhanced via a coherent interorbital tunneling of electron pairs (the Suhl-Kondo mechanism) [107, 108]. On the other hand, the multiorbital electronic correlations suppress the electron hopping-induced charge fluctuations and more effectively bind electrons into intraorbital pairs [76]. In this sense, the Coulomb interaction actually helps the local pairing, until it is strong enough to localize the electrons and drive a SMIT.

Such a local pairing picture has also been evidenced by a short coherence length ξ in A3C60 (1.5-2.6 nm), which amounts to only twice the separation between nearest neighboring C60x- [45, 46]. On the other hand, electrons in a superconductor with local non-retarded interactions are paired via a short-range static attraction, and thus the superconductivity is less sensitive to the DOS distribution near EF [109]. This happens to match the insensitivity of superconductivity in A3C60 to the merohedral disorder, which significantly modifies the t1u-derived DOS distribution (see Fig. 7a). The local pairing scenario differs distinctly from a conventional BCS mechanism where only partial electrons near EF participate in the Cooper pairing and Tc is essentially governed by the DOS(EF).

Despite of the dome-shaped Tc that peaks at half-filling, the local pairing scenario also predicts a rapid decay of Tc as x deviates from 3 for a large U/W [76]. This is consistent with our observation that ∆ shrinks faster in 9 ML RbxC60 than in 9 ML KxC60. This scenario naturally explains the enhanced ∆ in K3C60 but suppressed ∆ in Rb3C60 with reduced film thickness. In K3C60, U is relatively small and its enhancement at reduced film thicknesses stabilizes the local pairing and thus enhances superconductivity, whereas the opposite holds true in Rb3C60 due to the already strong U. A further enhancement of U pushes Rb3C60 thin films closer to a Mott transition and thus weakens the superconductivity.

Figure 19 schematically illustrates a unified phase diagram of the charged fullerides. No matter how the electronic correlation U varies with the alkali metal and film thickness, the superconductivity is universally optimal at half-filling. This finding is unusual and most probably stems from a decrease in the dynamical JT-related negative pair binding energy (Ux, x is electron doping) away from half-filling [68]. For the evenly charged fullerenes x = 2 or 4, U2 and U4 are positive and the JT coupling instead stabilizes two correlated insulating ground states. Notably, Δ is asymmetric with respect to x = 3 in 3 ML A3C60 thin films as the electronic correlations are strong at 2 D limit. This is related to a monotone shrinkage of U with the doping x in view of the enhanced Coulomb screening from itinerant electron carriers (see Fig. 15). In strongly correlated regimes, a small increase of U below half-filling would result in a Mott localization and leads to the observed dome asymmetry.

Fig. 19
figure 19

Unified phase diagram of Δ variation with electronic correlations U and doping. The empty circles and squares 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. Taken from ref. [46]

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As a final remark, we comment on the large gap ratio 2Δ/kBTc > 6 in both K3C60 and Rb3C60, which well exceeds the canonical BCS value of 3.53. The large gap ratio seems to be universal in high-Tc narrow-band superconductors, such as iron pnictides, cuprates, and fullerides [45, 56, 58, 74, 83, 85]. The gap large ratio is unexpected from a BCS theory, but falls into the theoretical framework of superconductivity with local nonretarded attractive interactions [109]. Experimentally, a local pairing mechanism has been recently proposed to explain the high-Tc superconductivity in monolayer FeSe epitaxial films on SrTiO3 substrate [51]. A question naturally arises as to whether the local pairing mechanism is applicable to other narrow-band superconductors, such as cuprates and multiband iron pnictides. Another important enlightenment from fulleride superconductors is that the s-wave superconductivity is compatible with the strong electronic correlation and the pseudogap. Whether this holds true in cuprates remains unsolved and merits further investigations. Notably, a nodeless pairing is indicated in superconducting copper-oxide monolayer films on Bi2Sr2CaCu2O8+δ [110].

Finally, we sum up our recent STM results on the structural, electronic, and superconducting properties of fcc A3C60 films [44,45,46]. By controlling the alkali-metal species, electron doping, and film thicknesses, AxC60 films exhibit a large tunability of C60x− orientations and their orderings. The tunneling spectra of CsxC60 (x =1, 2, 3, 4) are robustly characteristic of an energy gap, hallmarks of JT instability and strong electronic correlation. With reduced bandwidth or enhanced U/W by substituting Cs with K and Rb, a fully gapped s-wave superconductivity accompanied with a cuprate-like pseudogap, emerges in K3C60 and Rb3C60 down to at least 3 ML. The s-wave superconductivity exhibits a dome-shaped doping dependence with the optimized gap emerging exactly at half-filling. The strong correlation U drives ∆(x) to be asymmetric with respect to half-filling in KxC60 and RbxC60 trilayer films. In any case, the s-wave superconductivity retains over the entire phase diagram despite of the electronic correlation and presence of pseudogap. The s-wave pairing is further confirmed by its robustness against merohedral disorder, non-magnetic impurities, and step edges. Our experimental results of fulleride superconductors shed important light on the electron pairing in narrow-band high-Tc superconductors.