Research ArticleCONDENSED MATTER PHYSICS

Optimized unconventional superconductivity in a molecular Jahn-Teller metal

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Science Advances  17 Apr 2015:
Vol. 1, no. 3, e1500059
DOI: 10.1126/sciadv.1500059

Abstract

Understanding the relationship between the superconducting, the neighboring insulating, and the normal metallic state above Tc is a major challenge for all unconventional superconductors. The molecular A3C60 fulleride superconductors have a parent antiferromagnetic insulator in common with the atom-based cuprates, but here, the C603– electronic structure controls the geometry and spin state of the structural building unit via the on-molecule Jahn-Teller effect. We identify the Jahn-Teller metal as a fluctuating microscopically heterogeneous coexistence of both localized Jahn-Teller–active and itinerant electrons that connects the insulating and superconducting states of fullerides. The balance between these molecular and extended lattice features of the electrons at the Fermi level gives a dome-shaped variation of Tc with interfulleride separation, demonstrating molecular electronic structure control of superconductivity.

Keywords
  • superconductivity
  • Strong correlations
  • Jahn-Teller effect
  • Metal-insulator transitions

INTRODUCTION

The understanding of high-temperature superconductivity in unconventional superconductors such as the cuprates remains a prominent open issue in condensed matter physics (1, 2). Their electronic phase diagrams exhibit striking similarities—superconductivity emerges from an antiferromagnetic strongly correlated Mott insulating state upon tuning a parameter such as composition (doping control) and/or pressure (bandwidth control) accompanied by a dome-shaped dependence of the critical temperature, Tc (3, 4), a common feature of other classes of correlated electron materials such as the heavy fermion intermetallic compounds (5). This electronic phase diagram is adopted by molecular superconductors such as both polymorphs of the cubic alkali fulleride, Cs3C60 (68), which are continuously tunable by pressure control of the bandwidth W via outer wave function overlap of the constituent molecules. The molecular electronic structure plays a key role in the Mott-Jahn-Teller insulator (MJTI) formed at large interfulleride separations, with the on-molecule dynamic Jahn-Teller (JT) effect distorting the C603– units and quenching the t1u orbital degeneracy responsible for metallicity (9). The relationship between the parent insulator, the normal metallic state above Tc, and the superconducting pairing mechanism is a key question in understanding all unconventional superconductors (2, 10). The complexity associated with the comparable size of electron-electron and electron-phonon interactions and the electronic bandwidth in fullerides makes understanding of superconducting pairing challenging (1113). We show that applying chemical pressure transforms the MJTI first into an unconventional correlated JT metal (JTM) (where localized electrons coexist with metallicity and the on-molecule distortion persists), and then into a Fermi liquid with a less prominent molecular electronic signature. This normal state crossover is mirrored in the evolution of the superconducting state, with the highest Tc found at the boundary between unconventional correlated and conventional weak-coupling Bardeen-Cooper-Schrieffer (BCS) superconductivity, where the interplay between extended and molecular aspects of the electronic structure is optimized to create the dome.

RESULTS

Face-centered cubic (fcc) Cs3C60 (Fig. 1A)—an antiferromagnetic MJTI at ambient pressure—becomes superconducting under pressure: Tc reaches a maximum of 35 K at ~7 kbar and then decreases upon further pressurization (7). Alternatively, the Mott insulator-metal transition may be traversed and shifted to ambient pressure by applying chemical pressure (14, 15), through substitution of the smaller Rb+ for the Cs+ cation in Cs3C60. Solid-vapor reactions of stoichiometric quantities of Rb and Cs metals with C60 yield RbxCs3−xC60 (0.35 ≤ x ≤ 2) (16). High-resolution synchrotron x-ray powder diffraction (SXRPD) (Fig. 1B and tables S1 and S2) confirms the formation of cubic phases with fcc symmetry (space group FmEmbedded Imagem), with lattice constants decreasing monotonically with increasing Rb content (16). The fcc phase fractions in the samples increase from 76.5% (the remaining comprising coexisting CsC60 and Cs4C60) for the most expanded material, x = 0.35 to ≥94% for x ≥ 0.75. Bulk superconductivity at ambient pressure is confirmed by low-field magnetization measurements (Fig. 1C and fig. S1). Tc initially increases with x from 26.9 K (shielding fraction 32%) in overexpanded x = 0.35 to 32.9 K (85%) in optimally expanded x = 1, and then decreases to 31.8 K (91%) in underexpanded x = 2 (Fig. 1C, inset), mimicking the electronic response of Cs3C60 (8) upon physical pressurization.

Fig. 1 Crystal structure and superconductivity in fcc fullerides.

(A) Crystal structure of fcc A3C60 (A = alkali metal, green spheres represent cations on tetrahedral, and red on octahedral sites, respectively). The C603– anions adopt two orientations related by 90° rotation about [100]—only one is shown at each site. (B) Final observed (red), calculated (blue), and difference (green) SXRPD profiles for Rb0.5Cs2.5C60 (λ = 0.39989 Å) at ambient temperature. Ticks show the reflection positions of fcc [83.23(3)%, top], CsC60 [3.6(1)%, middle], and Cs4C60 [13.16(7)%, bottom]. Inset: Expanded view in the range 4.7 to 5.9° with reflections labeled by their (hkl) Miller indices. (C) Temperature dependence of the magnetization, M (20 Oe, zero-field cooling) for RbxCs3−xC60 (0.35 ≤ x ≤ 2). Inset: Expanded view near Tc. (D) Pressure evolution of Tc for RbxCs3−xC60 (0.35 ≤ x ≤ 2). The lines through the data are guides to the eye. Fcc Cs3C60 (8) and Rb3C60 (17) data (dashed lines) are also included. (E) Tc as a function of C60 packing density, V at 10 K for RbxCs3−xC60 (0.35 ≤ x ≤ 2). Data are displayed as in (D).

The response of the superconductivity to combined chemical and hydrostatic pressure was followed by magnetization measurements (fig. S2). The initial pressure coefficient, (dTc/dP)0, large and positive [+2.2(1) K kbar−1] for overexpanded Rb0.35Cs2.65C60, approaches zero [+0.2(1) K kbar−1] for optimal expansion (RbCs2C60) before becoming negative [–0.7(1) K kbar−1] in underexpanded Rb2CsC60. Further pressurization produces superconductivity Tc(P) domes, except for Rb2CsC60, with Pmax (pressure at which Tc, max is observed) decreasing smoothly with increasing x (Fig. 1D). Even for Rb2CsC60, Tc(P) is initially nonlinear, contrasting with the large negative linear dependence of underexpanded Rb3C60 and Na2CsC60 (17, 18). SXRPD at high pressure below Tc shows that the fcc structure is robust (figs. S3 and S4 and table S3) and allows us to extract the Tc dependence on C60 packing density, V (Fig. 1E). The Tc(V) domes peak at a Vmax of 755 to 760 Å3/C603− similar to that found for Cs3C60 under hydrostatic pressure. Tc,max is somewhat lower than the 35 K of fcc Cs3C60 and decreases slightly with increasing x, assigned to cation disorder on the tetrahedral interstitial sites.

Temperature- and substitution-induced insulator-to-metal crossover

The observation of a Tc(V) dome at ambient pressure in RbxCs3−xC60 allows deployment of multiple techniques to understand the normal states from which superconductivity emerges on either side of the maximum in Tc. We initially studied the temperature evolution of structural properties by SXRPD at ambient pressure, with all samples remaining cubic to 10 K. Overexpanded insulating Cs3C60 (8) and underexpanded superconducting Rb2CsC60 both show smooth lattice contraction with a temperature variation described by a Debye-Grüneisen model (19) (Fig. 2A and fig. S5). However, materials closer to the Tc(V) dome maximum on both sides display markedly different behavior, for example, on cooling overexpanded Rb0.35Cs2.65C60 below 70 K, the diffraction peaks suddenly shift to higher angles, demonstrating an anomalous rapid shrinkage of the unit cell size. No changes in relative peak widths and intensities are apparent, implying the absence of asymmetry-breaking phase transition or phase separation, as confirmed by Rietveld analysis (fig. S6). Initially, the lattice contracts on cooling (Fig. 2A), but below T′ ~70 K, the lattice distinctly collapses (∆V/V0 = −0.47%; Fig. 2A, inset). This effect survives further increases in x to 1.5. T′ increases to ~260 K with decreasing unit cell size, but the isosymmetric transition extends over a much broader temperature range and becomes smeared out with increasing x—nonetheless, (∆V/V0) approaches the same value for all compositions.

Fig. 2 Evolution of structural and magnetic properties.

(A) Temperature evolution of the C60 packing density, V, for RbxCs3−xC60 (0 ≤ x ≤ 2). The data for x = 0 and 2 are fitted with a Debye-Grüneisen (DG) model (16, 19) (solid line). V(T) for RbxCs3−xC60 (0.35 ≤ x ≤ 1.5) display clear anomalies below onset temperatures, T′ marked by arrows—the solid lines through the data are DG fits (for T > T′) with Debye temperatures, ΘD, fixed to that in Cs3C60. The dotted lines through the data at T < T′ are guides to the eye. Inset: Temperature dependence of the normalized volume change, ΔV/V0, for RbxCs3−xC60 (0.35 ≤ x ≤ 1.5)—ΔV is the difference between V derived from the DG fits below T′ and that measured by diffraction, and V0 is the volume/C603− at T′. (B) Temperature dependence of the magnetic susceptibility, χ(T), of RbxCs3−xC60 (0 ≤ x ≤ 2). Arrows mark the temperatures, T′, at which maxima are observed. χ(T) for metallic RbxCs3−xC60 (x = 1.5, 2) are shifted vertically for clarity—the room temperature Pauli susceptibility, χ ~1 × 10−3 emu mol−1 corresponds to N(EF) ~15 states eV−1 (molecule C60)−1.

Figure 2B shows the temperature dependence of the RbxCs3−xC60 paramagnetic susceptibility, χ at ambient pressure. At high temperatures, χ(T) of overexpanded and optimally expanded compositions (0.35 ≤ x ≤ 1) follows the Curie-Weiss law with negative Weiss temperatures (−100 to −160 K) and effective magnetic moments per C603− (~1.6 to 1.8 μB) comparable to those in MJTI Cs3C60 (8), implying that they also adopt S = ½ localized electron ground states with strong antiferromagnetic correlations at high temperatures. However, in sharp contrast to Cs3C60 (8), χ(T) shows well-defined cusps on cooling at temperatures, T′, which increase with increasing x and coincide closely with those at which the lattice anomaly occurs. The cusps broaden significantly with increasing x until none are visible for x = 1.5. Upon further lattice contraction for ≥1.5, χ(T) comprises a single nearly temperature-independent Pauli susceptibility term, consistent with a metallic ground state from which superconductivity emerges on cooling. These data suggest that both the susceptibility cusps and the correlated lattice collapse signify insulator-to-metal crossover driven by temperature- and substitution-induced lattice contraction effects. This is consistent with the negative volume change, ∆V = VMVI, across the transition (Fig. 2A), as virial theorem analysis of the metal-to-insulator (M-I) transition assigns itinerant electrons a lower volume (20). However, because χ(T) cusps can also indicate antiferromagnetic order onset, we used nuclear magnetic resonance (NMR) as a local probe sensitive to both lattice and electronic degrees of freedom to investigate the role of the changing lattice metrics on the RbxCs3−xC60 electronic properties.

The 13C spin-lattice relaxation rate, 1/13T1, of overexpanded and optimally expanded RbxCs3−xC60 (0.35 ≤ x ≤ 1) (Fig. 3A) does not follow the Korringa relationship (1/T1T = constant), characteristic of conventional metals. Instead, it traces the 1/13T1T temperature dependence of insulating Cs3C60 (8) until reaching a maximum at T′, implying adoption of the same low-spin S = ½ insulating state at high temperature, consistent with the χ(T) results. Below T′, 1/13T1T rapidly diminishes on cooling, but the absence of concomitant line-broadening (fig. S7) is inconsistent with the onset of antiferromagnetic order. 87Rb and 133Cs spin-lattice relaxation rates, 1/nT1 (n = 87,133), show comparable results (fig. S8). No thermal hysteresis or line splittings that would indicate phase coexistence below T′ are evident. As x increases, T′ increases monotonically in agreement with the trend established by the structural and χ(T) data (Fig. 2, A and B), and the transitions become smeared out with lattice contraction. The 1/13T1T maximum is detectable well into the underexpanded regime as a very broad cusp centered at ~330 K for x = 2 Rb2CsC60, but no anomaly is discernible for x = 3 Rb3C60 to 420 K (Fig. 3A and fig. S9). The rapid suppression of 1/13T1T below T′ echoes the behavior of Cs3C60 under hydrostatic pressure (21, 22) and of strongly correlated organic superconductors (23) and is similarly attributed to an insulator-to-metal crossover. In overexpanded and optimally expanded RbxCs3−xC60 (0.35 ≤ x ≤ 1) just above Tc at 35 K, 1/13T1T is strongly enhanced compared to the values in underexpanded fullerides and does not scale with the square of the density of states at the Fermi level, N(EF)2, calculated from density functional theory (DFT) (24) (Fig. 3A, inset and table S4), implying strong deviation from simple Fermi liquid behavior. Coupled with the strong temperature dependence of 1/T1T, this evidences the unconventional nature of the metallic state above Tc emerging from the MJTI at overexpansion and optimal expansion. The transition to the metallic state from the MJTI is also accompanied by an increased 1/13T1 distribution as measured by the stretch exponent, α. Deep in the insulating state of overexpanded Rb0.35Cs2.65C60, α ≈ 0.83, reflecting the 1/13T1 distribution due to the nonequivalent 13C sites in the fcc structure (25). However, close to the insulator-to-metal crossover, α suddenly drops to ~0.6 (fig. S10), implying the development of increased local-site inhomogeneities attributable to coexisting localized and delocalized electrons. A similar albeit less pronounced trend is evident for the other overexpanded fullerides and is also seen in 1/133T1 data (fig. S10). No anomalies in the temperature dependence of α are observed in underexpanded Rb2CsC60 and Rb3C60, implying that this local electronic inhomogeneity fades away with lattice contraction.

Fig. 3 NMR and IR spectroscopy.

(A) Temperature dependence of the13C spin-lattice relaxation rates divided by temperature, 1/13T1T, for RbxCs3−xC60 (0 ≤ x ≤ 3). Arrows mark the temperatures, T′, at which maxima are observed. Inset: 1/13T1T at T = 35 K as a function of V. Existing data for K3C60, Rb3C60, and Rb2CsC60 (gray symbols) (29) are also included. The dashed line marks the volume dependence of N(EF)2 calculated by DFT (24) and normalized to its Rb3C60 value (right axis). (B) Left: Temperature dependence of the T1u(4) C603– vibrational mode in IR spectra of RbxCs3−xC60 (x = 0.35, 1, 2). The spectra are shifted vertically for clarity. Right (top): Temperature dependence of the normalized IR background transmittance in the featureless 750 to 960 cm−1 spectral region for RbxCs3−xC60 (0.35 ≤ x ≤ 1) showing step-like changes fitted with sigmoidal functions. Arrows mark the midpoint temperatures, T′. The dashed line marks the metallic background for x = 2. Inset: IR spectra for x = 0.35 at 300 (MJTI) and 21 K (superconductor). Right (bottom): Temperature dependence of the Fano asymmetry parameter, q, of the T1u(4) peak shape for RbxCs3−xC60 (0.75 ≤ x ≤ 3). The lines through the data are guides to the eye. q→∞ corresponds to a Lorentzian lineshape.

Emergence of a new state of matter—the JTM

Infrared (IR) spectroscopy can sensitively probe the molecular JT effect and its consequences for electronic behavior, particularly the localized character of the electronic states (26). Molecular distortions result in multiplet peak structures and activation of IR-silent vibrational modes, whereas the presence of itinerant electrons is signaled by a continuous spectral background. Coupling of the vibrations to the free carriers turns vibrational peaks into Fano resonances (27). The T1u(4) IR mode of overexpanded Rb0.35Cs2.65C60 and Rb0.5Cs2.5C60 gradually changes from twofold to fourfold splitting on cooling (Fig. 3B and fig. S11), resembling the behavior of MJTI Cs3C60 (9) and reflecting decreasing rate of interconversion of the JT molecular conformers and distortion isomers. This T1u(4)-derived multiplet, signifying the molecular JT effect, survives well into the metallic and superconducting states. The crossover to metallicity is evidenced by a step-like decrease in background transmittance below a characteristic temperature, T′ (Fig. 3B and fig. S12), coinciding with those observed by diffraction , χ(T), and NMR, whereas the JT distortion persists as demonstrated by the lineshapes. Direct observation of the coexistence of the molecular JT effect with a metallic background demonstrates that loss of the insulating character of the MJTI does not result in loss of the JT distortion. The unconventional metal signaled by the enhanced and strongly temperature-dependent χ and 1/T1T is a JTM, where the t1u electrons remain localized on the fulleride ions long enough to be detected on the 10−11 s IR timescale. The resulting local electronic heterogeneity within a single structural phase is consistent with the decreasing NMR stretch exponent emerging from the MJTI. This JTM then becomes superconducting below Tc, where the molecular distortion persists.

As the lattice contracts with increasing x (x = 0.75, 1), the metallic background emerges at higher T′ and the insulator-to-metal crossover becomes increasingly smeared out (Fig. 3B and fig. S12), being no longer discernible for x ≥ 1.5. In the insulating state at high temperature, the splitting pattern of the T1u(4) peak for RbxCs3−xC60 (x = 0.75, 1, 1.5) is comparable to that for x = 0.35 and 0.5 and similarly survives into the metallic state. This again signifies the initial emergence from the MJTI of a poorly conducting JTM. However, on further cooling, a gradual lineshape evolution, as monitored by the asymmetry parameter, q (16), from Lorentzian toward Fano resonance occurs (Fig. 3B and fig. S13), signaling the increasing importance of phonon coupling to the emerging electronic continuum rather than simply lifting the degeneracy of localized t1u molecular orbitals. The unconventional features of the JTM persist in this composition range, particularly the enhanced and strongly temperature-dependent χ(T) and NMR 1/T1T, which directly measure conduction electron behavior rather than phonon coupling to these electrons, and the local electronic heterogeneity measured by α, all consistent with the continued importance of JT on-molecule coupling in the electronic structure. Finally, for underexpanded Rb2CsC60 and Rb3C60, the background transmittance decreases monotonically on cooling (fig. S12), whereas T1u(4) evolves from a slightly asymmetric Lorentzian [consistent with a high-temperature metallic state with enhanced localization (28)] to a Fano resonance (Fig. 3B and fig. S11).

Unconventional superconductivity emerging from the JTM

We now consider the influence of the crossover from the MJTI to the JTM on superconductivity in RbxCs3−xC60, initially by NMR spectroscopy. 1/T1 measurements below Tc reveal that all (13C, 133Cs, and 87Rb) 1/T1 approach zero on cooling (Fig. 3A and fig. S8) as an s-wave symmetry superconducting gap, ∆, opens, displaying a 1/T1 ∝ exp(–∆0/kBT) (∆0 = ∆(0 K)) variation for Tc/T > 1.25 (Fig. 4A and fig. S14). For underexpanded Rb3C60, we find 2∆0/kBTc = 3.6(1), close to 2∆0/kBTc = 3.52 predicted for the BCS weak-coupling limit and to those observed for other underexpanded superconducting fullerides (ranging from 3 to 4) (29). However, 2∆0/kBTc increases to 4.9(1) for optimally expanded RbCs2C60 and then further to 5.6(2) for overexpanded Rb0.35Cs2.65C60 (Fig. 5), where, in both cases, the superconductor is entered from the JTM.

Fig. 4 Superconductivity gap and specific heat jump.

(A) Temperature dependence of the 87Rb (tetrahedral site) spin-lattice relaxation rate, 1/87T1, normalized to its Tc value for RbxCs3−xC60 (0.35 ≤ x ≤ 3). Solid lines through the points are fits to the gap equation (see text). Dashed lines mark 2∆0/kBTc slopes between 3.5 and 6.5. (B) Left: Temperature dependence of specific heat, C, measured in zero magnetic field for RbxCs3−xC60 (x = 0.5, 1, 2, 3). The solid lines show the normal-state specific heat, Cn, for x = 0.5 and 3 obtained in the following way: the specific heat of pristine C60 was first subtracted from the total specific heat; the excess specific heat was then fitted at T > Tc by a combined Debye and Einstein term to obtain the background phonon contribution due to the C603−–C603− and alkali–C603− vibrational modes and extrapolated to temperatures below Tc (fig. S15). Right: Temperature dependence of the electronic specific heat measured in zero magnetic field divided by temperature, (CCn)/T (middle panel) for underexpanded and optimally expanded Na2CsC60,K3C60, and RbxCs3−xC60 (1 ≤ x ≤ 3) and (right panel) for overexpanded RbxCs3−xC60 (0.35 ≤ x < 1).

Fig. 5 Superconducting properties as functions of packing density.

Evolution of Tc (bottom), superconducting gap divided by Tc, 2∆0/kBTc (middle), and specific heat jump at Tc, ∆(CCn)/Tc (upper panel) as a function of V at low temperature for fcc fullerides. The dashed lines mark the gap value, 2∆0/kBTc = 3.52 (middle), and the specific heat jump, ∆(CCn)/Tc (top panel), in the weak-coupling BCS limit. The latter was calculated by ∆(CCn)/Tc = 1.43 [1 + 53(Tcln)2ln(ωln/3Tc)]γn, where γn = (2/3)π2kB2N(EF)(1 + λ), and assuming pairing via high-energy intramolecular Hg phonons with ωln = 1400 K and superconducting coupling constant, λ = 0.068 N(EF), with N(EF) obtained from DFT (12, 24).

The RbxCs3−xC60 superconducting properties were also probed by specific heat measurements. Narrow anomalies (width, ~2 to 3 K) in the temperature dependence of the electronic specific heat, (CCn)/T, associated with the superconducting transitions are observed (Fig. 4B and fig. S15)—Cn is the normal state specific heat. The specific heat jump at Tc, ∆(CCn)/Tc, is related to the product of N(EF) and the superconducting coupling strength, λ. It first increases gradually with increasing V for underexpanded Na2CsC60, K3C60 (30), and Rb3C60. It then increases sharply for Rb2CsC60 and remains essentially constant past optimal expansion and well into the overexpanded regime for Rb0.5Cs2.5C60. Finally, it drops for Rb0.35Cs2.65C60 as the metal/superconductor–Mott insulator boundary is approached upon lattice expansion (Fig. 5). In accord with the superconducting gap behavior, these data for x < 3 contrast markedly with the V dependence of Δ(CCn)Tc expected in the BCS weak-coupling limit for intramolecular Hg phonon-driven superconductivity (Fig. 5) and reassert the influence on pairing of the JTM bordering the superconducting state.

DISCUSSION

Optimal balance between molecular and extended features leads to highest Tc

The experimental data have allowed us to track the electronic states of the trivalent molecular fullerides with temperature as the C60 packing density, V, is varied across the full range of RbxCs3−xC60 compositions, allowing quasi-continuous access to the entire bandwidth-controlled phase diagram (Fig. 6)—this extends from a strongly correlated antiferromagnetic MJTI (Cs3C60) to a conventional metal (Rb3C60). Because the Mott transition between the insulator and the metal is of first order, a phase coexistence regime ending at a critical point in the volume-temperature phase diagram is expected, reminiscent of the liquid-gas transition (31). However, no such phase separation is evident here in all experimental data sets even for overexpanded Rb0.35Cs2.65C60, implying that for all samples, the temperatures, T′, of M-I boundary intersection are above the critical temperature, Tcr ≲ 50 K. The supercritical behavior is consistent with the smearing out of the M-I crossover over an increasingly broader temperature range with decreasing V upon moving further away from Tcr.

Fig. 6 Global phase diagram.

Electronic phase diagram of fcc RbxCs3−xC60 showing the evolution of Tc (ambient P: solid triangles, high P: unfilled triangles) and the MJTI-to-JTM crossover temperature, T′ (SXRPD: squares; χ(T): stars; 13C, 87Rb, and 133Cs NMR spectroscopy: hexagon with white, color, and black edges, respectively; IR spectroscopy: diamonds), as a function of V. Within the metallic (superconducting) regime, gradient shading from orange to green schematically illustrates the JTM to conventional metal (unconventional to weak-coupling BCS conventional superconductor) crossover. Dashed lines mark experimental V(T) tracks for selected compositions. Upper panels: Evolution of T1u(4) IR lineshape through conventional metal (Rb2CsC60, 30 K), JTM (Rb0.5Cs2.5C60, 37 K), and MJTI (Rb0.35Cs2.65C60,130 K), together with schematic depictions of the respective molecular electronic structure, intermolecular electron hopping, and JT molecular distortion. Lower panel: Variation in superconducting gap divided by Tc, 2Δ0/kBTc, with V.

Contraction of the x = 0 MJTI first destroys the Mott insulator and yields an unconventional metal in which correlations sufficiently slow carrier hopping to allow the molecular JT distortions to survive; the local heterogeneities then gradually disappear with recovery of conventional metallic behavior. The states at the two extremes of the phase diagram (Fig. 6) are thus straddled by an intermediate metallic phase where short-range quasi-localized electron behavior associated with the intramolecular JT effect and, therefore, traceable to the molecular origin of the electronic states coexists with metallicity. This new state of matter, which we term a JTM, is characterized by both molecular (dynamically JT distorted C603– ions) and free-carrier (electronic continuum) features as clearly revealed by IR spectroscopy (Fig. 3B). The JTM exhibits a strongly enhanced spin susceptibility (or 1/13T1T) relative to that of a conventional Fermi liquid (Fig. 3A, inset), characteristic of the importance of strong electron correlations. In the insulating phase, 1/13T1 is governed by antiferromagnetic spin fluctuations (8)—such fluctuations remain important in the JTM regime but gradually diminish with decreasing V as (U/W) decreases and conventional Fermi liquid behavior appears for underexpanded fullerides. There is a crossover from the JTM to a conventional Fermi liquid upon moving from the Mott boundary toward the underexpanded regime with the distortion arising from JT effect disappearing and the electron mean-free path extending to more than a few intermolecular distances.

The boundary with the JTM directly affects superconductivity: the s-wave superconductors forming from the underexpanded conventional metals where effects of the JTM are minimal display ratios of superconducting gaps to Tc, 2Δ0/kBTc, characteristic of weak-coupling BCS superconductors; on the other hand, although s-wave symmetry is retained, the coupling strength is anomalously large, with this ratio approaching and exceeding 5, for the optimally and overexpanded superconductors emerging from JTMs upon cooling (Fig. 5). Moreover, the superconducting gap does not correlate with Tc (22, 32) in the overexpanded regime, where molecular features play a dominant role in producing the unconventional superconductivity—in contrast to the dome-shaped dependence of Tc, the gap increases monotonically with interfullerene separation (Fig. 5). Notably, the maximum Tc occurs at the crossover between the two types of gap behavior. A similar picture is conveyed by the specific heat results—the change in the specific heat jump at Tc, Δ(CCn)/Tc, with increasing expansion is consistent with an increasing coupling strength (and Sommerfeld electronic specific heat coefficient, γn) on approaching the Mott boundary (Fig. 5). The enhancement is evident even deeper into the underexpanded regime for x = 2, coinciding with the unconventional Tc(V) dependence for the same composition (Fig. 1E).

Figure 6 illustrates the full context of our main result—in fulleride superconductors, because of the intrinsically high crystal symmetry and the initial t1u orbital degeneracy at EF, we can directly see via the dynamic JT distortion the manifestation of the electrons’ molecular origin at quantifiable intermolecular separations and link this to the understanding of the collective transport and superconducting pairing properties. In this way, the cause of the anomalous normal state properties can be precisely identified as the heterogeneous persistence of the molecular JT effect into the metal via the combined action of electron-electron and electron-phonon interactions, allowing us to link the onset of unconventional normal and superconducting state behavior with the highest Tc currently achievable in these systems. The superconductivity dome arises from the two distinct branches of the Tc(V) relationship. From the MJTI side, Tc increases from the M-I boundary as V decreases and the molecular character of the states at EF reduces. From the metallic side, the extended features in the electronic structure give a different, conventional N(EF) dependence of Tc, which declines as V decreases. The Tc maximum when x = 1 then corresponds to the optimal balance of extended and molecular characteristics at EF and thus occurs in the crossover region between the two behaviors. These molecular characteristics are specifically the on-molecule JT coupling controlling t1u degeneracy and thus the role of correlation, the resulting orbital ordering and interanion magnetic exchange, the C603− anion spin state, and the electron-phonon coupling to JT active modes. That such features are fundamental in optimizing Tc and creating the canonical dome demonstrates that molecular electronic structure, which is synthetically determined, can directly control superconductivity. Because synthetic chemistry allows the creation of new electronic structures distinct from those in the atoms and ions that dominate most known superconductors, this is strong motivation to search for new molecular superconducting materials.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/3/e1500059/DC1

Materials and Methods

Table S1. Refined parameters for the fcc RbCs2C60 (sample II) phase [space group FmEmbedded Imagem, phase fraction refined to 98.994(2)%] obtained from the Rietveld analysis of the SXRPD data collected at 10 and 300 K (λ = 0.40006 Å).

Table S2. Refined parameters for the fcc Rb0.5Cs2.5C60 (sample I) phase [space group FmEmbedded Imagem, phase fraction refined to 83.23(3)%] obtained from the Rietveld analysis of the SXRPD data collected at 5 and 300 K (λ = 0.39989 Å).

Table S3. Structural parameters for the fcc Rb0.35Cs2.65C60 phase [space group FmEmbedded Imagem, phase fraction refined to 82.05(4)% at 0.41 GPa] obtained from the Rietveld analysis of the SXRPD data collected at 0.41 and 7.82 GPa, at 7 K (λ = 0.41305 Å).

Table S4. 13C spin-lattice relaxation rates, 1/13T1, in RbxCs3−xC60 (0 ≤ x ≤ 3) at 300 K, calculated interfulleride exchange constants, J, and 13C spin-lattice relaxation rates divided by temperature at 35 K just above the superconducting transition temperatures.

Fig. S1. Temperature dependence of the ZFC and FC magnetization, M (20 Oe) for the RbxCs3−xC60 (0.35 ≤ x ≤ 2) compositions.

Fig. S2. Temperature dependence of the magnetization, M (20 Oe, ZFC protocol) for the RbxCs3−xC60 (0.35 ≤ x ≤ 2) compositions at selected pressures.

Fig. S3. Low-temperature, high-pressure SXRPD.

Fig. S4. Pressure dependence of the low-temperature unit cell volume of the RbxCs3−xC60 (0.35 ≤ x ≤ 2) phases (x = 0.35, 1.5, and 2 at 7 K; x = 0.5 and 1 at 20 K).

Fig. S5. Temperature evolution of the volume, V, occupied per fulleride anion for the RbxCs3−xC60 (x = 1.5, 2) compositions over the full temperature range of the present diffraction experiments.

Fig. S6. Final observed (red circles) and calculated (blue line) SXRPD profiles for the Rb0.5Cs2.5C60 (A, λ = 0.39989 Å) and RbCs2C60 (B, λ = 0.40006 Å) samples at 5 and 10 K, respectively.

Fig. S7. Temperature dependence of the square root of the second moment, (13M2)1/2, of the 13C NMR spectra of the RbxCs3−xC60 (0.35 ≤ x ≤ 3) compositions.

Fig. S8. Temperature dependence of the (A) 87Rb and (B) 133Cs T-site spin-lattice relaxation rates divided by temperature, 1/87T1T and 1/133T1T, respectively, for the RbxCs3−xC60 (0 ≤ x ≤ 3) compositions.

Fig. S9. Temperature dependence of the 13C spin-lattice relaxation rates divided by temperature, 1/13T1T, for Rb2CsC60 and Rb3C60.

Fig. S10. Temperature dependence of the stretch exponent, α, for the (A) 13C and (B) 133Cs magnetization recoveries in the RbxCs3−xC60 compositions.

Fig. S11. Temperature dependence of the IR active T1u(4) C603– vibrational mode for the RbxCs3−xC60 (0 ≤ x ≤ 3) compositions.

Fig. S12. Representative IR spectra for the RbxCs3−xC60 (0 ≤ x ≤ 3) compositions at selected temperatures illustrating the IR spectroscopic signatures of the various electronic states encountered.

Fig. S13. Representative peak fits in the spectral region of the T1u(4) vibrational mode at selected temperatures for Rb0.5Cs2.5C60 (A) and RbCs2C60 (B).

Fig. S14. Temperature dependence of the 13C (A) and the T-site 133Cs (B) spin-lattice relaxation rate, 1/T1, normalized to its value at Tc for the RbxCs3−xC60 (0.35 ≤ x ≤ 3) compositions.

Fig. S15. (Main panels) Temperature dependence of the electronic part of the zero-field specific heat divided by temperature, (CCn)/T, obtained after subtracting the background phonon contribution from the total specific heat in RbxCs3−xC60 (0.35 ≤ x ≤ 3), K3C60, and Na2CsC60.

Fig. S16. Temperature dependence of the specific heat C divided by temperature T, C/T, for RbxCs3−xC60 (0.35 ≤ x ≤ 3) and K3C60.

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REFERENCES AND NOTES

Acknowledgments: We thank A. Krajnc for help with the NMR measurements and I. Tüttő for fruitful discussions. Funding: We acknowledge financial support by the European Union/JST FP7-NMP-2011-EU-Japan project LEMSUPER (contract no. NMP3-SL-2011-283214), the UK Engineering and Physical Sciences Research Council (grant nos. EP/K027255 and EP/K027212), the Japan Science and Technology Agency under the ERATO Isobe Degenerate π-Integration Project, the Japan Society of Promotion of Sciences (Grant-in-Aid for Specially Promoted Research no. 25000003), and the Hungarian National Research Fund (OTKA) no. 105691. We thank the European Synchrotron Radiation Facility, SPring-8, and RIKEN for access to synchrotron x-ray facilities, and the Royal Society for a Newton International Fellowship (G.K.), a Research Professorship (M.J.R.), and a Wolfson Research Merit Award (K.P.). This work was sponsored by the “World Premier International (WPI) Research Center Initiative for Atoms, Molecules and Materials,” Ministry of Education, Culture, Sports, Science, and Technology of Japan. Author contributions: K.P. directed and coordinated the project. R.H.Z. carried out all solid-state synthetic work. A.Y.G. and M.J.R. made one sample by a liquid ammonia route. R.H.Z., Y.T., R.H.C., and K.P. performed ambient and high-pressure synchrotron XRD and magnetization measurements and analyzed the data. A.P., P.J., and D.A. carried out and analyzed the NMR measurements. G.K., P.M., and K. Kamarás performed IR measurements and analyzed the data. Y.K. and Y.I. carried out the specific heat measurements and analyzed the data. A.N.F., Y.O., G.G., and K. Kato technically supported the synchrotron x-ray experiments. K.P. wrote the paper with input from M.J.R., D.A., K. Kamaras, and Y.I. All authors discussed the experiments and commented on the manuscript. Competing interests: The authors declare that they have no competing interests.
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