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
  • 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).

  • 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.

  • 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.

  • 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).

  • 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.

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 FmFormulam, 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 FmFormulam, 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 FmFormulam, 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.

  • Supplementary Materials

    This PDF file includes:

    • Materials and Methods
    • Table S1. Refined parameters for the fcc RbCs2C60 (sample II) phase space group Fm 3 m, 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 Rb0.5CsC60 (sample I) phase space group Fm 3 m, 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 RbCsC60 phase space group Fm 3 m, 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 RbCsC60 (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, a, for the (A) 13C and (B) 133Cs magnetization recoveries in the RbxCs3−xC60 compositions.
    • Fig. S11. Temperature dependence of the IR active T1u(4) C60 3– 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 RbCsC60 (A) and RbCs2C60 (B).
    • Fig. S14. Temperature dependence of the 13C (A) and the T-site 133Cs (B) spinl-attice 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, (C − Cn)/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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