The non-equilibrium control of emergent phenomena in solids is an important research frontier, encompassing effects such as the optical enhancement of superconductivity1. Nonlinear excitation2,3 of certain phonons in bilayer copper oxides was recently shown to induce superconducting-like optical properties at temperatures far greater than the superconducting transition temperature, Tc (refs 4, 5, 6). This effect was accompanied by the disruption of competing charge-density-wave correlations7,8, which explained some but not all of the experimental results. Here we report a similar phenomenon in a very different compound, K3C60. By exciting metallic K3C60 with mid-infrared optical pulses, we induce a large increase in carrier mobility, accompanied by the opening of a gap in the optical conductivity. These same signatures are observed at equilibrium when cooling metallic K3C60 below Tc (20 kelvin). Although optical techniques alone cannot unequivocally identify non-equilibrium high-temperature superconductivity, we propose this as a possible explanation of our results.
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We acknowledge S. Kivelson and A. Georges for discussion. We are also grateful to A. Subedi for sharing microscopic calculations of anharmonic mode coupling. We thank L. Degiorgi for sharing optical data measured on single crystals. Technical support during sample handling was provided by H.-P. Liermann and M. Wendt. We additionally acknowledge support from M. Gaboardi (for SQUID magnetometry) and from J. Harms (for graphics). The research leading to these results received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement no. 319286 (QMAC). We acknowledge support from the Deutsche Forschungsgemeinschaft via the excellence cluster ‘The Hamburg Centre for Ultrafast Imaging — Structure, Dynamics and Control of Matter at the Atomic Scale’ and the priority program SFB925. This work was also supported by the Swiss National Supercomputing Center (CSCS) under the project ID s497.
The authors declare no competing financial interests.
Extended data figures and tables
a, Powder X-ray diffraction of K3C60 (black circles) fitted with a single f.c.c. phase Rietveld refinement (red). Positions of reflections are shown in green, fit residuals are in grey. b, Temperature dependent magnetic susceptibility, χm (FCC, field-cooled cooling; ZFC, zero-field cooling). The extracted superconducting transition temperature is Tc = 19.8 K.
a–d, Stationary electric field (a, c; grey) reflected at the sample–diamond interface, ER(t), and pump-induced changes in the same quantity, ΔER(t, τ), measured at τ = 3 ps (b) and at τ = 1 ps (d). Data are shown both below (blue) and above Tc (red). e, f, Corresponding frequency-dependent differential changes in reflectivity, ΔER/ER(ω, τ), calculated as Fourier transform magnitude ratios of the quantities in a–d.
a, Schematics of pump–probe penetration depth mismatch. b, c, Also shown are the single-layer model (b) and the multi-layer model with exponential decay (c) (see Methods) used to calculate the pump-induced changes in the complex refractive index, . d–f, Reflectivity, R(ω), and complex optical conductivity, σ(ω), of K3C60 at τ = 1 ps pump–probe delay and T = 25 K, extracted using the single-layer model (light blue) and the multi-layer model with exponential decay (dark blue).
a, Reflectivity (left column), and real and imaginary parts (respectively middle and right columns) of the optical conductivity of K3C60 displayed at different temperatures above Tc. Dashed lines are fits to the 25 K data performed with a Drude–Lorentz model. b, Same quantities displayed at different T < Tc. In the inset, the temperature dependent optical gap (filled circles) is compared with previously published data on K3C60 single crystals (open circles18). c, Optical properties of compressed powders of K3C60 from a and b shown at representative temperatures below and above Tc. The R(ω) has been recalculated at the sample–vacuum interface. d, Same quantities as in c, measured on single crystals18.
Columns as Extended Data Fig. 4; shown are values for K3C60 at equilibrium (red) and 1 ps after photo-excitation (blue) at T = 25 K. Error bars, displayed as coloured bands, have been propagated as follows: a, ±1% and ±2.5% uncertainty in the equilibrium R(ω); b, ±10% uncertainty in the equilibrium Fresnel phase coefficient β (see Methods); c, ±25% change in the pump penetration depth d = 220 nm. In d we analyse the effect of different functional forms for modelling the pump–probe penetration depth mismatch (see Methods): a single-layer model, or a multi-layer model with exponential decay or with Gaussian-like decay, all with the same pump penetration depth d = 220 nm.
Reflectivity (left column) and complex optical conductivity (middle and right columns) of K3C60 at equilibrium (grey) and after photo-excitation (red) at T = 25 K. Data have been measured with a pump fluence of ~1 mJ cm−2 and are shown at selected pump–probe time delays: 1.5 ps, 5.5 ps and 21 ps (top, middle and bottom rows, respectively). Hatched areas highlight pump-induced changes.
a, Calculated total energy curves as a function of Hg(1) mode amplitude () when the amplitude of the T1u(4) mode is 0.0 (blue) and 2.0 Å √amu (red). b, Calculated band structure and electronic density of states N(E) of K3C60. c, Calculated electron–phonon coupling function, α2F(ω). In b and c, blue lines are for the equilibrium structure and red lines are for the structure displaced along the Hg(1) coordinate with an amplitude of 1.5 Å √amu. d, Differential changes in the electron–phonon coupling function, evaluated from the curves in c.
a, Depiction of the x, y, z t1u orbital wavefunctions of C60 according to the Hückel model (left, middle and right column respectively, see Methods). Sphere sizes denote the magnitude of the wavefunction and colours indicate the sign. b, Snapshots of the calculated t1u(z) orbital at various points in the T1u(4) vibration polarized along the x axis. Colours and sizes follow those of a. c, Changes in the single-particle energies, εi, of the t1u orbitals over one period of the T1u(4) vibration with an amplitude A = 5 pm. d, Relative changes in the intra-orbital Coulomb repulsions, Ui/Ui(0). e, Maximum relative changes in the single-particle energies of the t1u orbitals, εi/εi(0), as a function the driving amplitude, A. f, Relative changes in the intra-orbital Coulomb repulsions, Ui/Ui(0), under the same driving conditions.
Reflectivity, R(ω), and complex optical conductivity, σ(ω), of K3C60 at equilibrium (red, dark blue) and 1 ps after photo-excitation (light blue), measured at T > Tc (a–c) and T < Tc (d–f). Data were taken using pump fluences of ~1 mJ cm−2 in a–c and ~0.5 mJ cm−2 in d–f. Hatched areas highlight pump-induced changes.
Columns as Extended Data Fig. 9; data were measured at equilibrium (grey) and after photo-excitation (red) at T = 10 K, with a pump fluence of ~0.5 mJ cm−2. Data are shown at selected pump–probe time delays: 3 ps (top row), 11 ps (middle row) and 21 ps (bottom row). Hatched areas highlight pump-induced changes.
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Mitrano, M., Cantaluppi, A., Nicoletti, D. et al. Possible light-induced superconductivity in K3C60 at high temperature. Nature 530, 461–464 (2016). https://doi.org/10.1038/nature16522
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