ARTICLES https://doi.org/10.1038/s41567-020-01148-1 Evidence for metastable photo-induced superconductivity in K3C60 M. Budden1 ✉ , T. Gebert1, M. Buzzi 1, G. Jotzu 1, E. Wang1, T. Matsuyama1, G. Meier 1, Y. Laplace1, D. Pontiroli 2, M. Riccò2, F. Schlawin 3, D. Jaksch 3 and A. Cavalleri 1,3 ✉ Excitation of high-Tc cuprates and certain organic superconductors with intense far-infrared optical pulses has been shown to create non-equilibrium states with optical properties that are consistent with transient high-temperature superconductivity. These non-equilibrium phases have been generated using femtosecond drives, and have been observed to disappear imme- diately after excitation, which is evidence of states that lack intrinsic rigidity. Here we make use of a new optical device to drive metallic K3C60 with mid-infrared pulses of tunable duration, ranging between one picosecond and one nanosecond. The same superconducting-like optical properties observed over short time windows for femtosecond excitation are shown here to become metastable under sustained optical driving, with lifetimes in excess of ten nanoseconds. Direct electrical probing, which becomes possible at these timescales, yields a vanishingly small resistance with the same relaxation time as that esti- mated by terahertz conductivity. We provide a theoretical description of the dynamics after excitation, and justify the observed slow relaxation by considering randomization of the order-parameter phase as the rate-limiting process that determines the decay of the light-induced superconductor. on-equilibrium orders in complex materials include experiments reported have indicated the presence of states that photo-induced ferroelectricity1,2, magnetic polarization in disappear immediately after optical excitation (see optical proper- antiferromagnets3 and transient superconductivity in the ties measured at 5 ps time delay in Fig. 1d). These short lifetimes N 4–9 normal state of cuprates and organic conductors . Among these, would prevent most applications and have even raised controversy 18,19 much work has been dedicated to alkali-doped fullerides of the A3C60 over the data interpretation itself . family (Fig. 1a), which exhibit tunable high-temperature supercon- In this Article, we explore the possibility of longer-lived super- ductivity at equilibrium10–15 (Fig. 1b). The dynamical manipulation conductivity under a sustained optical drive. First, we modified the of superconductivity in these materials6,7 has been demonstrated by experimental set-up used for the experiments shown in Fig. 1 and using optical pulses at mid-infrared frequencies that are tuned in lengthened the 7.3 µm wavelength pump pulses by making them the vicinity of local vibrational resonances of the C60 molecules. propagate in a dispersive CaF2 rod (Fig. 2a). These chirped pump The evidence reported so far is summarized in Fig. 1c,d. K3C60 pow- pulses had a duration τp ≈ 1 ps, which enabled a sixfold increase in 2 ders were held at a base temperature of T 100 K Tc 20 K and the pulse energy density (up to 18 mJ cm− ) without a correspond- ¼ ¼ irradiated with 100-fs-long, 7.3- m-wavelengthI (ℏω 170 meV, ing increase in the peak electric field. This longer pulse duration µ where ħ is Planck’s constant and ω is angular frequency)I pulses at allowed us to conduct these experiments at pulse energy densities a fluence of 3 mJ cm−2, which yielded a short-lived transient state that would damage the sample at femtosecond pulse durations, and with large changes in the terahertz optical properties. The transient hence it enabled the exploration of a new regime of excitation. optical response was probed with phase-sensitive, time-domain The pump-induced changes in the low-frequency reflectiv- terahertz spectroscopy, which directly yields the real and imagi- ity and complex optical conductivity (Fig. 2b) were measured on nary part of the reflectance and hence can be used to retrieve the the same sample and at the same temperature T = 100 K as for the complex optical conductivity without the need of Kramers–Kronig experiments of Fig. 1. Representative reflectivity spectra R(ω) and 6,7 transformations (Supplementary Section 4 and refs. ). The tran- complex optical conductivity, σ1(ω)+iσ2(ω), measured for a 1 ps sient low-frequency optical conductivity induced by femtosecond pump-pulse duration and 18 mJ cm−2 fluence are reported for time excitation was almost indistinguishable from that of the equi- delays of –5 ps, 10 ps, 300 ps and 12 ns. These plots indicate a simi- librium superconducting state measured in the same material at lar response to that shown in Fig. 1d (perfect reflectivity (R = 1), T Tc 20 K (compare to Fig. 1c). Such ‘superconducting-like’ gapped ( ) and a divergent ( )), although with a far longer ¼ σ1 ω σ2 ω opticalI properties consist of a perfect low-energy reflectance (R = 1), relaxation time of at least 300 ps. a vanishingly small real part of the optical conductivity σ1(ω) for all A more comprehensive exploration of sustained optical driving, photon energies lower than the energy gap 2Δ and an imaginary beyond the limited pulse-width tunability of the set-up shown in conductivity σ2(ω) that diverges toward low frequencies as 1/ω, Fig. 2, is shown in Figs. 3, 4 and 5. These measurements made use which itself is indicative of a large zero-frequency conductivity. of a newly developed optical device, based on a CO2-gas laser that These observations have generated interest, as they may make was optically synchronized to a femtosecond Ti:Al2O3 laser, and that it possible to achieve photo-induced superconducting states4–7,9,16,17 delivered 10.6 µm wavelength pulses with durations that could be at or in the vicinity of room temperature. However, all of the tuned between 5 ps and 1.3 ns (Fig. 3a). 1Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany. 2Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università degli Studi di Parma, Parma, Italy. 3Department of Physics, Clarendon Laboratory, University of Oxford, Oxford, UK. ✉e-mail: [email protected]; [email protected] NatURE PHysICS | www.nature.com/naturephysics ARTICLES NATURE PHYSICS a b Cs3C60 Rb3C60 K3C60 100 Metal ature (K) r Insulator empe T 10 Superconductor 1/Vcell c Equilibrium 900 900 1.0 ) 600 ) 600 y t –1 –1 cm cm 0.5 –1 –1 Ω Ω ( ( eflectivi 1 2 R σ σ 300 300 T > TC T < TC 0 0 0 4 10 20 40 4 10 20 40 4 10 20 40 Energy (meV) Energy (meV) Energy (meV) d Photoexcited 900 1.0 900 T = 100 K Δt = 1 ps Δt = 5 ps ) 600 ) 600 y t –1 –1 cm cm 0.5 –1 –1 Ω Ω ( ( eflectivi 1 2 R σ σ 300 300 0 0 0 6 10 20 40 6 10 20 40 6 10 20 40 Energy (meV) Energy (meV) Energy (meV) Fig. 1 | Crystal structure, phase diagram, equilibrium phase transition and short-lived, light-induced phase in K3C60. a, Crystal structure of the molecular superconductor K3C60. C60 molecules are arranged in a face-centred cubic lattice. Potassium atoms (red) occupy the interstitial voids. b, Phase diagram of the A3C60 alkali-doped fullerene family as a function of the inverse unit cell volume 1/Vcell. The ground state of the material can be tuned by chemical or physical pressure. The solid grey line indicates the boundary between the insulating and metallic/superconducting phases. The blue dashed line highlights the dependence of the superconducting transition temperature Tc as a function of 1/Vcell. The star indicates the K3C60 compound investigated in the present work, which becomes superconducting for T < Tc = 20 K. c, Equilibrium reflectivity (sample–diamond interface), real and imaginary part of the optical conductivity of K3C60 measured upon cooling across the equilibrium superconducting transition. The blue shading indicates the change of spectral weight in these quantities across the thermally driven superconducting transition. d, Same quantities measured at equilibrium (red lines), 1 ps (blue filled dots) and 5 ps (light blue triangles) after photoexcitation. The blue shading indicates the change of spectral weight in these quantities induced by photoexcitation. The light and dark blue lines are Drude–Lorentz fits to the transient optical data (Supplementary Section 6). These data were acquired at a base temperature T = 100 K with a fluence of 3 mJ cm−2 and a pulse duration of 100 fs. Near-infrared femtosecond pulses from a Ti:Al2O3 laser were The ‘front’ and the ‘back’ of the 1-ns-long CO2 pulses were ‘sliced’ converted to a wavelength of 10.6 µm with an optical parametric using a pair of photoexcited semiconductor wafers as plasma mir- 20 21–23 amplifier and were used to seed a CO2 laser oscillator . The oscilla- rors . As the wafers were set at Brewster’s angle and their band- tor emitted trains of nanosecond-long pulses, out of which the most gap was much larger than the 117 meV photon energy of the CO2 intense was selected by a Pockels cell and amplified to an energy laser, these were almost perfectly transparent when unexcited. of 10 mJ in a second, multi-pass CO2 laser amplifier. The dura- Pairs of femtosecond optical pulses struck each wafer at adjustable tion of these amplified pulses was then tuned as shown in Fig. 3a. time delays, making these reflective owing to the injection of dense NatURE PHysICS | www.nature.com/naturephysics NATURE PHYSICS ARTICLES a EOS Ti:Sa amplifier THz gen. Ti:Sa oscillator THz probe ~100 fs ~1 ps OPA DFG Ti:Sa amplifier CaF2 rod MIR pump b High-fluence photoexcitation 900 900 1.0 T = 100 K Δt = 10 ps 600 ) ) 600 y t –1 –1 cm cm 0.5 –1 –1 Ω Ω ( ( eflectivi 1 2 R σ σ 300 300 Equilibrium Photoexcited 0 0 0 4 10 20 40 4 10 20 40 4 10 20 40 900 900 1.0 Δt = 300 ps 600 ) ) 600 y t –1 –1 cm cm 0.5 –1 –1 Ω Ω ( ( eflectivi 1 2 R σ σ 300 300 0 0 0 4 10 20 40 4 10 20 40 4 10 20 40 900 900 1.0 Δt = 12 ns 600 ) ) 600 y t –1 –1 cm cm 0.5 –1 –1 Ω Ω ( ( eflectivi 1 2 R σ σ 300 300 0 0 0 4 10 20 40 4 10 20 40 4 10 20 40 Energy (meV) Energy (meV) Energy (meV) Fig.