Possible light-induced superconductivity in K3C60 at high temperature

Abstract

The non-equilibrium control of emergent phenomena in solids is an important research frontier, encompassing effects such as the optical enhancement of superconductivity. Nonlinear excitation 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 4-6). This effect was accompanied by the disruption of competing charge-density-wave correlations, 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.

Extended Data Figure 1.. K₃C₆₀ sample characterization

a, Powder X-ray diffraction of K₃C₆₀ (black circles) fitted with a single fcc phase Rietveld refinement (red). b, Temperature dependent magnetic susceptibility (FCC: Field cooled cooling. ZFC: Zero field cooling). The extracted superconducting critical temperature is T_c = 19.8 K.

Extended Data Figure 2.. “Raw” electric field transients below and above T_c

a-d, Stationary electric field reflected at the sample-diamond interface and pump-induced changes in the same quantity, measured at τ = 3 ps in a-b and at τ = 1 ps in c-d. Data are shown both below and above T_c. e-f, Corresponding frequency-dependent differential changes in reflectivity, calculated as Fourier transform magnitude ratios of the quantities in a-d.

Extended Data Figure 3.. Models for penetration depth mismatch

a, Schematics of pump-probe penetration depth mismatch. Single-layer model (b) and multi-layer model with exponential decay (c) (see Methods section) used to calculate the pump-induced changes in the complex refractive index $\tilde{n}\left(\omega \right)$. d-f, Reflectivity and complex optical conductivity 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).

Extended Data Figure 4.. Equilibrium optical properties

a, Reflectivity, real and imaginary part of the optical conductivity of K₃C₆₀ displayed at different temperatures above T_c. Dashed lines are fits to the 25 K data performed with a Drude-Lorentz model. b, Same quantities displayed at different T < T_c. In the inset, the temperature dependent optical gap (full circles) is compared with previously published data on K₃C₆₀ single crystals (open circles, from Ref. 18). c, Optical properties of K₃C₆₀ compressed powders from a and b shown at representative temperatures below and above T_c. The R(ω) has been recalculated at the sample-vacuum interface. d, Same quantities as in c, measured on single crystals by L. Degiorgi et al..

Extended Data Figure 5.. Uncertainties in determining the transient optical properties

Reflectivity and complex optical conductivity of K₃C₆₀ at equilibrium (red) and 1 ps after photo-excitation (blue) at T = 25 K. Error bars, displayed as colored bands, have been propagated from (a) a ±1% and ±2.5% uncertainty in the equilibrium R(ω); (b) a ±10% uncertainty in the equilibrium Fresnel phase coefficient β (see Methods); (c) a ±25% change in the pump penetration depth d = 220 nm. In d we analyze the effect of different functional forms for modeling the pump-probe penetration depth mismatch (see Methods): Single-layer model, multi-layer model with exponential and Gaussian-like decay, all with the same pump penetration depth d = 220 nm.

Extended Data Figure 6.. Relaxation dynamics at T>T_c

Reflectivity and complex optical conductivity of K₃C₆₀ at equilibrium (gray) and after photo-excitation (red) at T = 25 K. Data have been measured with a pump fluence of ~1 mJ/cm² and are shown at selected pump-probe time delays: 1.5 ps, 5.5 ps, and 21 ps.

Extended Data Figure 7.. Mode coupling and electronic structure calculations

a, Calculated total energy curves as a function of H_g(1) mode amplitude when the amplitude of the T_1u(4) mode is 0.0 (blue) and 2.0 Å √amu (red). b, Calculated band structure and electronic density of states of K₃C₆₀. c, Calculated electron-phonon coupling function α²F(ω). In b-c, blue lines are for the equilibrium structure and red lines are for the structure displaced along the H_g(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.

Extended Data Figure 8.. Changes in time of single particle energy and Coulomb repulsion

a, Depiction of the x, y, z t_1u orbital wavefunctions of C₆₀ according to the Hückel model (see Methods). b, Snap-shots of the calculated t_1u(z) orbital at various points in the T_1u(4) vibration polarized along the x axis. Color and sizes follow those of a. c, Changes in the single-particle energies of the t_1u orbitals over one period of the T_1u(4) vibration with an amplitude A = 5 pm. d, Relative changes in the intra-orbital Coulomb repulsions. e, Maximum relative changes in the single-particle energies of the t_1u orbitals as a function the driving amplitude A. f, Relative changes in the intra-orbital Coulomb repulsions under the same driving conditions.

Extended Data Figure 9.. Response at early time delays below and above T_c

Reflectivity and complex optical conductivity of K₃C₆₀ at equilibrium and 1 ps after photo-excitation, measured at T > T_c (a-c) and T < T_c (d-f). Data were taken using pump fluences of ~1 mJ/cm² in a-c and ~0.5 mJ/cm² in d-f.

Extended Data Figure 10.. Relaxation dynamics at Tc

Reflectivity and complex optical conductivity of K₃C₆₀ at equilibrium (gray) and after photo-excitation (red) at T = 10 K. Data have been measured with a pump fluence of ~0.5 mJ/cm² and are shown at selected pump-probe time delays: 3 ps, 11 ps, and 21 ps.

Fig.1. Structure and equilibrium optical properties of K₃C₆₀

a, Face centered cubic (fcc) unit cell of K₃C₆₀. Blue bonds link the C atoms on each C₆₀ molecule. K atoms are represented as red spheres. b, C₆₀ molecular distortion (red) along the T_1u(4) vibrational mode coordinates. The equilibrium structure is displayed in blue. c-e, Equilibrium reflectivity and complex optical conductivity of K₃C₆₀ measured at T = 25 K (red) and T = 10 K (blue).

Fig. 2. Transient optical response of photo-excited K₃C₆₀ at T = 25 K and T = 100 K

Reflectivity and complex optical conductivity of K₃C₆₀ at equilibrium (red) and 1 ps after photo-excitation (blue) at a pump fluence of 1.1 mJ/cm², measured at base temperatures T = 25 K (a-c) and T = 100 K (d-f). Fits to the data are displayed as dashed lines.

Fig. 3. Transient optical response of photo-excited K₃C₆₀ at T = 200 K and T = 300 K

Reflectivity and complex optical conductivity of K₃C₆₀ at equilibrium (red) and 1 ps after photo-excitation (blue) with a pump fluence of 1.1 mJ/cm², measured at base temperatures T = 200 K (a-c) and T = 300 K (d-f). Fits to the data are displayed as dashed lines.

Fig. 4. Scaling of the σ₁(ω) gap with experimental parameters

Photo-induced reduction in σ₁(ω) spectral weight, integrated between 0.75 – 2.5 THz (circles in all panels). The lost spectral weight is plotted as a function of base temperature (a), pump-probe time delay (b), pump fluence (c), and pump wavelength (d). Error bars represent maximum uncertainties estimated from different sets of measurements. The regions shaded in blue indicate the parameter ranges for which the transient response was fitted with a model for a superconductor. The red curve in b is the pump pulse profile (cross-correlation signal), while the dashed line is a double exponential fit (τ₁ ≃ 1 ps, τ₂ ≃ 10 ps). Dashed vertical lines in d are the frequencies of the four T_1u vibrational modes. The experiments were not possible for pump wavelengths between 6 and 3 μm due to absorption in the diamond window that contained the K₃C₆₀ powders. White and blue dots are data taken at fluence values of 0.4 and 1.1 mJ/cm², respectively. Data in b-d were measured at T = 25 K.