Evidence for Band Renormalizations in Strong-Coupling Superconducting Alkali-Fulleride Films

There has been a long-standing debate about the mechanism of the unusual superconductivity in alkali-intercalated fullerides. In this Letter, using high-resolution angle-resolved photoemission spectroscopy, we systematically investigate the electronic structures of superconducting ${\mathrm{K}}_3{\mathrm{C}}_{60}$ thin films. We observe a dispersive energy band crossing the Fermi level with the occupied bandwidth of about 130 meV. The measured band structure shows prominent quasiparticle kinks and a replica band involving the Jahn-Teller active phonon modes, which reflects strong electron-phonon coupling in the system. The electron-phonon coupling constant is estimated to be about 1.2, which dominates the quasiparticle mass renormalization. Moreover, we observe an isotropic nodeless superconducting gap beyond the mean-field estimation ($2\mathrm{\Delta }/k_B{T}_c\approx 5$). Both the large electron-phonon coupling constant and large reduced superconducting gap suggest a strong-coupling superconductivity in ${\mathrm{K}}_3{\mathrm{C}}_{60}$, while the electronic correlation effect is suggested by the observation of a waterfall-like band dispersion and the small bandwidth compared with the effective Coulomb interaction. Our results not only directly visualize the crucial band structure but also provide important insights into the mechanism of the unusual superconductivity of fulleride compounds.

Figure 1

(a) Schematic illustration of the crystal structure of bilayer ${\mathrm{K}}_3{\mathrm{C}}_{60}$ grown on an epitaxial bilayer graphene that was prepared by graphitizing the SiC substrate. The red and green spheres are the K atoms occupying octahedral and tetrahedral interstitial sites between ${\mathrm{C}}_{60}$ molecules. The zoom-in plot shows a ${\mathrm{C}}_{60}$ molecule with a diameter of about 10 Å. (b) The intensity of the specular spot in RHEED pattern as a function of sample growth time. The film thickness can be monitored by the oscillation in the RHEED curve. (c) STM surface topography of 5 monolayer (ML) ${\mathrm{K}}_3{\mathrm{C}}_{60}$ showing trilobe feature, acquired at sample bias $U=1.5\mathrm{V}$ and a constant tunneling current of $I=30\mathrm{pA}$. (d) Line profile along the red dashed arrow in (c) showing the homogenous superconducting gap. Data were collected at 4.7 K.

Figure 2

(a) Band structure of 3 ML pristine ${\mathrm{C}}_{60}$ film grown on bilayer $\text{graphene}/\mathrm{SiC}$ substrate. (b)–(e) Evolution of the band structure of ${\mathrm{K}}_{\mathrm{x}}{\mathrm{C}}_{60}$ film with K doping. (f) Integrated energy distribution curves (EDCs) of ${\mathrm{K}}_{\mathrm{x}}{\mathrm{C}}_{60}$ films in (a)–(e). Data were collected using a helium lamp ($h\nu =21.2\mathrm{eV}$) at 13 K.

Figure 3

(a)–(d) Band dispersion of 5 ML ${\mathrm{K}}_3{\mathrm{C}}_{60}$ film along $\overline{\mathrm{\Gamma }}\overline{\mathrm{M}}$ near $E_F$ collected at selected temperatures. (e) Integrated EDC at 8.5 K showing the reduction of spectral weight near binding energies of 18, 54, and 85 meV. (f) Comparison between the EDCs of ${\mathrm{K}}_3{\mathrm{C}}_{60}$ at Fermi momentum ($k_{\mathrm{F}}$) and polycrystalline gold showing the superconducting gap. (g),(h) Symmetrized ARPES spectra at 8.5 and 50 K, respectively. (i) Symmetrized EDCs integrated around $k_{\mathrm{F}}$ acquired at selected temperatures. The black dashed line is the fit to the Dynes function. The black arrows indicate the dip in the EDC. (j) Temperature dependent leading-edge gap from ARPES measurements (blue circles) and gap depth from STM measurements (orange diamonds). The red dashed line is the fit to the BCS model. (k) Angular distribution of superconducting gap extracted by fitting the symmetrized EDCs to the Dynes function.

Figure 4

(a) Comparison of the band dispersions at selected temperatures extracted from momentum distribution curve (MDC) fitting. The black dashed lines are the guides of eyes for the energy kinks in the band dispersion. (b),(c) Real and imaginary parts of the electron self-energy, respectively. (d) ARPES spectra in a large energy scale showing the band replication and waterfall-like band dispersion. (e) Integrated EDC obtained from (d).