Direct Observation of Full-Gap Superconductivity and Pseudogap in Two-Dimensional Fullerides

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Direct Observation of Full-Gap Superconductivity and Pseudogap in Two-Dimensional Fullerides

Ming-Qiang Ren, Sha Han, Shu-Ze Wang, Jia-Qi Fan, Can-Li Song, Xu-Cun Ma, and Qi-Kun Xue

Phys. Rev. Lett. 124, 187001 – Published 5 May 2020

Abstract

Alkali-fulleride superconductors with a maximum critical temperature $T_{c} \sim 40 K$ exhibit a similar electronic phase diagram to that of unconventional high- $T_{c}$ superconductors. Here we employ cryogenic scanning tunneling microscopy to show that trilayer $K_{3} C_{60}$ displays fully gapped strong coupling $s$ -wave superconductivity, accompanied by a pseudogap above $T_{c} \sim 22 K$ and within vortices. A precise control of the electronic correlations and potassium doping enables us to reveal that superconductivity occurs near a superconductor-Mott-insulator transition and reaches maximum at half-filling. The $s$ -wave symmetry retains over the entire phase diagram, which, in conjunction with an abrupt decline of the superconductivity below half-filling, indicates that alkali fullerides are predominantly phonon-mediated superconductors, although the electronic correlations also come into play.

Received 23 December 2019
Accepted 15 April 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.187001

Physics Subject Headings (PhySH)

Pseudogap Superconducting gap Superconducting order parameter Superconducting phase transition Vortices in superconductors

High-temperature superconductors Ultrathin films

Molecular beam epitaxy Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ming-Qiang Ren¹, Sha Han¹, Shu-Ze Wang ¹, Jia-Qi Fan¹, Can-Li Song ^1,2,*, Xu-Cun Ma^1,2,†, and Qi-Kun Xue^1,2,3,‡

¹State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
²Frontier Science Center for Quantum Information, Beijing 100084, China
³Beijing Academy of Quantum Information Sciences, Beijing 100193, China

^*clsong07@mail.tsinghua.edu.cn
^†xucunma@mail.tsinghua.edu.cn
^‡qkxue@mail.tsinghua.edu.cn

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Vol. 124, Iss. 18 — 8 May 2020

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Images

Figure 1
(a) Crystal structure of fcc $K_{3} C_{60}$ . The purple and red spheres denote K dopants at the octahedral and tetrahedral sites, respectively. (b) Schematic (side) view of $K_{3} C_{60} (111)$ films on graphitized SiC(0001) substrate. (c) STM topography ( $V = 1.0 V$ , $I = 10 pA$ ) of trilayer $K_{3} C_{60}$ . (d) Grid $d I / d V$ spectra ( $5 pixels \times 5 pixels$ ) in a field of view of $20 nm \times 20 nm$ . The set point is stabilized at $V = 20 mV$ and $I = 200 pA$ , unless otherwise specified. For comparison, each $d I / d V$ spectrum is normalized to a cubic background by fitting the raw conductance beyond the superconducting gap ( $| V | > 10 mV$ ). This normalization procedure is used throughout. (e) The $d I / d V$ spectrum and its best fit (red curve) to a single isotropic $s$ -wave superconducting gap with $Δ = 5.4 meV$ . (f) Spatially averaged tunneling spectra as a function of temperature, presenting a pseudogap above $T_{c} = 22 K$ (red curve). (g) Measured dependence on temperature of coherence peak amplitude (circles) and gap depth (squares), defined as the integration over red-shaded areas and difference between unity and the normalized zero-energy conductance $σ_{0, N}$ (see inset), respectively.
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Figure 2
(a) Spatial maps ( $300 pixels \times 300 pixels$ ) of zero-energy conductance $σ_{0} (V = 0)$ , revealing vortices (i.e., the orange and white regions with enhanced $σ_{0}$ ) at $B = 2$ , 4, and 8 T in the same field of view of $63 nm \times 63 nm$ . (b) Vortex-induced $σ_{0, N}$ versus the radial distance $r$ from the center of a vortex at 8 T. Solid lines are the best exponential fits ( $σ_{0, N} \sim e^{- r / ξ}$ ), giving the superconducting coherence length of $ξ$ . (c) Azimuthal dependence of $ξ (θ)$ . The statistical errors of $ξ$ indicate the standard derivations of $ξ (θ)$ obtained for different vortices at a given magnetic field. (d) Tunneling spectra measured at $T = 4.6 K$ and $B = 2 T$ along a 20-nm trajectory across a vortex core in trilayer $K_{3} C_{60}$ . The red line indicates a pseudogap at the vortex center.
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Figure 3
(a),(b) STM topographies of monolayer and bilayer $K_{3} C_{60}$ ( $V = 1.0 V$ , $I = 10 pA$ ). (c) Layer-dependent tunneling $d I / d V$ spectra over a wide energy range of $\pm 1.0 eV$ . Set point: $V = 1.0 V$ and $I = 100 pA$ . (d) Schematic energy bands (top panel) with only the UHB (unfilled) and LHB (green) shown, measured Hubbard $U$ , $W$ (middle panel) and $U / W$ (lower panel) of $K_{3} C_{60}$ as a function of layer index. The statistical errors indicate the standard derivations of $U$ and $W$ measured in various regions. (e),(f) Temperature-dependent tunneling spectra of 9 ML $K_{3} C_{60}$ , revealing a mild pseudogap (red curve) above $T_{c} = 18.4 K$ . (g) Conductance spectra measured at $T = 4.6 K$ and $B = 2 T$ along a 20-nm trajectory across a vortex core in 9 ML $K_{3} C_{60}$ . Red line marks the $d I / d V$ curve at vortex center. (h) Pseudogaps at 4.6 K (measured within vortices) and 22 K.
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Figure 4
Electronic phase diagram showing the evolution of $T_{c}$ (squares), $Δ$ (solid circles), and reduced gap $2 Δ / k_{B} T_{c}$ (stars, lower panel) at 4.6 K, as a function of K doping $x$ . Colored symbols distinctively mark the $K_{x} C_{60}$ films at varied layer (2, black; 3, red; 9 ML, blue). Gradient shading from green (cyan) to white schematically draws the superconducting dome of 3 ML (9 ML) $K_{x} C_{60}$ with a peaked $T_{c}$ and $Δ$ at $x = 3$ . Dashed lines correspond to the experimental tracks for $Δ$ and $2 Δ / k_{B} T_{c}$ . The $T_{c}$ has an uncertainty of 1.0 K and the statistical errors of $x < 0.5$ are smaller than the symbol size.
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