Proximity superconductivity in atom-by-atom crafted quantum dots

Abstract

Gapless materials in electronic contact with superconductors acquire proximity-induced superconductivity in a region near the interface1,2. Numerous proposals build on this addition of electron pairing to originally non-superconducting systems and predict intriguing phases of matter, including topological3–7, odd-frequency8, nodal-point9 or Fulde–Ferrell–Larkin–Ovchinnikov10 superconductivity. Here we investigate the most miniature example of the proximity effect on only a single spin-degenerate quantum level of a surface state confined in a quantum corral11 on a superconducting substrate, built atom by atom by a scanning tunnelling microscope. Whenever an eigenmode of the corral is pitched close to the Fermi energy by adjusting the size of the corral, a pair of particle–hole symmetric states enters the gap of the superconductor. We identify these as spin-degenerate Andreev bound states theoretically predicted 50 years ago by Machida and Shibata12, which had—so far—eluded detection by tunnel spectroscopy but were recently shown to be relevant for transmon qubit devices13,14. We further find that the observed anticrossings of the in-gap states are a measure of proximity-induced pairing in the eigenmodes of the quantum corral. Our results have direct consequences on the interpretation of impurity-induced in-gap states in superconductors, corroborate concepts to induce superconductivity into surface states and further pave the way towards superconducting artificial lattices.

Analogous electronic states in graphene and planer metallic quantum dots

“…At the end we state that, while the electronic states near the Fermi energy, such as those facilitated by intravalley scattering, can find potential applications in transport and optical devices 3 , 5 , 6 , 68 – 70 , the high energy confined states in atomic GQD are not appealing in this context, but could impact selective chemical bonding and mediate catalytic processes through their hybridization with other high energy electronic bands. Furthermore, the energy of these states can be brought closer to the Fermi energy in artificial molecular GQDs such as those produced by STM tip-manipulation of on-surface adatoms 18 – 20 , and can thereby be utilized to modulate electronic properties of materials or induce some functionality via proximity effect 71 .…”

Spatially Dependent in-Gap States Induced by Andreev Tunneling through a Single Electronic State

“…This is due to the negligible scattering into the gapped bulk states; the lifetime of the impurity state located within the superconducting gap is greatly enhanced. 29,30 For different rings shown in the dI/dV maps in Figure 2b,c, their relative energy positions between the impurity state and the Fermi level could be different. Figures 2h and 2i are the dI/ dV linecut profiles across another ring shown in Figure 2c with 0 and 1.5 T magnetic fields, respectively.…”

The Imaginary Universe

“…We note that the discretization of charges by integer multipliers q of the elementary charge e seems too far-reaching, considering the fractional charges of quasiparticles, in particular in the open research problem of the fractional quantum Hall effect (cf. Appendix I), and energy-dependent fractional charges in electron pairing [38].…”

“…And this configuration is capable of storing both the curvature and the charge. The Planck area ℓ 2 P (38) and the R × I imaginary Planck area ℓ P ℓ Pi = ℓ 2 P α 3 2 /α 3 ≈ ±0.9666iℓ 2 P , which is smaller in modulus, can be considered in a polyspherical coordinate system, in which gravitation/acceleration acts in a radial direction (with the entropic gravitation acting inwardly and acceleration acting in both radial directions) [5], while electrostatics act in a tangential direction.…”