Fig. 2: In-gap states of near-zero-energy pitched QD eigenmodes.
From: Proximity superconductivity in atom-by-atom crafted quantum dots
a, dI/dV spectra measured at two different positions (grey and blue crosses in Fig. 1e) in the QD shown in Fig. 1d–f. The values of the tip’s superconducting gap eV = ±Δt and the sum eV = ±(Δt + Δs) with the proximity-induced Ag bulk gap Δs are marked by dashed orange and purple lines, respectively. In-gap states appear at energies ±(Δt + ε±), marked by black arrows. b, Left, constant-height dI/dV maps measured at the energies of the in-gap state peaks in the same area as in Fig. 1e. Right, particle-in-a-box simulation evaluated at zero energy with dominant contribution of the eigenmode with [nx, ny] = [3, 1]. c, Evolution of averaged dI/dV spectra from dI/dV line profiles measured along the central vertical axis of different QDs (see dashed orange lines in Fig. 1c,d) as a function of Lx. The dashed white lines mark the evolution of the eigenmodes with ny = 1 and nx = {1, 2, 3, 4} obtained from fitting the dI/dV spectra at energies outside the gap (see Supplementary Note 2). The length of the QD presented in panels a and b is marked by the blue arrow on the left side. d, Linewidths Γ of different QD eigenmodes extracted from fitting data from different QDs to Lorentzian peaks at energies outside the gap (see Supplementary Note 2). These are compared with the minimal energies of the in-gap states found when Er ≈ 0 (error bars are standard deviations extracted from fitting the data; see Supplementary Note 2 for details). The dashed grey line is the expected theoretical relation for a spin-degenerate level coupled to a superconducting bath12 (based on equation (13) in Methods). Data on further QDs constructed and analysed as described in Supplementary Note 3 are included in panel d. a.u., arbitrary units.
