Visualization of defect-induced interband proximity effect at the nanoscale

The vast majority of superconductors have more than one Fermi surface, on which the electrons pair below the critical temperature $T_C$, yet their superconducting behavior can be well described by a single-band Bardeen-Cooper-Schrieffer theory. This is mostly due to interband scattering, especially in superconductors in the dirty limit, rigidly linking the pairing amplitude of the different bands. This effect has severely limited experimental studies of the complex physics of multiband superconductivity. In this study, we utilize the fact that elementary Pb - as a clean limit system - has two Fermi surfaces that are only weakly coupled by interband scattering, allowing the formation of two separate condensates. By studying crystallographic defects in the form of stacking fault tetrahedra with our millikelvin scanning tunneling microscope, we show how to locally tune interband coupling ranging from weak to strong coupling and modify the superconducting order parameters from two well separated gaps to one merged gap around defects. The experiments critically test the theory of multiband superconductors and give a route to access a wide range of predicted quantum effects in these systems.

💡 Research Summary

The paper presents a direct nanoscale visualization of how crystallographic defects can locally tune the interband proximity effect in a multiband superconductor. Lead (Pb) is chosen because it is a clean‑limit, two‑band superconductor: one compact Fermi surface gives a larger superconducting gap (Δ₂) and an open Fermi surface gives a smaller gap (Δ₁). In most superconductors, non‑magnetic impurity scattering couples the two bands strongly, merging the gaps into a single effective gap, which masks multiband physics. In ultra‑pure Pb, however, the intrinsic interband scattering is weak, allowing two distinct condensates to coexist.

The authors exploit stacking‑fault tetrahedra (SFTs), a common subsurface defect in fcc metals with low stacking‑fault energy. An SFT consists of a tetrahedral nanocrystal bounded by (111) stacking faults; its interior hosts quantum well states (QWS) that strongly modify the local density of states (LDOS) and scattering rates. By preparing a Pb(111) crystal, cleaning it, and rapidly cooling it, a population of buried SFTs (≈70 nm lateral size) is generated. Using a millikelvin scanning tunneling microscope (STM), the authors map topography, differential conductance (dI/dU) maps at the energies of the two gaps, and full spectra across the defects.

Three characteristic defect regions are identified: (i) small surface depressions (argon bubbles), (ii) a screw dislocation, and (iii) the buried SFT. The SFT exhibits a triangular region directly above the tetrahedron and a surrounding hexagonal region. dI/dU maps reveal that the coherence peak associated with Δ₂ is dominant in the hexagonal region, while the triangular region shows a strong variation: sometimes the Δ₂ peak is suppressed, sometimes both peaks merge into a single feature. Spectra taken at different positions across several SFTs (labelled #1‑#3) demonstrate a systematic evolution from weak interband coupling (two well‑separated peaks) to strong coupling (merged gap).

To interpret these observations, the authors employ the Sung‑Wong (S&W) model, which extends the Suhl‑Matthias‑Walker two‑band framework by including both interband (Γ_ij) and intraband (Γ_i) elastic scattering rates. The model yields self‑consistent, energy‑dependent gap functions Δ₁(ω) and Δ₂(ω). Using parameters extracted from defect‑free regions (Δ₀₁ = 1.252 meV, Δ₀₂ = 1.40 meV, T = 139 mK) and varying the density‑of‑states ratio η = N₂(E_F)/N₁(E_F) (0.2 and 1.5) together with Γ_21, the calculated density of states reproduces the experimental spectra. With Γ_21 = 0 the two gaps are independent; increasing Γ_21 gradually merges the peaks, and for sufficiently large Γ_21 the gaps become indistinguishable. The model also shows that a larger η enhances the intensity of the higher‑energy peak, consistent with the observed dominance of Δ₂ in the hexagonal region.

The authors further analyze quasiparticle interference (QPI) patterns observed in the normal‑state dI/dU maps. Fourier transforms reveal distinct scattering vectors q₁, q₂, q₃ whose magnitudes correspond to nesting vectors of the projected (111) surface Fermi sheets. First‑principles calculations of the surface‑projected density of states identify the open and compact Fermi surfaces and their flat regions. The measured q‑vectors match these nesting features: q₁ and q₂ correspond to intraband scattering on the open and compact sheets, respectively, while q₃ reflects interband scattering between the two sheets. Importantly, these QPI patterns persist when a magnetic field suppresses superconductivity, confirming that they arise from normal‑state quasiparticles rather than superconducting coherence.

Overall, the study demonstrates three key points: (1) clean Pb provides a rare platform where two superconducting condensates are weakly coupled; (2) a buried SFT can locally enhance interband scattering via its quantum‑well states, effectively tuning the system from a two‑gap to a single‑gap regime; (3) the S&W theoretical framework accurately captures the evolution of the tunneling spectra in the presence of spatially varying scattering rates. By establishing a method to control interband coupling at the nanoscale, the work opens pathways to experimentally access predicted multiband phenomena such as Leggett collective modes, fractional‑flux vortices, non‑Abrikosov vortex structures, and topological knot excitations. The combination of atomically resolved STM, quantitative modeling, and first‑principles band analysis sets a new benchmark for probing and engineering multiband superconductivity.