From a wide band gap to the superconducting proximity effect: Fe on Pb(111)

Epitaxially grown Fe nanostructures on Pb(111) were studied by low-temperature scanning tunneling microscopy and spectroscopy. The deposited Fe assemblies are classified into two groups according to their electronic behavior close to the Fermi energy. One group exhibits a wide energy gap of 0.7 eV that is independent of the temperature ranging from 5 K to room temperature. These Fe islands indicate the absence of the superconductivity proximity effect in their interior. The other group shows a metallic behavior at the Fermi level. The substrate superconducting phase locally enters into these islands, which is evidenced by a sharp resonance at the Fermi energy presumably signaling Andreev reflection at the magnet–superconductor interface.


Introduction
The magnet-superconductor interface is of fundamental and device-oriented interest. Fundamentally, this interface enables studies of proximity effects, i.e. of spatial changes in magnetic and superconducting correlations in both materials [1]. Applications of this interface may be found in quantum computers and magnetic information storage [2][3][4].
The prime motivation for the studies presented here is a previous proposal to achieve chiral superconductivity in two dimensions [17]. Monatomically high ferromagnetic Fe islands on Pb(111) were suggested promising in that respect because of the reported one-dimensional (1D) topological superconductivity of ferromagnetically ordered Fe atom chains on Pb(110) [10]. It was demonstrated that the Yu-Shiba-Rusinov (YSR) states [21][22][23] that are induced in the Bardeen-Cooper-Schrieffer (BCS) energy gap of Pb(110) by the individual Fe atoms of the chain hybridize and form the band structure of a 1D p-wave superconductor with Majorana bound end states [8,24]. Similarly, for the proposed 2D Fe islands on Pb(111) [17], p-wave superconductivity should be signaled by chiral Majorana bound states at the island edges [17]. In the simulated adsorption geometry, Fe atoms occupy face-centered cubic (fcc) and hexagonal close-packed (hcp) stacking sites of the Pb(111) lattice giving rise to a honeycomb arrangement of the adsorbed atoms [17].
Here, in a surface science approach, Fe has been deposited on Pb(111) with submonolayer coverage. Deviating from the previous proposal [17] our experimental observations indicate that the resulting Fe islands are at least two atomic layers high. In scanning tunneling microscope (STM) images, the Fe islands exhibit a complex surface structure, which most likely results from the relief of mechanical strain. Two classes of islands can be identified. The first class of islands exhibits a 0.7 eV-wide electronic energy gap around the Fermi energy (E F ), which is essentially independent of the temperature of the experiments (5 K, 78 K, 293 K). Moreover, Fe islands of this class effectively suppress the superconducting proximity effect, as evidenced by the absence of the Pb(111) BCS energy gap in spectroscopy of the differential conductance (dI/dV, I: current, V: bias voltage) recorded above the island interior. In contrast, Fe islands of the second class show ample density of states (DOS) at E F , with the presence of a residual superconducting phase of the substrate signaled by spectral structure close to E F and which we interpret as the signature of Andreev reflection at the Fe-Pb interface. The recently proposed adsorption geometry of Fe islands on Pb(111) [17] has not been realized in the experiments reported here, nor is the sought-after Majorana bound state found to occur at the edges of the islands.

Experiment
Our experiments were performed with an STM operated in ultrahigh vacuum (10 −9 Pa) and at various temperatures (5 K, 78 K, 293 K). Clean (111) surfaces of Pb were prepared by repeated Ar + ion bombardment and annealing. Iron was deposited on clean Pb(111) at room temperature using the electron beam heating of a purified (99.99%) Fe rod. The deposition was followed by an annealing at 500 K for 30 min to smooth the otherwise strongly corrugated surface. Tips were fabricated from chemically etched W wire and further prepared in situ by field emission on Au substrates, as well as by single-atom transfer in controlled tip-surface contacts [25][26][27][28]. Topographic data were acquired in the constant-current mode with the bias voltage applied to the sample. Spectroscopy of dI/dV was recorded by sinusoidally modulating the bias voltage (100 µV rms for spectroscopy of the superconducting energy gap, 5 mV rms for spectroscopy in a wide voltage range, 700 Hz) and measuring the first harmonic of the current response with a lock-in amplifier. STM images were processed with WSxM [29]. Figure 1(a) shows a representative overview STM image of Fe-covered Pb(111) in the submonolayer range. Two types of islands, referred to as α and β in the following, can be distinguished owing to their clearly different topographic appearance. Before suggesting Fe atom assemblies that may underlie the observed topographic data, it is worth mentioning that depressions are sometimes observed close to both types of islands (arrow in figure 1(a)). These depressions are reminiscent of surface structures previously reported for Cr on Au(100) [30], Co on Cu(111) [31,32] and Au(100) [33], Fe on Cu(100) [34] and Cu(111) [35] and associated with intermixing processes and the incorporation of the adsorbate into the substrate surface due to appreciably different surface energies. The surface energies of Fe (2.50 J m −2 [36]) and Pb (0.54 J m −2 [37]) differ significantly, too, which lends support to atom exchange mechanisms and the encapsulation of Fe into the Pb surface layers being at the origin of the depressions. As a consequence, it is difficult to identify the absolute number of atomic Fe layers by STM data alone.

Structural properties
Island type α is characterized by straight edges oriented parallel to crystallographic directions of the Pb(111) substrate surface. In addition, their interior exhibits a low corrugation, the apparent height varying on the order of 10 pm at 1 V. Images of α-island surfaces depend strongly on the bias voltage (appendix A). For all explored voltages, a stripe pattern ( figure 1(b)) is observed. While the orientation of the stripes is uniform within a given island, it varies from island to island, mostly being in a direction nearly parallel to a Pb(111) crystallographic direction or subtending an angle of approximately 30 • (appendix A). At voltages |V| < 0.4 V, atomic structure with approximate hexagonal symmetry can be resolved. A Fourier transform of the STM image (right inset to figure 1(b)) exhibits a non-uniform hexagonal array of spots, typical of that given by a bcc(110) lattice (left inset to figure 1(b)). Using a variety of Fourier transforms, lattice constant |a 1 | results as 0.27 ± 0.02 nm. Comparing with the corresponding distance in a standard Fe bcc(110) lattice, 0.248 nm [38], the Fe atom lattice at the α-island surfaces is seen to be strained. The Fourier transform also yields the periodicity and orientation of the stripe motif, which, for this specific island, are respectively ≈ 1.3 nm and at 30 • relative to the shorter bcc(110) conventional lattice vector (a 1 in the left inset to figure 1(b)). The origin of the stripe pattern is unveiled by analyzing cross-sectional profiles (appendix A) perpendicular to the stripe direction (arrow in figure 1(b)). The Fe-Fe separation along this direction is 0.26 ± 0.03 nm in the small diamond unit cell (denoted d 1 in figure 1(b)) and 0.37 ± 0.03 nm in the large diamond unit cell (d 2 ); that is, the stripe motif can be assigned to differently dense atom rows. The occurrence of such variations in the atom packing most likely reflects the tendency of the island to reduce the mechanical strain [39]. Indeed, α-islands are proposed here to comprise two atomic layers-a top bcc(110) layer and a bottom pseudomorphically grown fcc(111) layer to be discussed next.
The strong variation of α-island STM data with the voltage is atypical for a metal adsorbate on a metal substrate. Moreover, the electronic structure of α-islands to be presented in the following section reveals an appreciable energy gap around E F . Therefore, a stacking of at least two Fe atomic layers is suggested for α-islands. Cross-sectional profiles of α-island edges (appendix A) are compatible with this suggestion. Because Fe is known to grow pseudomorphically on surfaces such as on Ni(111) [40][41][42][43], Cu(111) [44][45][46][47], Pt(111) [48,49] and Au(111) [50][51][52][53][54][55][56], with a concomitant fcc(111)-to-bcc(110) transition with Fe film thickness observed to occur at two to three atomic layers [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], it is likely that the bottom layer of the presumed bilayer α-islands here adopts an fcc(111) arrangement with dimension close to that of Pb(111). The resulting nearest-neighbor distance in the bottom Fe layer would significantly be increased relative to that of a conventional Fe fcc(111) lattice. Direct evidence for the presence of a strained fcc(111) layer is a hexagonal moiré lattice that was occasionally (≈ 5% of the α-islands) observed in addition to the stripe motif ( figure 1(d)). This pattern is consistent with a coincidence lattice formed at the interface between the bottom Fe and the Pb surface layer, where the Fe-Fe nearest-neighbor spacing is assumed to be 0.315 nm in order to reproduce the observed moiré periodicity of 3.1 nm (figure 1(e)). The bottom Fe layer is thus strained by a factor slightly larger than 1.2 with respect to the genuine fcc(111) nearest-neighbor distance (0.254 nm [57]). The strained Fe layer may provide a rationale for the peculiar electronic structure of the α-islands to be discussed below.
Islands β have jagged boundaries and the tendency to three-dimensional growth. Within a single atomic layer the corrugation at 1 V is nearly ten times larger than in α-islands. The surfaces of β-islands show a mixture of a honeycomb and square network of protruding lines (figure 1(c)) that most likely reflect dislocation lines. A rationale for the observed surface structure of β-islands is difficult based on the STM data alone, and so we base this interpretation on previous reports of similar patterns. The epitaxial growth of Fe on Mo(110) [58] gives rise to hexagonal and square meshes of dislocation lines at the surface of Fe islands of height at least three atomic layers. The patterns seen in STM images in that system are akin in structure and dimensions to the superstructures we observe. Owing to this comparison, the β-islands of Fe on Pb(111) reported here are assumed to be at least three atomic layers high and to exhibit dislocation networks at their surfaces, which continue the reduction of mechanical strain observed in bilayer α-islands. The suggested β-island thickness is in agreement with cross-sectional profiles of island edges (appendix A).

Electronic properties at the Fermi energy
Tunneling spectroscopy measurements show that α and β Fe islands on Pb(111) differ in their electronic structure both in a wide and in a narrow energy range around E F . In the following, these ranges are discussed separately. Figure 2 compares I-V characteristics and dI/dV spectra of α and β islands in the bias voltage range −1 V ⩽ V ⩽ 1 V. Intriguingly, at 5 K spectra recorded from α-islands reveal a gap in the range of bias voltages −0.38 V ≲ V ≲ 0.35 V where I and dI/dV drop to zero (figures 2(a) and (b)). This gap persists at 78 K, and even at room temperature (appendix B). In contrast, β-islands exhibit an evolution of I and dI/dV that is typical of STM junctions comprising a metal tip and substrate (figures 2(c) and (d)) and which is independent of the dislocation network (appendix B).

Wide energy range
The depletion of the local DOS in a similarly wide energy range around E F as observed for α-islands is known from sulfide or oxide Fe compounds [59][60][61]. However, we exclude the possibility of contamination leading to the formation of such compounds, as additional Fe deposition experiments performed in our set-up but on Cu(111) reproduced previously reported clean Fe adsorbate structures [46]. In addition, the metals Fe and Pb are immiscible [62], which excludes the presence of a PbFe compound. Calculations of hypothetical Pb n Fe m band structures (appendix B) indeed reveal densely dispersing states close to E F throughout the Brillouin zone (BZ), in clear contradiction to the observed energy gap. Therefore, it is reasonable to assume that α and β islands represent pure Fe phases without intermixing of substrate material. The origin of the observed electronic gap may then arise due to a deviation of the α-island lattice constant from the genuine nearest-neighbor distance in the Fe bulk. As suggested above, the bottom Fe atomic layer pseudomorphically grows on Pb(111) with an appreciably strained lattice. In an electron-hopping picture, too large an interatomic separation prevents orbitals from overlapping and forming bands, which in turn results in an electronic gap. Preliminary density functional calculations (appendix B) show an energy gap in an extended wave vector range around the surface BZ center when the Fe-Fe nearest-neighbor distance is increased with respect to the equilibrium separation in an fcc(111) lattice.
In order to further characterize the electronic gap its spatial evolution across an α-island step edge was explored. In the interior of the island (positions marked 1-4 in figure 3(a)) spectra of dI/dV (figure 3(b)) exhibit the fully developed gap with dI/dV = 0 around V = 0. For the step edge region of the island (positions 5 and 6) a depletion of dI/dV is visible (spectra 5 and 6 in figure 3(b)), albeit with a finite nonzero dI/dV signal. The interior of the island is characterized by the clearly visible stripe phase, while the step edge region does not continue this pattern. Possibly, the stacking in the edge region of the islands is different from the interior, with the bottom Fe atomic layer exhibiting a smaller lattice constant. Such stacking differences between the interior and boundary regions were previously reported for Fe islands on Cu(111) [46]. Therefore, spatially resolved dI/dV spectroscopy supports the idea that the gapped electronic structure is related to the specific Fe atom arrangement in the island, in particular to the strained Fe assembly in the bottom fcc(111) atomic layer. Before discussing the narrow energy range in spectroscopy, it is noteworthy that due to pseudomorphic growth β-islands most likely exhibit a strongly strained bottom Fe layer as well. In the top (third) atomic layer, however, the strain is probably relieved to an extent that allows Fe atoms to adopt mutual distances that are close to their genuine bcc(110) separations. Concomitantly, the electronic structure around E F resembles the one of a metal. Therefore, we think that the top island layer has a marked influence on the electronic behavior of both island classes.

Narrow energy range
The impact of the Fe islands on the Pb(111) BCS energy gap has been studied through spectroscopy spanning a narrow range of energies around E F , with measurements at locations moving from the clean Pb surface toward the interior of α and β Fe islands used to investigate the spatial evolution of the BCS energy gap. Figure 4(a) shows the STM image of an α-island with a marked (1-8) path of spectroscopy locations. Up to the island edge (spectra 1-4 in figure 4(b)) the BCS energy gap remains virtually invariant compared to the gap observed from Pb(111), which can be seen by the distance evolution of the gap depth a (figure 4(c)) defined as the difference between the mean average of the condensation peaks and the minimum gap value at zero bias. Atop the edge (spectrum 5 in figure 4(b), d = 0 in figure 4(c)) the BCS gap is strongly attenuated. Due to the depletion of the local DOS starting in the step edge region ( figure 3(b)) the tip had to be vertically displaced by 0.5 nm toward the surface at this point to continue to detect the spectral signature of the BCS gap. Moving further in toward the interior of the island (spectra 5-7 in figure 4(b)) we find the BCS gap is progressively suppressed, and that beyond approximately 1 nm of the boundary (spectrum 8 in figure 4(b)), i.e. well in the island interior where the stripe pattern is present, it is completely quenched.
The suppression of the BCS energy gap is likely related to the entire depletion of the DOS in a wide energy range in the interior of α-islands (figure 2). The weak but finite local DOS close to E F in the island step edge region (figure 3) still enables the BCS energy gap to be present in dI/dV spectroscopy, albeit in a strongly attenuated manner compared to bare Pb(111). This rationale is compatible with findings reported for superconductor-semiconductor junctions. By measuring the critical temperature of superconducting films on semiconductors as a function of film thickness, the coherence length in the semiconductor was experimentally found to depend on the cubic root of its charge carrier concentration [63,64], in agreement with predictions [65]. As a result, the lower the DOS at E F the smaller is the coherence length in the semiconductor. The case of entire depletion of charge carriers at E F would then entail a vanishing coherence length and, thus, the absence of the superconducting proximity effect, as observed here where α-island exhibit an electronic gap around E F , similar to semiconductors.
An additional effect supporting the suppression of the superconducting phase in α-islands is their magnetic structure. It is reasonable to assume magnetic order in both classes of islands because Fe atom chains on Pb(110) [10, 12, 13] and two-dimensional Fe islands on Pb(111) [17] were shown to be ferromagnetically ordered. In addition, preliminary calculations of the Fe island electronic band structure (appendix B) show that magnetism is an essential ingredient for the structure and energetics. Consequently, the quenching of the BCS gap may additionally be compared with previous results obtained at the superconductor-ferromagnet interface [66]. The coherence length in ferromagnets, i.e. the penetration depth of Cooper pairs into the magnetic film, can be estimated as ξ fm = ℏv F /E ex (ℏ = h/(2π), h: Planck constant). With a typical value for the Fermi velocity v F = 10 6 m s −1 and for the exchange energy E ex = 1 eV, ξ fm is on the order of 1 nm, which represents the correct order of magnitude to explain the suppression of the BCS energy gap in the island interior as well as its lateral attenuation upon approaching the island from clean Pb(111). Figure 5 shows a representative example of the evolution of the Pb(111) BCS energy gap upon approaching and entering a β-island. Local dI/dV spectroscopy at positions marked 1-5 in figure 5(a) indicate that the BCS gap is weakly attenuated approaching the island from the clean Pb(111) surface. The gap depth a is attenuated by ≈ 25% at the island step edge (spectrum 4 in figure 5(b), d = 0 in figure 5(c)). The attenuation is less pronounced than for α-islands, where at the step edge a is already below 50% (figure 4(c)).
Surprisingly, at some positions in the interior of the island a sharp zero-bias resonance is observed in dI/dV spectra. Figure 6 shows two dI/dV spectra acquired atop positions 1 ′ and 2 ′ marked in figure 5(a).
These reveal a spectral signature close to 0 V with a width that matches the width of the Pb(111) BCS energy gap. To see the zero-bias resonance more clearly, we followed a previous approach [67] and subtracted spectral data of the BCS energy gap of clean Pb(111) from dI/dV data acquired atop Fe β-islands. The apparent height of the island was taken into account in order to attenuate the Pb(111) BCS energy gap via the tunneling transmission factor prior to subtraction from the island data. Typical difference spectra, δ(dI/dV), are presented in figures 6(c) and (d). Statistics of dI/dV spectra showing a peak inside the BCS gap give rise to a scattering of the peak position of ≈ ±0.2 mV around zero bias. Because of the narrow zero-bias peak width, an Abrikosov-Suhl resonance due to the Kondo effect is excluded. Resonance widths related to the Kondo effect of atomic magnetic impurities often clearly exceed 10 meV [68,69]. Furthermore, Abrikosov-Suhl resonances of single magnetic atoms tend to give rise to asymmetric Fano line shapes [68,70,71] with a few exceptions [72][73][74][75]. Inelastic processes, such as vibrational or spin excitations, lead to a symmetric gap rather than a peak around 0 V in dI/dV spectra. Therefore, such excitations are likewise excluded as the origin of the zero-bias feature. In addition, YSR bands as predicted for Fe on Pb(111) [17] and previously reported from Mn islands on Nb(110) [76] are unlikely because bands of hybridized YSR states are expected to appear everywhere in the magnetic layer [76]. A possible rationale for the resonance is Andreev reflection at the Fe-Pb interface, which according to the Blonder-Tinkham-Klapwijk model [77] and approaches that take a spin polarization of the current into account [78][79][80] is expected to give rise to a peak replacing the BCS energy gap [81][82][83]. The probability of  Andreev reflection depends on the quality of the magnet-superconductor interface. Only in case of a highly transparent interface the conversion of an electron into a Cooper pair by retroreflection of a hole efficiently takes place and causes a peak in dI/dV at 0 V. As mentioned in the discussion of structural aspects of the Fe islands, atom exchange processes at the interface are likely to occur ( figure 1(a)). Therefore, the magnet-superconductor interface probably is not uniform, which may lead to local variations of the transparency and, thus, to the presence or absence of the zero-bias resonance. The suggested changes in the local transparency are reflected by the non-gradual spatial evolution of the zero-bias spectroscopic signature (appendix B). Since Andreev reflection is considered the microscopic origin of the superconducting proximity effect [84], the suggested explanation of the resonance would indicate the proximitized superconducting phase in β-islands.

Summary
Room temperature deposition of Fe on Pb(111) with subsequent annealing gives rise to islands with distinct geometric and electronic structure. The wide electronic gap of one class of island is traced to a bilayer stacking of a pseudomorphically grown and strained Fe fcc(111) film covered by a likewise strained Fe bcc(110) layer. Due to the gap-induced quenching of the DOS in the vicinity of E F , the superconducting proximity effect and, thus, the BCS energy gap of Pb(111) is absent in this class of Fe islands. The other class of islands continues to relieve the mechanical strain imposed by the pseudomorphic growth of the bottom layer, which is reflected by a network of dislocation lines atop the third atomic layer of these islands. The metallic behavior in spectroscopy of the electronic structure shows the presence of ample DOS at E F . Spectroscopic evidence for Andreev reflection at the Fe-Pb(111) interface signals a proximitized superconducting phase in this type of Fe islands.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors. Figure A1 shows the voltage dependence of STM images of α-island surfaces. Well outside the electronic gap, i.e. for bias voltages |V| ⩾ 0.8 V the stripe pattern is dominant. Reaching the voltage range of the gap (|V| ⩽ 0.6 V) additional atomic structure becomes visible. Contrast inversion can occur by switching the polarity of the bias voltage (±0.40 V, ±0.60 V, ±0.80 V in the top two rows of the gallery; for all voltages in the bottom two rows). Using voltages close to or even inside the electronic gap is accompanied by a reduction of the tip-surface distance in the constant-current STM images. Therefore, atomic resolution is expected. STM images at ±0.07 V are likely acquired in the contact mode, i.e. with collapsed tunneling barrier, due to the entirely quenched sample DOS at such electron energies. Different α-islands were observed to exhibit different stripe orientations as depicted in figure A2. Preference for an orientation of the stripes parallel to crystallographic directions of the Pb(111) surface or subtending an angle of 30 • can be concluded from an analysis of a multitude of STM images.
The different atom-atom distances in a direction perpendicular to the stripes at α-island surfaces can be extracted from cross-sectional profiles. Figure A3(a) reproduces the STM image of figure 1(b) with a solid line indicating the position of the cross-sectional profile shown in figure A3(b). For this particular cross-sectional profile the distances are δ 1 = 0.36 nm and δ 2 = 0.24 nm.
The suggested thickness of α-islands is corroborated by cross-sectional profiles of island edges. Figure A4(a) shows an STM image of a Fe cluster on Pb(111) containing an α-island in the lower left part of the image. For a bias voltage range 0.75 V ⩽ V ⩽ 1.1 V the apparent height does not vary strongly. A cross-sectional profile ( figure A4(b)) gives rise to an apparent height of 390 pm, which is compatible with two atomic layers. This apparent height is the average of the majority (95%) of the α-islands. A minority (5%) of α-islands exhibited an apparent height of 100 pm only, which is most likely due to the embedding of the Fe island in the Pb(111) surface.
The majority of β-islands has a thickness of three atomic layers. Owing to the three-dimensional growth of β-island all three layers can be inferred from a β-cluster ( figure A5(a)). The bottom layer exhibits an apparent height of 100 pm and is most likely embedded in the substrate surface. The successive second and third layer give rise to apparent heights of 195 pm and 190 pm, respectively. These heights are in good agreement with the expected distance of 203 pm between adjacent bulk Fe bcc(110) planes.      Figure B1 shows the I-V characteristics, which is similar to the observations at 5 K and 78 K. Kinks in the I(V) evolution are due to instabilities of the junction, which is typical of measurements at room temperature and likely induced by diffusing adsorbates.

B.2. Wide-range electronic structure of β-islands
Spectra of dI/dV acquired atop β-islands in a wide bias voltage range (|V| ⩽ 1.3 V) do not depend on the dislocation network. Figure B2 shows that spectroscopic data are virtually independent of the site on a given Fe layer (I, II, III in figure B2(a)) of a β-island. The broad resonances (asterisks in figure B2(b)) appear at nearly the same bias voltages in a given Fe layer and may be due to d-states of the Fe island. In different layers, however, the spectra exhibit some differences. In particular, in layer I only a single broad resonance occurs at positive voltage, which splits into two resonances as seen from dI/dV spectra of layer II and III.

B.3. Band structure calculations
The band structures have been calculated within density functional theory (DFT) using the plane wave density-functional code CASTEP [85], using 'on-the-fly' ultrasoft pseudopotentials, the Perdew-Burke-Ernzerhof energy functional [86], 450 eV cut-off for the plane wave basis, and self-consistency achieved using 12 × 12 × 12 k-point sampling for the cubic structures, and 15 × 15 × 1 k-point sampling for the Fe hexagonal monolayers (with 1.5 nm layer-layer spacing to minimize interactions between the periodic repetitions). Structural optimization of the bulk systems minimized forces to 0.2 eV nm −1 , and stresses to 0.04 GPa. Prior to the computation of the electronic band structure of Fe on Pb(111), lattice constants and band dispersions of bcc and fcc Fe as well as of bulk Pb were calculated and successfully compared with literature data.   Figure B3 shows the band structure of hypothetical PbFe (figures B3(a) and (b)) as well as of L1 2 structures of PbFe 3 (figure B3(c)) and Pb 3 Fe ( figure B3(d)). Due to the known immiscibility of Pb and Fe, ordered alloys of these components do not exist under normal conditions. The clearly visible dense electronic band dispersion close to E F in all considered cases excludes such compounds to be at the origin of the observed α-islands with a wide energy gap around E F .
Before presenting electronic-structure calculations for Fe atomic layers on Pb(111) it is important to note that the inclusion of magnetism gives rise to more stable structures. Ferromagnetic order of the Fe layer with an atomic magnetic moment of 2.62 µ B gives rise to a 0.64 eV more stable Fe lattice than without magnetic order and the same lattice constant (0.24 nm). Moreover, the optimized non-magnetic solution exhibits a lattice constant of 0.23 nm and is 0.5 eV less stable than the optimum magnetic state.
An electronic gap is tentatively indicated in the calculation for an fcc(111) lattice of Fe with increased lattice constant. To see this, the band structures of a single Fe layer with optimized ( figure B4(a)) and artificially increased ( figure B4(b)) lattice constant are compared. A gap has indeed opened for the atomic layer with increased atom-atom spacing in extended region around the Γ-point of the BZ. There are still electronic bands that cross the Fermi level along the Γ-M and Γ-K direction of the BZ. These band crossings at E F can be reduced and shifted to larger wave vectors by increasing the electron correlation. Indeed, in additional calculations, stronger electron correlations were accounted for by the Hubbard U in the DFT+U formalism. For U = 1 eV (figure B4(c)) the gap around Γ is already similar to the experimental observation, while for U = 2 eV (figure B4(d)) the gap is further increased and even larger than in the experiments. A band crossing at E F remains along the Γ-K direction; that is, the band gap does not span the entire BZ. The gap observed in the experiments can still be compatible with the calculations because of the exponential suppression in dI/dV spectroscopy of electron states with elevated wave vector. The exponential damping of the tunneling current is given by the factor exp(−2κz) (z: distance to the surface) with (m: free-electron mass, E: energy of the tunneling electron relative to E F , k ∥ : electron wave vector parallel to the surface, G ∥ : reciprocal surface lattice vector). Consequently, the experimental dI/dV spectra mainly reflect the electronic band structure close to the BZ center, i.e. for small k ∥ . For this k-space region the calculations predict a gap with comparable width (figure B4(c)).

B.4. Superconducting energy gap of pristine Pb(111)
The acquisition of the BCS energy gap of pristine Pb(111) is important for extracting estimates of the tip and sample temperature. In addition, the data are needed for the analysis of the zero bias resonance observed from β-islands. Figure B5 shows a representative spectrum of the BCS energy gap (dots) recorded on a wide and clean Pb(111) terrace with a normal-metal (W) tip.
To fit the experimental data, the BCS DOS (ϱ n (E F ): normal-state DOS at E F , E = eV: quasiparticle energy with e the elementary charge, ∆: order parameter of the sample) was convolved with functions accounting for the temperature broadening, (k B : Boltzmann constant) and the modulation broadening,   (V m : amplitude of the ac sinusoidal modulation voltage) [87].
The fit function [(ϱ * χ T ) * χ m ](V) ( * denotes the convolution) contains three fit parameters, i.e. ϱ n (E F ), ∆ and T. In the Tersoff-Hamann approximation [88,89] applied here the tip DOS is assumed to be constant over the relevant energy range. Moreover, the relevant temperature in χ T is the temperature of the tip. The sample temperature is contained in the temperature-dependent order parameter of the sample [90].
The spatial evolution of dI/dV spectra acquired atop β-islands can be seen from a representative data set (figure B6). A gradual evolution of the spectra is absent, which corroborates the absence of an identifiable correlation between the site of the spectrum and the occurrence of the zero-bias peak.