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The one-atomic-layer films of Pb and In studied here were grown with atomic precision on bulk-terminated Si(111) substrate using molecular beam epitaxy. The one-atomic-layer films of Pb have two different structural phases depending on the coverage (for sample preparation, see the Methods section). Figure 1a,d shows the schematic structure and scanning tunnelling microscopy (STM) topograph of the so-called striped incommensurate (SIC) phase, which has a Pb coverage of 4/3 monolayers (ML; refs 11, 12, 13, 14). Here 1 ML is defined as the surface atomic density of the Si(111) with areal density n=7.84 atoms nm−2. In a unit cell of the SIC-Pb phase, there are four Pb atoms per three surface Si atoms. Three of the four Pb atoms each form a covalent bond with an underlying Si atom, leaving one Pb atom without bonding to the Si substrate. Besides the covalent bonds with the Si substrate, the metal atoms also form metallic bonds within the metal overlayer. As all Pb atoms are located exactly in the same atomic-layer sheet (see the large-scale STM image and cross-section height profiles in Supplementary Fig. S1), the resulting areal density of Pb atoms is 10.44 nm−2. Compared with the bulk Pb(111) plane, the lattice of the SIC phase is compressed by 5%.

Figure 1: One-atomic-layer superconducting metal films of Pb and In.
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a–f, Schematic structure models11,12,13,14,19,22 (a–c) and high-resolution STM images (d–f) of the SIC-Pb (a,d), (b,e) and (c,f) phases grown on Si(111) substrate. Imaging conditions are V=0.1 V and I=0.05 nA.

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Ultralow-temperature (down to 0.40 K) scanning tunnelling spectroscopy (STS) on the SIC phase reveals a clear signature of superconductivity. Figure 2a shows the tunnelling spectra taken on the SIC phase using a superconducting Nb tip. At 0.42 K, the differential conductance shows a zero conductance region near the Fermi level (EF) and two sharp peaks at bias voltages V ∼±1.8 meV. This is the classical hallmark of a superconductor–insulator–superconductor (SIS) tunnelling junction, which has a zero quasiparticle density of states (DOS) at EF and two Bardeen–Cooper–Schrieffer (BCS)-like DOS peaks at V =±(Δtip+ΔSIC)/e. Here Δtip and ΔSIC are the superconducting gaps of the Nb tip and the SIC phase, respectively; e is the electron charge. Starting from 1.05 K, two extra peaks at V =±(Δtip−ΔSIC)/e become evident. This is caused by thermally excited holes/electrons15. The observation also demonstrates the high energy resolution of our STS measurements16,17. With increasing temperature, the spectra are broadened and the coherence peaks are suppressed. The energy gap ΔSIC becomes nearly invisible at 1.82 K, suggesting that the superconducting transition occurs around this temperature. The superconducting characteristics are further demonstrated by using a non-superconducting PtIr tip (Supplementary Fig. S2). Using a superconducting gap Δtip=1.46 meV (TC=9 K) for the Nb tip, which was calibrated by a separate measurement on Ag islands (Supplementary Fig. S3), we obtain the temperature evolution of ΔSIC, as shown in Fig. 2b. Fitting the data using the BCS gap function18 yields ΔSIC(0)=0.35 meV, TC=1.83 K and the BCS ratio 2ΔSIC/kBTC=4.4 (kB is the Boltzmann constant). The BCS ratio is very close to the value of 4.3 in bulk Pb, suggesting that the SIC phase is a strongly coupled BCS superconductor.

Figure 2: Superconductivity in one-atomic-layer metal films.
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a, The differential conductance of single-particle tunnelling measured with a Nb tip on the SIC-Pb phase as a function of temperature. The tunnelling junction (also applies to c and e) was set at V=0.01 mV and I=0.2 nA. The curves at different temperatures are offset vertically for clarity. b, The superconducting gap of the SIC-Pb phase as a function of temperature. The open circles show the measured gap, and the solid curve shows the fitting by the BCS gap function (see the text). c–f, The tunnelling conductance (c,e) and superconducting gap (d,f) for the (c,d) and (e,f) phases.

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Another one-atomic-layer film of Pb has the same fundamental building block as SIC but a smaller coverage of 6/5 ML (refs 12, 13, 14, 19, 20, 21). Hereafter this is called the phase (Fig. 1b,e). In a unit cell of the phase, there are six Pb atoms per five surface Si atoms. Five of the six Pb atoms each form a covalent bond with an underlying Si atom, leaving one Pb atom without bonding to the Si substrate. The areal atom density is nearly the same as that of the bulk Pb(111) plane, with a slight lattice expansion of 0.1%. Figure 2c shows the tunnelling spectra of the SIS junction in the phase, which is qualitatively the same as that of the SIC phase, except for a reduction of the energy gap. The superconducting gap Δ, TC and the 2Δ/kBTC ratio deduced from the BCS fitting of the experiment are 0.27 meV, 1.52 K and 4.12, respectively (Fig. 2d).

Indium atoms grow on Si(111) with the same structure as that of Pb (refs 22, 23) (Fig. 1c,f). The In coverage is 6/5 ML, and the areal atom density is 9.40 nm−2. Thus, its lattice is 0.3% expanded compared with that of the bulk In(001) plane. Figure 2e shows the tunnelling spectra of the phase. The values of Δ, TC and 2Δ/kBTC extracted from the BCS fit (Supplementary Fig. S4) are 0.57 meV, 3.18 K and 4.16, respectively (Fig. 2f). Unlike the Pb films, where TC is strongly suppressed compared with the bulk value, the phase has a surprisingly high TC close to the bulk value 3.4 K, as predicted previously23. More significantly, the enhanced 2Δ/kBTC ratio compared with the bulk (3.6) implies that it is transformed into a strongly coupled superconductor by reducing the dimension.

The occurrence of superconductivity in the one-atomic-layer films is further confirmed by the presence of superconducting vortices under magnetic field. The magnetic measurement on the SIC phase is shown in Fig. 3 and Supplementary Fig. S5. As seen in the zero bias conductance (ZBC) spectra mapping, the vortices start to form at a field of around 0.03 T (Fig. 3a), and increase in density with the field (Fig. 3b,c). The vortex image becomes severely blurred at B∼0.12 T (Fig. 3d), suggesting that the superconducting state is almost completely suppressed around this field. From a systematic field-dependence study of ZBC (ref. 24), an upper critical field HC2 of 1,450 G is obtained (Fig. 3e). In a type II superconductor, HC2(T) is determined by the coherence length ξGL through HC2(T)=Φ0/2πξGL2(T), where Φ0 is the magnetic flux quanta. The 1,450 G upper critical field renders a coherence length ξGL=49 nm, which tells us the size of the Cooper pair and vortex core in this phase.

Figure 3: Superconducting vortices in the SIC-Pb phase.
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a–d, The vortices at different magnetic fields (0.03–0.12 T) measured at 0.42 K using a PtIr tip. In each vortex image, the superconducting regions of low conductance are shown in maroon colour and the gapless normal state inside the vortex cores are yellow coloured. The tunnelling junction was set at V=0.01 mV and I=0.1 nA. The bias voltage was ramped to 0 V with feedback off at each pixel to record the ZBC. e, Normalized ZBC measured at locations between two vortices under different magnetic fields. The upper critical field of the SIC phase is estimated to be 1450 G.

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To understand the mechanism of the superconductivity in these one-atomic-layer superconductors, we have carried out high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements3,25. The electronic structure revealed by ARPES shows that despite the extreme 2D geometry and the coupling with the Si substrate, the one-atomic-layer films show well-developed 2D free-electron-like metallic bands21,23. Figure 4a shows an ARPES spectrum of the SIC phase along the direction at T=30 K. , , and , , denote the symmetry points of 1×1 and surface Brillouin zones (SBZs) of Si(111), respectively. Two parabolic bands (red solid lines in Fig. 4a) crossing EF are centred at 0.62 and 1.26 Å−1 (the points), which are attributed to the surface states of SIC because they are situated above the edge of Si bulk bands21. The ARPES data along the direction (not shown) reveal other parabolic surface bands with larger Fermi circles centred on and . Therefore, the surface states of SIC reflect the periodicity with a large electron pocket at and a small one at (Fig. 4b). The total sheet carrier density estimated by the sizes of the two kinds of electron pocket is about 9×1014 cm−2. The ARPES data for are shown in Fig. 4c,d, and agree with the previous study21. Despite a different Fermi-surface shape, its electronic structure (as well as that of the ; ref. 23) could also be understood on the basis of a 2D free-electron-like band.

Figure 4: The ARPES spectra of one-atomic-layer Pb films on Si.
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a, The energy band measured along the direction for the SIC phase on p-type Si at 30 K. The photon energy was 21.218 eV (He Iα). Free-electron-like bands (indicated by parabola) are observed around k∥=0.6 and 1.26 Å−1. The parabolic feature centred at the point near EF and dispersing to higher binding energy is the edge of the Si bulk valence band. b, The SBZ of the SIC-Pb phase. c, The energy band measured along the direction for the phase on p-type Si at 30 K. d, The SBZ of the phase.

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The Si substrates used for the growth of the one-atomic-layer films shown above are heavily doped with boron (hole concentration ∼8×1018 cm−3). To clarify the possible role of the dopants on superconductivity, we have studied the SIC-Pb phases prepared on both heavily p-type (4×1019 cm−3) and normally n-type (∼1016 cm−3) doped Si substrates. The SIS spectra of the two films are shown together in Supplementary Fig. S6. The nearly identical results exclude any significant role of the dopants in Si, and suggest that the electronic property of the metal overlayer is dominated only by the intra-overlay metallic and the Pb–Si interface covalent bondings. In this sense, the superconducting films seem to be electronically ‘isolated’ from the underlying Si lattice. Thus, only the metal overlayer and the metal–Si interface are responsible for the occurrence of superconductivity.

We now discuss the possible roles of the Si substrate. Through the formation of covalent bonds at the interface11,12,13,14,19,20,21,22,23, the Si substrate serves as a structural support stabilizing the crystal structure of the metal overlay. This is important because free-standing monolayer films of metals such as Pb or In are unstable, unlike graphene. To investigate whether Si takes part in the electron pairing, we have carried out a variable-temperature ARPES measurement where the dimensionless electron–phonon coupling parameter λ can be evaluated by the temperature-dependent photoemission spectra26. The result for the SIC phase is λ=1.07±0.13 (for details, see Supplementary Fig. S7), which is greatly enhanced compared with the λ<0.9 of the much thicker Pb films25,27, apparently owing to the presence of the metal–Si interface. The strongly enhanced λ (∼1) in the film23 is particularly significant, because now its surprisingly high TC∼3.18 K can be explained by the strong-coupling McMillan formula28. The similar λ values in the Pb and In films suggest that the phonon modes from interface bonding must contribute to electron–phonon coupling in a significant way27.

As for the intra-overlay metallic bonding, the development of nearly free-electron-like metallic bands seen in Fig. 4 implies that the supercurrent should be carried by the carriers in the metal overlay. The difference between SIC and further highlights the crucial role of the overlayer structure. The denser packing in the SIC phase leads to a stronger superconductivity, which remains an interesting subject to be further investigated.

These observations suggest a new route towards 2D superconductivity: the metal overlay serves as a charge reservoir and the electron–phonon interactions that glue the electrons to form pairs are provided both by the intralayer metallic and more importantly the interface bonds. The situation is rather different from that of the 2 ML Pb film superconductivity reported recently9, which is essentially a property of the film itself with the same mechanism of superconductivity as that of thicker films.

Methods

To investigate the electronic structure and superconductivity of the one-atomic-layer films, we have used two ultrahigh-vacuum systems, both equipped with molecular beam epitaxy for film growth. The first system features an in situ ultralow-temperature STM system (Unisoku and RHK) operated at a base temperature of 0.40 K and under a magnetic field up to 11 T (refs 16, 17). The energy resolution is better than 0.1 meV at 0.40 K when a Nb tip is used16. This proves critical because the superconducting gap of the samples is well below 1 meV. The second system features in situ low-temperature STM (Omicron) and high-energy-resolution (10 meV) ARPES with a Scienta R4000 analyser3,25. To prepare high-quality samples, we used pure Pb (99.9999%) and In (99.9999%), which were respectively evaporated from two Knudsen cells for molecular beam epitaxy (Omicron). The clean Si(111)-7×7 surface was used as substrate for preparing the one-atomic-layer films of Pb and In. The Si(111)-7×7 surface was prepared by cycles of annealing and flashing up to 1,480 K of the as-supplied Si wafer in the ultrahigh-vacuum chamber. The deposition rate of Pb or In and thus the metal coverage and film thickness was carefully calibrated by the Pb (In)-induced phase on the clean Si(111) surface, which is known to have a precise surface coverage of 1/3 ML. The Pb-SIC phase was prepared by depositing ∼1.5 ML Pb atoms on Si(111)-7×7 surface at room temperature and subsequently annealing at 550 K for 30 s. The deposition rate of Pb/In was 0.1 ML min−1. The phase was prepared by annealing the SIC phase at 550 K for two minutes to reduce the Pb coverage. The phase was prepared by depositing ∼1.5 ML In atoms on Si(111)-7×7 surface at room temperature and subsequently annealing at 700 K for 4 min. To ensure that the same phase is studied in two separate systems, in each experimental run the structure of the film was first checked by the atomically resolved STM images (Fig. 1d–f), followed by STS measurement of the characteristic electronic states near EF (Supplementary Fig. S1d,e).