## Introduction

Topological superconductors (TSCs) are a peculiar class of superconductors where the nontrivial topology of bulk leads to the emergence of Majorana bound states (MBSs) within the bulk superconducting gap1,2,3,4,5. Since MBSs are potentially applicable to the fault-tolerant quantum computation, searching for a new type of TSCs is one of the central challenges in quantum science. A straightforward way to realize TSCs would be to synthesize an odd-parity p-wave superconductor; however, intrinsic p-wave pairing is rare in nature, as highlighted by a limited number of p-wave superconductor candidates hitherto reported (e.g., refs. 6,7). A different approach to realize TSCs is to utilize the superconducting proximity effect (SPE) in a heterostructure consisting of a conventional superconductor and a spin-orbit coupled material such as a topological insulator (TI), as initiated by the theoretical prediction of effectively p-wave superconductivity induced in helical Dirac fermions and Rashba states8,9. This approach has been widely applied to various superconducting hybrids10,11,12,13,14,15,16,17, whereas the existence of MBSs is still under intensive debates. A part of the difficulty in establishing the SPE-derived topological superconductivity may lie in the SPE process itself, since the searched MBSs are expected to be localized in the vortex core at the interface within the heterostructure, and hence are hard to be accessed by surface-sensitive spectroscopies such as scanning tunneling microscopy (STM). Therefore, it would be desirable to invent an alternative way to realize TSCs without using bulk p-wave superconductor or the SPE.

In this work, we present the possibility to realize TSCs by using the topological proximity effect (TPE)18; such a novel approach was discovered through our angle-resolved photoemission (ARPES) study of a heterostructure consisting of an epitaxial Pb thin film grown on a three-dimensional (3D) TI, TlBiSe2.

## Results

### Fabrication and characterization of Pb film on TlBiSe2

The studies of SPE for generating TSCs have often employed a heterostructure consisting of a TI thin film as a top layer and a Bardeen-Cooper-Schrieffer (BCS) superconductor as a substrate14,15,16,17. On the other hand, in our TPE approach, the stacking sequence is reversed, and a superconducting Pb thin film was grown on TlBiSe2 (Fig. 1a). We have deliberately chosen this combination, because (i) Pb films are known to maintain the superconductivity down to a few monolayers (MLs)19, and (ii) TlBiSe2 serves as a good substrate for epitaxial films18. Using the low-energy-electron-diffraction (LEED) (inset to Fig. 1d, f, h) and the ARPES results, we have estimated the in-plane lattice-constant a to be 3.5 and 4.2 Å for Pb (~20 ML) and TlBiSe2, respectively. While the a value of Pb film is close to that of bulk20, there is a sizable lattice mismatch of 19.5% between the Pb film and TlBiSe2.

First, we discuss the overall electronic structure. As shown in Fig. 1c, d, the electronic band structure of pristine TlBiSe2 is characterized by a Dirac-cone surface state (SS) around the $$\overline{\Gamma}$$ point that traverses the bulk valence and conduction bands21,22,23, forming a small Fermi surface (FS) centered at $$\overline{\Gamma}$$. Upon evaporation of Pb on TlBiSe2, the electronic structure drastically changes as seen in Fig. 1e, f; the holelike valence band of TlBiSe2 disappears, while several M-shaped bands emerge. The outermost holelike band crosses the Fermi level (EF) and forms a large triangular FS (Fig. 1e). The M-shaped bands are ascribed to the quantum well states (QWSs) due to the quantum confinement of electrons in the Pb thin film. This is supported by the experimental fact that similar M-shaped bands are also observed in a Pb(111) thin film grown on Si(111) (Fig. 1h).

The QWSs in Pb thin films with various thickness on Si(111) have been well studied by spectroscopies and calculations19,24,25,26,27,28. Since the in-plane lattice constant of Pb/TlBiSe2 is close to that of Pb/Si(111), we expect a similar electronic structure between the two. By referring to the previous studies and our band-structure calculations, we estimated the film thickness to be 17 ML for the case in Fig. 1e, f; see Supplementary Fig. 1 and Supplementary Note 1. We observed no obvious admixture from other MLs (e.g., 16 and 18 MLs) that would create additional QWSs24,26, suggesting an atomically flat nature of our Pb film. The LEED pattern of 17ML-Pb/TlBiSe2 as sharp as that of pristine TlBiSe2 (inset to Fig. 1f, d, respectively) also suggests the high crystallinity of Pb film. A careful look at Fig. 1f reveals an additional intensity spot near EF above the topmost M-shaped band. This band is not attributed to the QWSs, and is responsible for our important finding, as described below.

### Topological proximity effect

Next we clarify how the band structure of TlBiSe2 is influenced by interfacing with a Pb film. One may expect that there is no chance to observe the band structure associated with TlBiSe2 because the Pb film (17 ML ~ 5 nm) is much thicker than the photoelectron escape depth (~0.5–1 nm). Figure 2a shows the ARPES-derived band structure near EF obtained with a higher resolution for 17ML-Pb/TlBiSe2, where we clearly resolve an X-shaped band above the topmost QWSs. This band resembles the Dirac-cone SS in pristine TlBiSe2 (Fig. 2c), and is totally absent in 17ML-Pb/Si(111) (Fig. 2b), thereby ruling out the possibility of its Pb origin. The appearance of a Dirac-cone-like band in 17ML-Pb/TlBiSe2 is surprising, because the Pb film thickness is about ten times larger than the photoelectron escape depth. This in return definitely rules out the possibility that the observed Dirac-cone-like band is the Dirac-cone state embedded at the Pb/TlBiSe2 interface. Furthermore, this band is not likely to originate from the accidentally exposed SS of TlBiSe2 through holes in Pb, since the observed bands do not involve a replica of pristine TlBiSe2 bands and no trace of the Tl core-level peaks was found in Pb/TlBiSe2; see Supplementary Fig. 2 and Supplementary Note 2. In fact, the bulk valence band lying below 0.4 eV observed in pristine TlBiSe2 (Fig. 2c) totally disappears in Pb/TlBiSe2, and in addition, the Dirac point of Pb/TlBiSe2 is shifted upward with respect to that of pristine TlBiSe2, as clearly seen in Fig. 2d–f. These observations led us to conclude that the Dirac-cone band has migrated from TlBiSe2 to the surface of Pb film via the TPE when interfacing Pb with TlBiSe218. Such a migration can be intuitively understood in terms of the adiabatic bulk-band-gap reversal29,30 in the real space where the band gap (inverted gap) in TlBiSe2 closes throughout the gapless metallic overlayer and starts to open again at the Pb-vacuum interface. It is noted that the upper branch of the Dirac-cone-like band would be connected to the quantized conduction band of the Pb film above EF because it only crosses EF once between Γ and M.

The band picture based on the TPE well explains the observed spectral feature in Pb/TlBiSe2. As shown in Fig. 2g–i, the spin-degenerate topmost QWS of Pb (Fig. 2g) and the spin-polarized Dirac-cone SS of TlBiSe2 (Fig. 2h) start to interact each other when interfacing Pb and TlBiSe2. Due to the spin-selective band hybridization18, the Dirac-cone band is pushed upward, while the QWS is pulled down (Fig. 2i). This is exactly what we see in Fig. 2a. Our systematic thickness-dependent ARPES measurements revealed a detailed hybridization behavior between the Dirac-cone band and the QWSs, supporting this scenario; see Supplementary Fig. 3 and Supplementary Note 3. Noticeably, the migration of Dirac-cone state is observed at least up to 22 ML thick (~6.5 nm thick) Pb film. Such a long travel of the Dirac cone in the real space is unexpected, and hard to be reproduced by the band calculations due to large incommensurate lattice mismatch between Pb and TlBiSe2. In fact, we have tried to calculate the band dispersion of Pb/TlBiSe2 slab by expanding the in-plane lattice constant of Pb film to hypothetically form a commensurate system, but it caused a sizable change in the whole band structure of Pb film, resulting in the band structure totally different from the experiment. Alternatively, a calculation that uses a larger in-plane unit cell might be useful to achieve an approximate lattice match between Pb and TlBiSe2. It is noted here that the coherency of electronic states may play an important role for the observation of a coupling with the substrate (i.e., the TPE in this study) as in the case of other quantum composite systems involving metallic overlayer31. We estimate the electronic coherence length in Pb film to be larger than 22 ML (~6.5 nm) because the topological SS is observed even in the 22 ML film; see Supplementary Fig. 3 and Supplementary Note 3.

### Superconducting gap

The next important issue is whether the Pb/TlBiSe2 heterostructure hosts superconductivity. To elucidate it, we first fabricated a thicker (22 ML) Pb film on TlBiSe2 and carried out ultrahigh-resolution ARPES measurements at low temperatures. Figure 3b shows the energy distribution curve (EDC) at the kF point of the Pb-derived triangular FS (point A in Fig. 3a) measured at T = 4 and 10 K across the superconducting transition temperature Tc of bulk Pb (7.2 K). At T = 4 K, one can clearly recognize a leading-edge shift toward higher EB together with a pile up in the spectral weight, a typical signature of the superconducting-gap opening. This coherence peak vanishes at T = 10 K due to the gap closure, as better visualized in the symmetrized EDC (Fig. 3c). We have estimated the superconducting-gap size at T = 4 K to be 1.3 meV from the numerical fittings. This value is close to that of bulk Pb (~1.2 meV)32, suggesting that the Tc is comparable to that of bulk Pb.

Since the superconductivity shows up on the Pb film, we now address an essential question whether the migrating Dirac-cone band hosts superconductivity. We show in Fig. 3d–i the EDCs and corresponding symmetrized EDCs at T = 4 and 10 K for the 17 ML sample measured at three representative kF points (points A–C in Fig. 3a). At point A on the Pb-derived FS, we observe the superconducting-gap opening (Fig. 3d), similarly to the 22 ML film. At point B (C), where the migrating Dirac-cone band crosses EF along the $$\overline{\Gamma {\rm{K}}}$$ ($$\overline{\Gamma {\rm{M}}}$$) line, we still observe a gap as seen in Fig. 3f (Fig. 3h). This indicates that an isotropic superconducting gap opens on the migrating Dirac-cone FS. We observed that this gap persists at least down to 12 ML, confirming that the superconducting gap is not an artifact that accidentally appears at some specific film thickness; see Supplementary Fig. 4 and Supplementary Note 4. We have also confirmed that the gap opening is not an inherent nature of the original topological SS in pristine TlBiSe2, by observing no leading-edge shift or spectral-weight suppression at EF at 4 K in pristine TlBiSe2 (Fig. 3j, k).

## Discussion

The present results show that the superconducting gap opens on the entire FS originating from both the Pb-derived QWSs and the migrating Dirac-cone band (Fig. 3l). The emergence of an isotropic superconducting gap on the Dirac-cone FS suggests that the 2D topological superconductivity is likely to be realized, since this heterostructure satisfies the theoretically proposed condition for the effectively p-wave superconducting helical-fermion state8. In this regard, one may think that such realization is a natural consequence of making heterojunction between superconductor and TI. However, the present study proposes an essentially new strategy to realize the 2D topological superconductivity. In the ordinary approach based on the SPE (Fig. 3m), the topological Dirac-cone state hosts the effective p-wave pairing at the interface due to the penetration of Cooper pairs from the superconductor to the TI. On the other hand, the present approach does not rely on this phenomenon at all, because the topological Dirac-cone state appears on the top surface of a superconductor (Fig. 3n) via the TPE.

One can view this effect as a conversion of a conventional superconductor (Pb film without topological SS) to a TSC (Pb film with topological SS) by interfacing. The present approach to realize 2D TSCs has an advantage in the sense that the pairing in the helical-fermion state (and the MBS as well) is directly accessed by surface spectroscopies such as STM and ARPES. The superconducting helical fermions would be otherwise embedded deep at the interface and are hard to be accessed if the TPE does not occur. Moreover, the observed gap magnitude on the topological SS is comparable to that of the original Pb, unlike the SPE-induced gap that is usually smaller. This result tells us that the so-far overlooked TPE had better be seriously taken into account in many superconductor-TI hybrids. Also, the present study points to the possibility of realizing even wider varieties of 2D TSCs by using the TPE. It is noted that the topological states in Pb/TlBiSe2 are electrically shorted out by the metallic QWSs, unlike the case of some TI films on top of superconductors. This needs to be considered in the application because single conducting channel from the Dirac-cone states would be more preferable. In this regard, the present approach utilizing the TPE and the existing approach using the SPE would be complementary to each other.

## Methods

### Sample preparation

High-quality single crystals of TlBiSe2 were grown by a modified Bridgman method21. To prepare a Pb film, we first cleaved a TlBiSe2 crystal under ultrahigh vacuum with scotch tape to obtain a shiny mirror-like surface, and then deposited Pb atoms (purity; 5 N) on the TlBiSe2 substrate using the molecular-beam epitaxy technique while keeping the substrate temperature at T = 85 K. A Pb(111) film on Si(111), used as a reference, was fabricated by keeping the same substrate temperature. The film thickness was controlled by the deposition time at a constant deposition rate. The actual thickness was estimated by a comparison of ARPES-derived band dispersions with the band-structure calculations for free-standing multilayer Pb.

### ARPES measurements

ARPES measurements were performed with the MBS-A1 electron analyzer equipped with a high-intensity He discharge lamp. After the growth of Pb thin film by evaporation, it was immediately transferred to the sample cryostat kept at T = 30 K in the ARPES chamber, to avoid the clusterization of Pb that is accelerated at room temperature (note that such clusterization hinders the detailed investigation of the surface morphology by atomic-force microscopy). We used the He-Iα resonance line ( = 21.218 eV) to excite photoelectrons. The energy resolution of ARPES measurements was set to be 2–40 meV. The sample temperature was kept at T = 30 K during the ARPES-intensity-mapping measurements, while T = 4 and 10 K for the superconducting-gap measurements. The Fermi level (EF) of the samples was referenced to that of a gold film evaporated onto the sample holder.

### Band calculations

First-principles band-structure calculations were carried out by a projector augmented wave method implemented in Vienna Ab initio Simulation Package code33 with generalized gradient approximation potential34. After the crystal structure was fully optimized, the spin-orbit coupling was included self-consistently.