## Abstract

A single atomic slice of α-tin—stanene—has been predicted to host the quantum spin Hall effect at room temperature, offering an ideal platform to study low-dimensional and topological physics. Although recent research has focused on monolayer stanene, the quantum size effect in few-layer stanene could profoundly change material properties, but remains unexplored. By exploring the layer degree of freedom, we discover superconductivity in few-layer stanene down to a bilayer grown on PbTe, while bulk α-tin is not superconductive. Through substrate engineering, we further realize a transition from a single-band to a two-band superconductor with a doubling of the transition temperature. In situ angle-resolved photoemission spectroscopy (ARPES) together with first-principles calculations elucidate the corresponding band structure. The theory also indicates the existence of a topologically non-trivial band. Our experimental findings open up novel strategies for constructing two-dimensional topological superconductors.

## Main

Confining superconductivity to a two-dimensional (2D) plane engenders a variety of quantum phenomena^{1,2}. Of late, the realization of highly crystalline and atomically thin superconductors has triggered a flurry of discoveries, including the Griffiths singularity behavior^{3} and a quantum metallic phase^{4,5}, as well as an extremely large critical magnetic field in the plane^{6,7}. One strategy for achieving 2D superconductors is to epitaxially grow superconductive single elements, such as Pb, In and Ga, for just one or two atomic layers^{3,8,9}. Among the single elements, tin (Sn) is the very material in which the Meissner effect was first discovered^{10}, but realizing ultrathin Sn in the superconductive β-phase, known as white tin^{11}, remains challenging. The epitaxially grown Sn in the ultrathin limit tends to fall instead in the α-phase^{12}, whose bulk is semi-metallic and non-superconductive.

Recently, however, intensive research has been devoted to investigate the thinnest possible slice of α-tin(111)—a counterpart of graphene called stanene^{13}. Stanene promises various exotic features, such as highly efficient thermoelectrics^{14}, topological superconductivity^{15}, and high-temperature quantum spin Hall^{16} and quantum anomalous Hall effects^{17}. Monolayer stanene that has been successfully fabricated by molecular beam epitaxy on Bi_{2}Te_{3}(111) (ref. ^{18}) and PbTe(111) (ref. ^{19}) is the focus of current research. On the other hand, few-layer stanene is expected to show significant thickness-dependent properties due to the strong quantum confinement^{20}, but its exploration is still lacking.

In this Letter, by going from monolayer to few-layer stanene, surprisingly, we discover superconductivity. We report the stable superconducting properties of uncapped few-layer stanene films on PbTe (111)/Bi_{2}Te_{3} substrates. The superconducting transition temperature (*T*
_{c}) can be effectively enhanced by varying the thickness of the PbTe buffer layer. Concomitantly with a doubling of *T*
_{c}, we observe a single-band to two-band transition, which is further elucidated by photoemission spectroscopy and theoretical calculations. The calculated band structure further indicates the existence of inverted bands in our system. Our results therefore underscore the potential of an in-plane integration of 2Dtopological insulator and superconductor—of the same material. The heterostructure, vertically consisting of superconducting few-layer stanene and topological insulator Bi_{2}Te_{3}, may also be of interest for inducing topological superconductivity via the proximity effect^{21}.

Figure 1a schematically illustrates the sandwich structure of our system with a trilayer Sn on top of PbTe/Bi_{2}Te_{3}/Si(111). The α-phase of Sn is confirmed by in situ structural analysis (see Extended Data Figure 1). The dangling bonds on the top surface (Fig. 1a) are presumably saturated, which is evidenced by our ARPES data showing large band gaps at the K/K′ points^{18,19}. The saturation might be caused by hydrogen, a ubiquitous residue in the crystal growth environment^{22}, resulting in chemically stable samples. Figure 1b shows that superconductivity emerges starting from a bilayer. By increasing the number of Sn layers (*N*
_{Sn}), the transition temperature is consecutively promoted. In general, *T*
_{c} scales with 1/*N*
_{Sn} (Fig. 1d), as has been seen previously in other ultrathin films^{1,2}. We confirm the Meissner effect by a two-coil mutual inductance technique in Extended Data Figure 2. Extended Data Figure 3 further reveals the 2D nature of such a superconductor, evidenced by anisotropic critical magnetic fields and the Berezinskii–Kosterlitz–Thouless transition. As shown in Fig. 1c, superconductivity also depends keenly on the thickness of the PbTe layer (*N*
_{PbTe}). It emerges at *N*
_{PbTe} = 6, and *T*
_{c} further doubles when *N*
_{PbTe} exceeds 8. We speculate that this evolution stems from the change in density of states as well as the release of strain from the lattice mismatch (see Methods)^{19}. A thicker PbTe might host more surface vacancies due to the lowered formation energy^{23,24}, thus providing more electron doping into Sn, as we will reveal by ARPES later. Notably, the superconductivity in these uncapped samples barely changes after exposure to air, as exemplified by the data taken in the second cool-down after more than two weeks of storage (Fig. 1c). Extended Data Figure 2 further documents the superconductivity after one year of storage. In contrast, previous ex situ transport studies on ultrathin Pb, In, and Ga films all rely on capping with an additional layer of Au or Ag^{1,2,3}. We also show traces from two pairs of samples with the same nominal thicknesses, attesting to precise growth control. The transition temperature *T*
_{c} as a function of *N*
_{PbTe} is given in Fig. 1e. The shaded regions represent two regimes corresponding to samples with *T*
_{c} ~ 0.5 K and those with *T*
_{c} ~ 1.2 K.

Transport properties of trilayer stanene in regimes I and II are distinctly different. For 3-Sn/10-PbTe in regime II, the critical current displays two steps with increasing temperature, with a kink at about 0.5 K (Fig. 2a)—a characteristic feature of two-band superconductivity^{25}. This two-band nature is further confirmed by the temperature dependence of the upper critical field^{26,27}. The 3-Sn/10-PbTe sample displays a concave function of *μ*
_{0}
*H*
_{c}(*T*) (Fig. 2b), which can be fitted by a formula designated for the two-band situation^{26} (see Methods). In contrast to the behaviours of samples in regime II, we observe no deviation from a single-band superconductor for samples in regime I to the lowest attainable temperature. Furthermore, they show different activated behaviours in the presence of a magnetic field. For 3-Sn/8-PbTe, fittings to the activated region extrapolate to a fixed point: 1/*T*
_{c}. In contrast, 3-Sn/10-PbTe displays a continuous shift of the crossing between the adjacent extrapolated lines (dashed in Fig. 2d). The distinction is better captured by the extracted activation energy *U*
_{
H
} and the intercept of the fitting ln *R*
_{0}(*µ*
_{0}
*H*). In regime I, *U*
_{
H
} scales linearly with ln(*μ*
_{0}
*H*), which can be described by the collective creeping of vortices^{4}, and the slope yields a London penetration depth *Λ* of 700 nm (see Methods). The Ginzburg–Landau parameter *κ* = *Λ*/*ξ* is therefore about 23, which is much larger than $1\u2215\sqrt{2}$, as expected for a type II superconductor. In regime II, we obtain instead a convex dependence of both *U*
_{
H
} on ln(*μ*
_{0}
*H*) (Fig. 2e) and ln *R*
_{0} on *U*
_{
H
}/*k*
_{B}
*T*
_{c} (Fig. 2f). This nonlinearity may stem from field-dependent superconducting parameters of *d*
_{sc} and *Λ* for multiband superconductors^{28,29}.

The transition from a single-band to a two-band system is corroborated by ARPES. Figure 3a displays the data of a trilayer stanene with increasing *N*
_{PbTe}. Two valence bands can be identified: a parabolic band with its highest intensity (dark colour) below the Fermi level (*E*
_{F}) and a linearly-dispersed band (white) with its two arms crossing *E*
_{F}. The position of the Fermi level is distinctly different from that of bulk α-Sn (refs ^{30,31}). Superconductivity in few-layer stanene here may therefore stem from the enhanced density of states. By increasing *N*
_{PbTe}, the two valence bands sink, evidenced by the decrease in energy (Fig. 3b) of the parabolic band as well as the shrinking Fermi momentum for the linear band (Fig. 3c). This indicates an increase of electron transfer from PbTe. Concomitantly, a third band becomes discernible at the Fermi level. We focus on the region just below the Fermi level in the momentum range of [−0.2, 0.2] Å^{−1}. The overall shape evolves from a rounded pyramid for 3-Sn/6-PbTe to an hour-glass structure for *N*
_{PbTe} ≥ 10. Such an evolution is in direct contrast to the monotonic behaviour of the residual photoelectron intensities in the gapped region, as seen in SrTiO_{3} due to correlation effects^{32}. We therefore attribute the hour-glass feature to the emergence of an electron pocket around the Γ point. In the case of 3-Sn/6-PbTe, this electron pocket may just touch the Fermi level, providing negligible contribution to transport. With further doping, the central electron pocket is significantly enlarged while the outer linear band shrinks. The trilayer stanene on PbTe with *N*
_{PbTe} ≥ 10 therefore behaves as a two-band superconductor. At higher doping, the enhanced interband scattering may suppress superconductivity^{33}, thus explaining the drop of *T*
_{c} for 3-Sn on 20-PbTe (Fig. 1c,e). In addition, we estimate electron–phonon coupling constant to be 0.5 ± 0.2 for the hole band^{34}, which agrees with our transport result by fitting the upper critical field data (Fig. 2b). In comparison, for the bulk β-Sn *λ* ~ 0.7 (ref. ^{11}).

We also performed first-principles calculations for a trilayer stanene grown on PbTe (see Methods). The calculated band structure, displayed in Fig. 4, looks somewhat complicated, since orbitals of stanene and PbTe hybridize strongly with each other, showing significant Rashba splitting. Nevertheless, there exist two series of valence bands mainly contributed by stanene located about 0–0.6 eV below the valence band maximum. Importantly, the top valence bands are “M” shaped, which could introduce an “electron pocket” centred at Γ if *E*
_{F} is placed slightly below the valence band maximum. These features echo the ARPES data. Furthermore, orbital analysis shows that Sn s (p) orbitals make a significant contribution to the lowest conduction (highest valence) band, except at Γ, where an s–p band inversion happens. This band inversion results in a topologically non-trivial phase^{16,20,35}. The trilayer stanene grown on PbTe is therefore a 2D topological insulator with *Z*
_{2} = 1 in theory (see Extended Data Figure 5). We note that a band inversion may be induced in Pb_{1 − x
}Sn_{
x
}Te alloy by increasing Sn, which is accompanied by reopening of the bulk band gap^{24,36,37}. Experimentally, we observed no bulk band gap closing in PbTe with the low-temperature deposition of Sn^{19}, ruling out a possible topological transition in the PbTe substrate.

The delicate dependence of *T*
_{c} on *N*
_{Sn} can be employed for an in-plane integration of topological insulator and superconductor in the same material with tunable properties. Another direction for future endeavour is to investigate the proximity effect in the vertical direction. Our sandwich structure allows atomically sharp interfaces between a superconductor, a tunable barrier and a topological insulator—Bi_{2}Te_{3}. The Fermi momentum of few-layer stanene is comparable to that of Bi_{2}Te_{3}. Furthermore, the superconducting thickness we estimated can be larger than the total thickness of Sn and PbTe layers (Extended Data Figure 3d), such that Cooper pairs may travel into Bi_{2}Te_{3}. In addition, stanene is robust against air exposure and can protect the more sensitive Bi_{2}Te_{3}. In general, the observation of superconductivity in few-layer stanene enriches the material pool for constructing topological devices.

## Methods

### Growth

We use molecular beam epitaxy to grow our heterostructures (Omicron, base pressure 1×10^{−10} mbar). To ensure lattice matching, five quintuple layers of Bi_{2}Te_{3} were first grown on top of Si(111) substrates. This was followed by the layer-by-layer growth of PbTe. Finally, we deposited Sn at a substrate temperature of around 120 K. The sample is then annealed at temperatures up to 400 K to improve the film quality. The crystalline quality is monitored by in situ reflective high-energy electron diffraction and scanning tunnelling microscopy (see Extended Data Figure 6). A layer-by-layer growth is maintained from a monolayer up to the quintuple layer. Above five layers, the growth tends to form islands. The lattice constant of stanene expands as the number of PbTe layers increases, as revealed by reflective high-energy electron diffraction^{19}.

### Transport

Samples grown on intrinsic Si(111) substrate were employed for low-temperature transport measurements in a closed-cycle system (Oxford Instruments TelatronPT) equipped with an He-3 insert (base temperature = 0.25 K). The temperature sensor was placed directly below the sample stage and positioned in an orientation with minimal magnetoresistances. Freshly cut indium cubes were cold pressed onto the sample as contacts. Standard lock-in techniques were employed to determine the sample resistance in a four-terminal configuration with a typical excitation current of 100 nA at 13 Hz.

To fit upper critical field as a function of temperature in the two-band regime, we employ the formula^{26}

where $U\left(x\right)\mathrm{=}\psi \left(\frac{1}{2}\mathrm{+}x\right)-\psi \left(\frac{1}{2}\right)$, with *ψ* the digamma function. *D*
_{1} and *D*
_{2} reflect the diffusivities of the two bands. *λ*
_{11}, *λ*
_{22} and *λ*
_{12} are intraband and interband electron–phonon coupling constants, respectively. We fit the data of 3-Sn/10-PbTe with *D*
_{1}, *D*
_{2}, *λ*
_{11}, *λ*
_{22} and *λ*
_{12} as fitting parameters. We then use the extracted values of *λ*
_{11}, *λ*
_{22} and *λ*
_{12} and fit the data of 3-Sn/12-PbTe with *D*
_{1} and *D*
_{2} as free parameters.

For the activated transport, we use ${R}_{\mathrm{sheet}}\mathrm{=}{R}_{0}\left({\mu}_{0}H\right){\mathrm{e}}^{-\frac{{U}_{H}}{T}}$ to fit the data. *U*
_{
H
} represents the activation energy. In regime I, *R*
_{0}(*µ*
_{0}
*H*) scales as ${R}_{0}{\mathrm{e}}^{\frac{{U}_{H}}{{T}_{\mathrm{c}}}}$, with *R*
_{0} being independent of *µ*
_{0}
*H*. Also, *U*
_{
H
} scales linearly with In(*μ*
_{0}
*H*) such that $-\frac{\mathrm{d}{U}_{H}}{\mathrm{d}\phantom{\rule{0.3em}{0ex}}\mathrm{ln}\phantom{\rule{0.3em}{0ex}}{\mathit{\mu}}_{0}H}\mathrm{=}\frac{{\Phi}_{0}^{2}d}{256{\mathit{\pi}}^{3}{\Lambda}^{2}}$ (ref. ^{38}). Here *Φ*
_{0} is the flux quantum and *Λ* the London penetration depth normal to the superconducting film.

### ARPES

Samples grown on highly doped Si(111) substrates were transferred to the analysis chamber without breaking the ultrahigh vacuum. ARPES with a photon energy of 21.22 eV (He-I light) was carried out with a Scienta R4000 spectrometer. For a quantitative analysis, we first extract the momentum *k* at a series of binding energies by fitting the peaks in the corresponding momentum distribution curves with Lorentzian functions. The obtained data points *k*(*E*) (white circles in Fig. 3a) are then linearly fitted (dashed lines) to extract d*E*/d*k* as well as *k*
_{F}.

### First-principles calculations

Density functional theory calculations were performed with the Vienna ab initio simulation package, using the projector-augmented-wave potential, the Perdew–Burke–Ernzerhof exchange–correlation functional and the plane-wave basis with an energy cut-off of 400 eV. The periodic slab approach was employed to model stanene grown on PbTe, using a vacuum layer of 12 Å and a 12 × 12 × 1 Monkhorst–Pack *k* grid. A slab of two Pb–Te bilayers with a surface lattice constant of 4.568 Å (based on the experimental value of bulk) was used to simulate the substrate, in which the bottom Pb–Te bilayer was fixed during relaxation and the bottom Pb atoms were saturated by fluorine to remove the dangling bonds on the bottom. The spin–orbit coupling was included in the self-consistent calculations of electronic structure.

### Data availability

The data that support the findings of this study are available from the authors upon reasonable request.

## Additional information

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## Acknowledgements

We thank Hong Yao and Canli Song for useful discussions. This work is financially supported by the Ministry of Science and Technology of China (2017YFA0304600, 2017YFA0302902), the National Natural Science Foundation of China (grant no. 11604176) and the Beijing Advanced Innovation Center for Future Chip (ICFC). Y.X. acknowledges support from Tsinghua University Initiative Scientific Research Program and the National Thousand-Young-Talents Program. S.-C.Z. is supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under contract no. DE-AC02-76SF00515.

## Author information

### Author notes

Menghan Liao and Yunyi Zang contributed equally to this work.

### Affiliations

#### State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, China

- Menghan Liao
- , Yunyi Zang
- , Zhaoyong Guan
- , Haiwei Li
- , Yan Gong
- , Kejing Zhu
- , Xiao-Peng Hu
- , Ding Zhang
- , Yong Xu
- , Ya-Yu Wang
- , Ke He
- , Xu-Cun Ma
- & Qi-Kun Xue

#### Collaborative Innovation Center of Quantum Matter, Beijing, China

- Xiao-Peng Hu
- , Ding Zhang
- , Yong Xu
- , Ya-Yu Wang
- , Ke He
- , Xu-Cun Ma
- & Qi-Kun Xue

#### RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama, Japan

- Yong Xu

#### Department of Physics, McCullough Building, Stanford University, Stanford, CA, USA

- Shou-Cheng Zhang

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### Contributions

M.L. and Y.Z. contributed equally to this work. D.Z., K.H. and Q.-K.X. conceived the project. Y.Z. grew the samples and carried out ARPES measurements with the assistance of Y.G., M.L. and D.Z. carried out the transport measurements with the assistance of K.Z., M.L., D.Z., H.L., X.-P.H. and Y.-Y.W. made the two-coil mutual inductance measurements. Z.G. and Y.X. carried out first-principles calculations. D.Z. and Y.X. analysed the data and wrote the paper with input from K.H., X.-C.M., S.-C.Z. and Q.-K.X. All authors discussed the results and commented on the manuscript.

### Competing interests

The authors declare no competing financial interests.

### Corresponding authors

Correspondence to Ding Zhang or Yong Xu or Qi-Kun Xue.

## Supplementary information

### Extended data

Extended data Figs. 1–6.

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