Introduction

Topological superconductors have attracted intense attention due to the potential for Majorana-based qubits of fault-tolerant quantum computation1,2,3. One way of searching TSC, is to realize s-wave superconductivity on spin helical states4, such as semiconductor nanowires with strong spin–orbit coupling (SOC) or ferromagnetic atomic chains proximitized with an s-wave superconductor1,3,5,6,7,8,9, vortex cores in a proximitized topological insulator4,10. An alternative route to TSC is to realize a p-wave superconductor, which is an intrinsic topological superconductor; prominent candidates are Sr2RuO411,12,13, UPt314, CuxBi2Se315,16, iron-based superconductors17,18,19,20 and recently discovered Kagome superconductors AV3Sb5 (where A is K, Rb or Cs)21. In these cases, TSC is evidenced by the Majorana zero-energy modes (MZM), which were spectroscopically identified as zero-energy conductance signals, localized at the ends of the one-dimensional (1D) chain or in the vortex core, or at boundaries and defects; Another evidence is spin-rotational symmetry breaking in the SC state observed by nuclear magnetic resonance (NMR)15,22,23 and point-contact spectra in CuxBi2Se316. However, the proximity-induced TSC heterostructures require a long superconducting coherence length, in principle prohibiting the use of high-temperature superconductors. Additionally, the complex heterostructures make further exploration and applications challenging. Meanwhile, the existing intrinsic TSC needs special symmetry-protected non-trivial topological bands, which place limitations on materials and are also very sensitive to disorder.

In this work, we propose a new type of intrinsic TSC, namely intrinsic surface topological superconductor (IS-TSC) as well as demonstrated it in layered material AuSn4. Instead of requiring the specific topological bands, an IS-TSC is introduced by multiple surface bands with Rashba splitting across the EF and further condensing into a coherent paired state. We employ ultralow temperature scanning tunneling microscopy/spectroscopy (STM/STS), angle-resolved photoemission spectroscopy (ARPES), transport, point-contact spectroscopy (PCS), and density functional theory (DFT) calculations, to investigate intensively the atomic structure, superconductivity, band structure and surface states of AuSn4. Transport measurements reveal that the AuSn4 is a superconductor with Tc ~ 2.4 K and the upper critical field (Hc2(0)) ~643 Oe and 1621 Oe for H || a and H || ab, respectively. Two-fold symmetric superconductivity is observed in both magneto-transport and point-contact spectroscopy with the fields rotating in ab plane. A superconducting gap develops below Tc in tunneling spectrum; its temperature and field dependencies agree well with the results of transport measurements. ARPES and first-principle calculations, further visualize multiple surface bands crossing the EF as well as their Rashba splitting, which suggests the observed unconventional SC can ascribe to a mixing of s + p wave pairing.

Results

Structure, superconductivity, and anisotropic upper critical fields of AuSn4

Noble metal alloys ASn4 (A = Au, Pt, and Pd), have been regarded as promising candidates of TSC owing to both topological band structure24,25,26,27 and superconductivity28,29,30. For example, the work31 reported the superconductivity (Tc ~2.7 K) and possible non-trivial band topology in PtPb4. Recent works found the superconductivity of AuSn432 and claimed it as a 2.6 K topological superconductor with non-trivial surface states33. Here we grew high-quality single crystals of AuSn4 by the flux method (see Methods). An optical image in Fig. 1a shows a square-shaped AuSn4 crystal with ~1 mm size and ~0.1 mm thick and a large shiny surface indicating the ab plane. The structure of AuSn4 samples is determined by atomic-level scanning transmission electron microscopy imaging, electron diffraction image, and x-ray single crystal diffraction, as shown in Fig. 1b, c, Supplementary Tab. S1 and Figs. S1 and S2. The AuSn4 has stacked Sn-Au-Sn trilayers, each Au layer is sandwiched by two Sn layers forming a square lattice (see the structural model in Supplementary Fig. S2a, b). The structure is in the space group Aba2 (No. 41) with the lattice constants of a, b = 6.476 Å, and c = 11.666 Å, distinct from the previously reported structures of PtSn4 and PdSn4, which hold orthorhombic (Ccca, No. 68) space group34,35. Further, the electron diffraction image (Fig. 1c) meets well with the simulated one based on the structure of space group Aba2 (No. 41), instead of Ccca (No. 68) (see Supplementary Fig. S2c, d).

Fig. 1: Superconductivity and anisotropic upper critical fields of single crystal AuSn4.
figure 1

a An optical image of the grown AuSn4 crystal. b High-resolution TEM image of the ab plane. (inset) top view shows the square-net lattice of Sn-Au-Sn trilayer. c The measured electron diffraction image of AuSn4 sample along the c axis. d The temperature dependence of the resistivity with current flowing in the ab plane. The inset shows ρ(T) in zero field at temperatures near Tc. e–f The low-temperature resistivity curves under magnetic fields with H || ab and H || c, respectively. g Temperature dependence of the upper critical field μ0Hc2 with magnetic field directions parallel (μ0Hc2,||) and perpendicular (μ0Hc2,⊥) to the crystal plane.

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Figure 1d displays the temperature dependence of resistivity ρxx(T) for AuSn4 single crystals with the current applied in the ab plane by the standard four-probe method at zero magnetic field. The normal state resistivity shows a metallic behavior with a moderately small residual resistivity of ~0.75 μΩ cm, and the residual resistivity ratio [RRR = ρxx(300 K)/ρxx(3 K)] is about 85, indicating high crystalline quality and low density of defects. A sharp SC transition appears at the onset temperature Tc ~ 2.4 K, defined by the intersection of the tangent line and the R–T curves, indicated by the thin arrow (the inset of Fig. 1d). The low-temperature R(T) under various magnetic fields with H || ab (Fig. 1e) and H || c (Fig. 1f), display the SC transition shifts gradually towards lower temperatures with increasing fields. Extracted from Fig. 1e, f, the temperature dependence of upper critical fields (μ0Hc2,|| and μ0Hc2,⊥), have an upward curved feature for H || ab and a linear behavior for H || c, respectively (Fig. 1g). The linear temperature dependence can be described by Ginzburg–Landau (GL) theory Hc2,⊥(T) = (ϕ0/2π\({{\xi }}_{{{{{\rm{GL}}}}}}^{2}\)) (1-T/Tc)2, where ϕ0 is the magnetic flux quantum and ξGL is the zero temperature GL coherence length. As shown in Fig. 1g, the red line gives ξGL = 71.69 nm, roughly equal to the reported value30, and the upper critical field at T = 0 K for H || c is accordingly estimated as μ0Hc2,⊥(0) = 643 Oe. For H || ab, μ0Hc2,|| deviates from the GL equation. The enhancement of μ0Hc2,|| at low temperatures can be interpreted by impurity-induced disorder36, dimensional crossover37, quantum melting of the vortex lattice38, or multiband effect39. The first three are obviously irrelevant here because of high crystal quality, ξGL is much larger than the layer distance and no trace for the quantum critical point. Moreover, the calculated band structure later shows that several surface bands cross the Fermi level. Therefore, μ0Hc2,|| is fitted by the equation for a two-band superconductor (blue curve)40,41 with μ0Hc2,||(0) = 1621 Oe (see the details of two-band fitting in Supplementary Note 4), which indicates the superconductivity was more susceptible to perpendicular magnetic fields than to in-plane magnetic fields. The ratio of μ0Hc2,||(0)/μ0Hc2,⊥(0) is 2.5, suggesting a strong anisotropy and 2D nature for superconductivity.

Two-fold symmetric magnetoresistance and point-contact spectra in superconducting regime

With standard four-probe method (Fig. 2a), we performed the angle-dependent magnetoresistance measurements by rotating magnetic field H in the ab plane under the current I along a and b axis (see the angular relationship in Supplementary Fig. S17). Figure 2b–e present the angular dependences of normalized resistance R(θ) at 1.8 K with various fields rotating in the ab plane. A two-fold symmetry are clearly observed when the fields are below the upper critical field μ0Hc2,|| at 1.8 K ( ~ 480 Oe), in contrast to isotropic magnetoresistance with the fields above the critical field, irrespective of the current I || a or b axis. Meanwhile, two-fold symmetry of the resistance gradually decreases with increasing the field up to 450 Oe, inferring it originated from the superconductivity. Such pronounced two-fold symmetric resistivity is shown clearly in Fig. 2d with the dumbbell-shape only under the fields below μ0Hc2,|| at 1.8 K, and becomes isotropic in the normal state (see Supplementary Fig. S3 for other samples), which excludes the extrinsic oscillation from small misalignment of between crystalline plane and the field direction. Besides, a 90° angle between the C2 axes of angle-dependent magnetoresistance for I || a and I || b on the same sample in Fig. 2e, indicates that it is intrinsic and independent of the current direction. The zero-resistance temperature also shows twofold modulation and a 90° angle between the C2 axes for I || a and I || b (see Supplementary Fig. S18). These observations strongly evidence an unconventional pairing mechanism in AuSn4 below Tc.

Fig. 2: Two-fold angular dependence of the resistance and point-contact spectra of superconducting AuSn4 under in-plane magnetic fields.
figure 2

a Schematic measurement configuration under in-plane magnetic fields. b, c The angular dependence of the normalized magnetoresistance at various in-plane magnetic fields and 1.8 K with the current along b and a axis, respectively. θ is the angle between the directions of fields H and current I. d Polar plot of angular-dependent resistance in c (the radial scale is resistivity). e Angular-dependent normalized resistance at 240 Oe and 1.8 K with the current I along a and b axis, respectively. Red and green dashed lines show the C2 axis for I || a and I || b, respectively. Solid lines in b, c, and e are the fittings with a cos(2θ + φ) form. f Temperature dependence of junction’s resistance for the Ag-surface of AuSn4 sample using the modified four-point probe setup. The inset shows junctions’ resistance in zero field at temperatures near Tc. g Color plot of the point-contact spectra at angles from 0 to 360° in a 120 Oe external magnetic field. h A representative point-contact spectra obtained on Ag-paste/AuSn4 junction at 1.8 K (black dashed line in g). i Angle dependence of the normalized differential conductance (dI/dV) at selected angles from 0 to 360° at V = 6 and 0 mV (blue and red dashed lines in g), respectively. The red solid line in i is the best fit for a cos(2θ + φ) form.

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Point-contact spectroscopy (PCS), has been widely used to examine the pairing symmetry for unconventional SC. We prepared a soft-point contact (see schematic diagram in Supplementary Fig. S4) for the point contact measurement of AuSn4. Temperature dependence of junction’s resistance (Fig. 2f) presents a sharp superconducting drop at around 2.4 K. In particular, with soft-point contact technique42, differential conductance spectra under a 120 Oe in-plane magnetic field were measured at T = 1.8 K by changing θ from 0 to 360°, as shown in Fig. 2g. Here, when θ = 0°, the magnetic field B is parallel to b axis. The angle-dependent PCS at angles from 0 to 360° (Fig. 2g) presents a clear two-fold modulation with the dip positions varying in a narrow energy range. Meanwhile, the normalized dI/dV intensity at 6 mV (outside of the dip energy) presented in Fig. 2i, has less than a 0.2% variation versus the angle, indicating negligible anisotropy for normal state. On the contrary, the angular dependence of the normalized dI/dV intensity at 0 mV (inside of the dip energy), displays a clear two-fold modulation (Fig. 2i). Consistent with the aforementioned two-fold symmetry observed in both magnetoresistance and zero-resistance temperature, which indictes these observations are clearly an intrinsic character rooted from the unconventional pairing symmetry of AuSn4 and the superconducting state dominates the PCS. Figure 2h shows a typical PCS curve at θ = 80° with observing a zero-bias-conductance peak (ZBCP) and two side dips. Concerning about the observation of ZBCP, the heating effect can be excluded for the reasons that the sample is in SC state and no sharp-spiky dips appear at energies larger than gap36,43,44. Pronounced side dips and the peak without splitting, are also clearly against with the Blonder-Tinkham-Klapwijk (BTK) theory for conventional Andreev reflection45.

Moreover, the minima of two dips reside at the energies of ±3 mV, in accordance with the gap energy measured by STS later, which strongly suggests that the observed ZBCP is intrinsic and related with the unconventional Andreev bound state (ABS)46,47,48. The ABS is a signature of unconventional SC, owing to the interference of the SC wave function at the surface39. Furthermore, the ZBCP with no more than 4% conductance increasing observed in the point-contact spectroscopy, indicates that the existence of unusual surface states, evidenced by ARPES results later, may evidences TSC16.

Surface topography, superconducting gap measured by STM/STS

High-resolution STM image on the surface terrace (Fig. 3a) shows the square-net lattice of topmost Sn-terminated layer and a quasi-one dimensional (Q1D) super modulation, resembling to the surface superstructure of cuprate Bi2Sr2CaCu2O8+d (Bi2212)49. Zoom-in atomic resolution image (Fig. 3b) clarifies the existence of a \(\sqrt{2}\times 2\sqrt{2}\) superstructure with the unit cell of 6.6 Å × 12.2 Å, may indicate the formation of charge density wave (CDW) state, which has not been reported for this material. Comparing the density of states measured by STS between the terrace and step edge (Supplementary Fig. S5), we confirm that surface states are prominent on the terrace and get greatly suppressed at the edge.

Fig. 3: Surface topography and the superconducting gap with variable temperatures and fields.
figure 3

a High-resolution image reveals a superstructure with the modulation of wavy troughs, the image size is 40 × 40 nm2. The bright spots on the surface can be attributed to the residual Sn from the cleavage. b Zoom-in atomic resolution image shows a square-net lattice and \(\sqrt{2}\times 2\sqrt{2}\) superstructure with the unit cell size of (6.3~6.6) Å × (11.6~12.23) Å (6.6 Å × 13.2 Å in theory) for surface Sn lattice. c A representative dI/dV spectrum taken at 0.16 K, showing a superconducting gap with the size and depth of gap ~0.487 meV and 87%, respectively. Here, we adopt small lock-in modulation bias (Vmod) ~ 40 μV in order to eliminate the broadening effect. d A series of normalized dI/dV spectra with perpendicular fields varying from 0 Oe to 500 Oe (left) and temperatures from 0.38 K to 2.5 K (right), respectively. Set points: Vb = 10 mV, It = 400 pA, the Vmod is 0.3 mV. Note, the STS taken at 0.38 K with 0.3 mV Vmod, give a dual-gap feature with enlarged gap size and shallower depth, probably due to the thermal broadening effect and large lock-in modulation bias. e Temperature (upper) and field (lower) dependences of normalized ZBC extracted from panel d. The deduced Tc and Hc are 2.64 K and 660 Oe, respectively. f The gap evolution with temperatures above Tc.

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A typical normalized dI/dV spectrum measured at 0.16 K (Fig. 3c) shows a superconductive gap feature, a deep V-shaped gap about Δ~0.487 meV (defined as half of the gap width) with the depth of gap ~87%. The temperature and magnetic field dependence of dI/dV spectra (Fig. 3d) show the suppression of the gap and increased zero-bias-conductance (ZBC) at higher temperatures and magnetic fields, indicating a typical characteristic of superconductor. To estimate the Tc and critical field (Hc), the normalized ZBC are extracted from Fig. 3d and a rough linear fitting gives the deduced Tc and Hc values of ~2.64 K and 660 Oe, respectively (Fig. 3e), both values agree well with transport measurements (Fig. 1). The ratio 2Δ(0)/kBTc (kB is the Boltzmann constant) is estimated to be ~4.7, which is in the range of the medium coupling Bardeen–Cooper–Schrieffer (BCS) superconductors. The upper critical fields μ0Hc2,c(0) at T = 0 K for H || c (~660 Oe) is deduced from STS, in accordance with the value of μ0Hc2,⊥(0) (643 Oe) from transport measurement. All confirms the observed gap is a superconducting gap. It is worth noting that there is still a 13% residue DOS at EF, which may indicate there exists gap nodes/nodal lines or un-gapped bands. Furthermore, we perform vortex measurement under magnetic fields, however, zero-bias-conductance (ZBC) maps do not show the existence of vortex, which may due to the overlaps of vortex50 (see the details of analysis in Supplementary Note 18). Our STS measurements taken at 160 mK, show clearly the SC gaps are modulated with both \(\sqrt{2}\times 2\sqrt{2}\) superstructure (CDW) and stripe pattern (Supplementary Fig. S16), suggesting that the observed CDW state is relevant to the superconductivity. Interestingly, STS measurements on the flat terrace and at the edge at 160 mK (Supplementary Fig. S15), show that a slightly smaller size and shallower depth of SC gap measured at the edge, comparing to the gap measured on the flat terrace. The depth and size of SC gap at the edge are both suppressed to 82% and 0.446 meV, compared to the values on the terrace (87.8% and 0.516 meV). The variation of SC gap due to CDW modulation on the terrace are much smaller, 0.486-0.516 meV of gap size without observable change in the depth. These observations suggest the possible existence of dispersive Majorana edge mode51. Further elevating temperatures from 5 K to 10 K, a pseudogap-like feature develops above Tc and persists up to 10 K, which may correspond to the gap of observed CDW.

Band structure, Fermi contour, and surface states revealed by ARPES and DFT calculations

The calculated band structures of the bulk AuSn4 is presented in Supplementary Fig. S7. Furthermore, the monolayer AuSn4 and the surface states of bulk AuSn4 are also calculated and shown in Fig. 4b, c, respectively, where two surface bands SS1 and SS2 near the EF are marked. Figure 4d shows the band dispersions measured along the cut of \(\bar{X}-\bar{\Gamma }-\bar{X}\) direction at ky = 0 (left) and the derivative ARPES plot measured along the cut of \(\bar{Y}-\bar{\Gamma }-\bar{Y}\) direction at kx = 0 (right), respectively, where both monolayer bands (marked by green dashed lines) and surface bands SS1 and SS2 (red dashed lines), are clearly observed and matched well with DFT calculations. Besides, the Rashba splitting of SS1 is clearly resolved in the inset of Fig. 4d. Bulk Brillouin zone (BZ) and resultant surface BZ are shown in Fig. 4e. Visualizing of monolayer bands in ARPES suggests possibly a 2D electronic nature and weak van der Waals (vdW) interlayer coupling. Notably, surface band SS1 has the highest intensity and both SS1 / SS2 bands run across the EF, which has dominant contribution into the observed SC. Figure 4e shows the Fermi contour mapping with integrated ARPES intensity. The Fermi surface (FS) along \(\bar{\Gamma }-\bar{X}\) and \(\bar{\Gamma }-\bar{Y}\) directions are highly identical and give a fourfold symmetry. Moreover, the FS consists of one central pocket at \(\bar{\Gamma }\) point (white dashed circle, assigned to SS1), surrounded by four peripheral spots located in the middle of \(\bar{\Gamma }-\bar{X}\) and \(\bar{\Gamma }-\bar{Y}\) directions (assigned for the SS2). More ARPES data, e.g., multiple surface states near EF and constant energy contours (CECs) at various energies, can be found in Supplementary Figs. S8 andS9. These surface states, e.g., SS1 and SS2, observed in our ARPES measurement, implies that they could participate in unconventional SC pairing, responsible for the observed two-fold symmetric SC. A good agreement between the ARPES data and the calculated band structure for monolayer AuSn4, despite the difference in the binding energies, which is probably caused by the existence of long-range Coulomb in AuSn452. Further photon-energy-dependent ARPES (Fig. S19) suggests the 2D nature of electronic bands in AuSn4; different slab calculations (Fig. S20) shows neither the slabs with various thickness nor superstructure agrees with the ARPES-measured results. All suggest that the monolayer AuSn4 band structure matches the ARPES results best.

Fig. 4: Band structure, Fermi contour, and the observation of surface states.
figure 4

a The unit cells (UC) for the calculations of bulk and monolayer of AuSn4. b The calculated band structures along high symmetric directions in momentum space with considering SOC effect for the monolayer of AuSn4. c The calculated surface states from the bulk structure along \(\bar{Y}\)-\(\bar{\Gamma }\)-\(\bar{Y}\) direction, where surface bands, SS1 and SS2 are marked accordingly. d (Left) Large energy-scaled band dispersion measured along \(\bar{X}\)-\(\bar{\Gamma }\)-\(\bar{X}\) direction, where both predicted monolayer (green dashed lines) bands and surface bands SS1 and SS2 (marked as red dashed curves) are clearly observed. (Right) the derivative plot of band dispersion measured along \(\bar{Y}\)-\(\,\bar{\Gamma }\)-\(\,\bar{Y}\) direction (right) from ARPES. (Inset) Rashba splitting of surface state. e Fermi-surface (FS) plot of the ARPES intensity integrated within 10 meV of the chemical potential (bottom). The central circle is contributed from the SS1. Four peripheral spots (marked as white dashed circles) located along \(\bar{\Gamma }\)- \(\bar{{X}}\) and \(\bar{\Gamma }\,\)- \(\bar{{Y}}\) directions can be assigned to the SS2. (Top) Brillouin zones (BZ) of the bulk and monolayer AuSn4. f The mixture of p-wave surface and s-wave bulk superconductivity, leads to a full-gap and two-fold symmetric superconductivity.

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The ARPES results show that the electronic structure of AuSn4 is mainly determined by the topmost AuSn4 monolayer whose space symmetry can be described by point group C4v. Due to the breaking of inversion symmetry on the surface, a typical Rashba band splitting emerges in the band structure and opposes a four-fold rotational symmetric normal state. When T < Tc, the superconductivity should happen in one certain irreducible representations (IR) channel, and only the multi-dimensional channel allows multi-component superconductivity exists and consequently breaks the rotation symmetry. Due to two-dimension limitation, the stable superconductivity order parameter ΔE(k) is naturally reduced to a node p-wave superconducting gap, only occurred at the surface, as shown in Fig. 4f. In the bulk, the superconducting symmetry is constrained by D2h point group that has no multi-dimensional IR, as the result, isotropy s-wave superconductivity is favored in the bulk. While the proximity effect can naturally mix two different kinds of superconductivity, the total pairing potential includes the mixture of p-wave surface and s-wave bulk superconductivity (more details in Supplementary Note 12).

Discussion

Such mixed-SC-pairing scenario has been proposed previously, for instance, the mixing between two competing pairing instabilities, namely the s-wave of bulk NbSe2 and an unconventional channel in few-layers in NbSe253. Likewise, when introducing a small orthorhombic distortion into the CuO2 plane of cuprates, the d-wave pairing mixed with s-wave ingredient54, gives rise to twofold in-pane critical field55,56. Contrast to the mixing s- with d-wave pairing in these cases, the p-wave pairing induced by Rashba splitting of surface bands in our AuSn4 is dominant. By carefully fitting the angular dependence of resistivity at various magnetic fields (Supplementary Fig. S10), we find neither anisotropic s-wave nor isotropic s-wave and d-wave gap functions could fit the data well. These data can be fitted by the mixed s + p wave gap function. All this evidence point out an unconventional s + p mixed SC pairing is responsible for the observed SC in AuSn4.

In summary, we fabricated high-quality AuSn4 single crystals and observed a twofold symmetric superconductivity in both transport measurements and point-contact spectroscopy. The in-plane angular dependence of the resistivity at different magnetic fields below Tc and the SC gap observed in STS, indicate its nature of unconventional SC. Both the Tc and critical field Hc2 of AuSn4 agree well in tunneling spectroscopic and transport measurements. The results of DFT calculation and ARPES confirm the existence of multiple surface states across EF. The twofold symmetric superconductivity in AuSn4 can be interpreted with the frame of the mixed s + p pairing induced by Rashba splitting of surface bands.

Methods

Crystal growth

High-quality single crystals of AuSn4 were grown by the flux method. The mixture of Au wire (99.999%) and Sn ingots (99.999%) was placed into an alumina crucible with a molar ratio of 1:8 and sealed in an evacuated quartz tube. The quartz tube was heated to 600 °C, and held there for 20 h. The temperature was then cooled to 300 °C in 1 h, and further cooled to 240 °C at a rate of 1 °C/h, and kept at 240 °C for 80 h. Finally, the excess Sn flux was removed with a centrifuge. The obtained single crystals are of thin-plate shape with typical dimensions of about 1 × 1 × 0.1 mm3. The crystal structure of as-prepared AuSn4 was characterized using a Bruker diffractometer with Cu Kα radiation at room temperature. The energy dispersive X-ray spectroscopy analysis of AuSn4 was performed in a field emission electron microscope (Nova NanoSEM450, Czech). Spherical aberration-corrected (Cs-corrected) high angle annular dark field scanning transmission electron microscopy was performed using a FEI Titan Themis 60–300 kV microscope equipped with a Super-X detector and operating at 200 kV.

STM characterization

Our STM experiments were carried out on an ultrahigh vacuum (UHV) commercial STM system (Unisoku) which can reach a temperature of 400 mK by using a single-shot 3He cryostat. The base pressure for the experiment was 3.0 × 10−10 Torr. AuSn4 samples were cleaved in situ at 78 K and then transferred into STM. The bias voltage was applied to the samples. The STS data were obtained by a standard lock-in method that applied an additional small AC voltage with a frequency of 973.0 Hz. The dI/dV spectra were collected by disrupting the feedback loop and sweeping the DC bias voltage. WSxM software was used for the post-processing of all STM data.

Angle-resolved photoemission spectroscopy

ARPES measurements were performed with a Scienta Omicron DA30-L analyzer and monochromatized He Iα (\(h\nu\)  = 21.218 eV) light source at School of Physics and Information Technology, Shaanxi Normal University and Institute of Physics, Chinese Academy of Sciences. The samples were cleaved in situ and measured at 7.8 K under an ultrahigh vacuum below 6 × 10−11 Torr. The total convolved energy and angle resolutions were better than 2.5 meV and 0.2°, respectively.

First-principles calculations

First-principles calculations were performed by DFT using the Vienna ab initio simulation package57,58. The plane-wave basis with an energy cutoff of 350 eV was adopted. The electron-ion interactions were modeled by the projector augmented wave potential59 and the exchange-correlation functional was approximated by the Perdew-Burke-Ernzerhof-type generalized gradient approximation60. The structural relaxation for optimized lattice constants and atomic positions was performed with an energy (force) criterion of \({10}^{-8}\) eV (0.01 eV/Å) and by using the DFT-D361 method to include van der Waals corrections. Surface state calculations were performed with the WannierTools package62, based on the tight-binding Hamiltonians constructed from maximally localized Wannier functions (MLWF)63.