Surface-extended Andreev bound states emerging from intrinsic surface superconductivity of PtBi 2

The gist: This work demonstrates that PtBi2 hosts a sizable surface SC gap that remains remarkably homogeneous over length scales ranging from hundreds of nanometers down to the atomic level, and within this gap, spatially extended Andreev bound states are visualized which indicate an anisotropic chiral nature of the pairing symmetry.

Sizable Surface Superconducting Gap

Trigonal PtBi2 is a layered material with a noncentrosymmetric space group (P31m), in which each monolayer adopts a Bi–Pt–Bi sandwich structure Owing to the absence of inversion symmetry, cleaved PtBi2 crystals exhibit two distinct surface terminations: A twisted kagome lattice and a decorated honeycomb lattice In this study, we focus on the decorated honeycomb surface shown in Fig. 1a, where the topmost Bi atoms form a simple triangular lattice, in contrast to the more intricate structure of the twisted kagome termination Pronounced SC gaps with welldefined coherence peaks symmetrically centered around the Fermi level (EF) are reproducibly observed using four different tips The gap sizes determined from the positions of the coherence peaks in Fig. 1d-g are 12 meV, 16 meV, 10 meV, and 10 meV, respectively. These results indicate that sizable SC gaps persist across such macroscopic length scales, although their magnitudes exhibit measurable variation >

Spatial Homogeneity of the SC Gap

The research establishes the multi-scale homogeneity of the superconducting gap, noting that it is highly uniform from macroscopic to atomic length scales. This uniformity is supported by measurements performed with sub-lattice constant resolution using a different STM tip. The consistent appearance of coherence peaks across all positions indicates a spatially homogeneous SC gap of 10 meV. This multi-scale homogeneity supports the formation of a coherent superconducting order parameter ∆(k), enabling identification of the pairing symmetry.

Visualization and Nature of Andreev Bound States (ABSs)

The characteristics of these ABSs are strongly influenced by the phase structure of the SC gap, making them a powerful probe of the underlying pairing symmetry. The conductance intensity within the SC gap exhibits stronger spatial variation than the relatively flat background outside the coherence peaks. The observation of spatial variation of the in-gap states is attributed to subtle fluctuations in the tip–sample distance, suggesting an origin distinct from bulk states. These findings reveal intriguing in-gap states with symmetric spectral features inside the SC gap, which are consistent with and indicative of ABSs. Their enhanced spectral definition at reduced tip-sample distance points to a strongly surface-localized character >

Pairing Symmetry Determination

Theoretical modeling of the experimental results reveals an anisotropic chiral nature of ∆(k) in PtBi2. The close agreement between experiment and theory provides strong evidence for an anisotropic chiral pairing symmetry in the SC state of PtBi2, while also underscoring the possible topological origin of the ABSs from a Majorana cone. The simulation results in Extended Data Fig. E6g and h closely reproduce the hump-shaped dI/dV spectra obtained in our measurements.

Surface-Extended ABSs

The study confirms that the ABSs are spatially extended across the surface, rather than being confined to structural defects or irregularities. The emergence of such delocalized ABSs points to the existence of boundary states with a well-defined dispersion within the superconducting gap, consistent with the behavior expected for a chiral SC order parameter. This surface-extended nature is further corroborated by high-resolution measurements using a different tip, with sub-lattice constant spatial sampling. The emergence of such delocalized ABSs points to the existence of boundary states with a well-defined dispersion within the superconducting gap, consistent with the behavior expected for a chiral SC order parameter >

Summary

This work demonstrates that PtBi2 hosts a sizable surface SC gap that remains remarkably homogeneous over length scales ranging from hundreds of nanometers down to the atomic level. Within this gap, we directly visualize ABSs that are spatially extended across the surface. Theoretical modeling of the experimental results reveals an anisotropic chiral nature of ∆(k) in PtBi2. The coexistence of a large SC gap and readily accessible surface states renders PtBi2 as a superior platform for realizing and studying exotic topological superconductivity. Its spectroscopic accessibility at elevated temperatures further opens avenues for uncovering Majorana physics and advancing toward practical quantum technologies >

Acknowledgments

X.H. would like to thank for the financial support from the DFG through the Hallwachs-R¨ontgen Postdoc Program of ct.qmat (EXC 2147, Project No. 390858490). L.Z. would like to thank for the financial support from the Guangdong Provincial Quantum Science Strategic Initiative (GDZX2401011). M.B. acknowledges ct.qmat (EXC 2147, Project No. 390858490). C.H. and B.B. acknowledge support from the Deutsche Forschungsgemeinschaft (grant 566479091).

Author Contributions

X.H., S.S., C.H., B.B., and M.B. conceived and supervised the project. L.Z. synthesized the single crystals. X.H carried out the STM/STS experiments with assistance from S.S. and P.H. The theoretical model was developed by S.S. and X.H. Under the supervision of C.H., S.S., and J.B wrote the code and performed the simulations. X.H wrote the initial draft of the manuscript.

References

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1. This research can improve AI systems by developing highly sensitive materials characterization tools capable of detecting subtle electronic phase variations across multiple length scales. The improved system can perform spatially resolved dI/dV spectra to map the sizable SC gap and anisotropic chiral topological superconductivity from macroscopic lengths down to the atomic level.

2. The AI can be trained to distinguish between different pairing symmetries by analyzing the energy dependence of observed states. This allows the system to determine if anisotropic chiral pairing symmetry of ∆(k) is present, which is crucial for designing materials with specific topological properties.

3. The system can be used to identify and characterize low-energy Andreev bound states (ABSs) that ubiquitously emerge within the SC gap across the surface. This capability enables AI-driven discovery of novel topological quasiparticles, as these ABSs are of topological origin and provide insights into Majorana modes.

4. The system can predict the behavior of superconducting systems under varying tip-sample distances by modeling the relative weighting between IT and the ABS contributions, which is governed by a parameter related to distance 'd'. This enables predictive modeling for tuning surface properties by controlling external parameters, as the relative weighting between IT and the ABS contributions are governed by the exponential dependence on α, reflecting the tunneling barrier sensitivity to the tip–sample distance d.

5. The AI can be leveraged to simulate complex superconducting phenomena using a hierarchical model that includes the Dynes density of states, the surface ABS current, and an empirical term. This simulation capability allows for testing theoretical predictions against experimental data, as the model successfully reproduces hump-shaped dI/dV spectra and confirms the existence of features in the gap.

Intrinsic topological superconductivity remains one of the central open questions in condensed-matter physics. The three-dimensional Weyl semimetal PtBi 2 has recently been shown by angle-resolved photoemission spectroscopy to host a superconducting gap that opens exclusively on its Fermi-arc surface states and exhibits a nodal structure, making it a promising platform for exploring unconventional and potentially topological superconductivity. However, despite these momentum-resolved insights, the real-space spectroscopic signatures of unconventional superconductivity in PtBi 2 remain unclear. Here, using scanning tunneling microscopy and spectroscopy, we reveal a sizable and spatially homogeneous gap (Δ> 10, meV) on atomically pristine terraces of PtBi 2. Within this gap, we detect surface-extended in-gap states exhibiting pronounced atomic-scale spatial modulation. Analysis of the tunneling spectra indicates that these states are most consistently interpreted as Andreev bound states within a superconducting gap. Further phenomenological modeling shows that their characteristic spectral features are naturally captured by a chiral pairing scenario. Our results establish a direct real-space connection between the superconducting gap and surface-extended quasiparticle states in PtBi 2, and provide new insight into the nature of its unconventional surface superconductivity. These findings highlight PtBi 2 as a versatile platform for exploring exotic quasiparticle excitations and potential Majorana physics.