Topological nodal i-wave superconductivity in PtBi2
Summary
The authors report high-resolution ARPES measurements and complementary theory showing nodal superconductivity on the surface Fermi arcs of trigonal PtBi2. The gap on those arcs has symmetry-imposed nodes at the arc centres; symmetry analysis and modelling indicate the order parameter follows an i-wave form (l = 6, A2 irreducible representation, proportional to sin(6ϕ)). Because the Fermi-arc states are chiral and nondegenerate, the sign change of the surface order parameter implies the formation of multiple surface Majorana cones (six per surface) and predicts zero-energy, dispersionless Majorana hinge modes at sufficiently large step edges. DFT–BdG and tight-binding modelling reproduce the anisotropic gap and support a surface pairing strength V0 ≈ 15–20 meV. Experimentally the superconducting gap on the arcs is anisotropic, closes at a node when the arc crosses the Γ–M line, and disappears above a critical temperature in the 10–15 K range.
Key Points
- ARPES with very low photon energy (6 eV laser) resolves exceptionally sharp Fermi-arc states in PtBi2 and maps the superconducting gap along the arc with high precision.
- The superconducting gap on the surface Fermi arcs is strongly anisotropic and shows nodes at arc centres (node at θ = 0°), consistent across multiple samples.
- Symmetry analysis for the C3v point group selects the A2 irrep, giving an i-wave (l = 6) gap form proportional to sin(6ϕ), implying sign changes along each arc.
- The sign change on chiral, nondegenerate arcs produces surface Majorana cones (six on a given surface) that are topologically protected with equal winding numbers; opposite-surface cones carry opposite winding numbers (quantum anomaly / anomalous topological superconductivity).
- Theoretical modelling (DFT–BdG and effective tight-binding) reproduces the gap profile and predicts dispersionless zero-energy Majorana hinge modes localised at surface step edges; a Zeeman field gaps the cones and shifts hinge states — an experimentally testable signature.
- Bulk remains metallic and does not superconduct; this limits immediate quantum-computation applications, but proposals include using ultrathin flakes, breaking time-reversal symmetry to engineer chiral edge or corner Majorana modes, or building planar Josephson devices to harness Majorana states.
Content summary
The work combines improved ARPES (laser, 6 eV) mapping of PtBi2 surface states with detailed numerical modelling. The experiments reveal extremely sharp, spatially and energetically localised Fermi-arc states and an anisotropic superconducting gap that closes at the arc centre (Γ–M), indicating nodes. Temperature scans confirm the gap closes above ≈10–15 K. Symmetry classification of possible superconducting order parameters in C3v rule out trivial and most E-type states; only A2 symmetry enforces nodes at all arc centres. The lowest-order A2 basis function is sin(6ϕ) — i-wave — implying six sign changes and hence six Majorana cones per surface. DFT–BdG slab calculations with surface-only pairing (V0 ≈ 15–20 meV) reproduce the measured gap magnitude and angular dependence. An effective tight-binding model further shows that these surface Majorana cones are topologically protected (class DIII winding numbers) and that their nonzero net winding on a single surface is compensated by cones on the opposite surface. In prism geometries the theory predicts zero-energy, dispersionless hinge-localised Majorana modes between projections of top and bottom cones. Practical obstacles include the metallic bulk, but proposed routes to isolate useful Majorana physics include thinning samples, applying Zeeman fields, or engineering Josephson junctions or time-reversal breaking to create gapped, manipulable Majorana modes.
Context and relevance
This is potentially the first spectroscopic observation (ARPES) of superconductivity beyond d-wave symmetry in a crystalline material, with compelling evidence for i-wave pairing on topological Fermi arcs. The result sits at the intersection of unconventional pairing and topological condensed-matter physics: surface-localised superconductivity of topological states gives rise to multiple Majorana cones and predicted hinge modes. For researchers in superconductivity, topological materials and quantum information, this opens new experimental directions and design ideas for devices that could host and manipulate Majorana modes — albeit with caveats because the bulk remains metallic. The paper combines world-class ARPES data with solid theoretical support, making the claims experimentally accessible and falsifiable (e.g. Zeeman-field dependence, hinge/step-edge probes).
Why should I read this?
Short answer: because this might be the first clean ARPES evidence of an exotic i-wave, topological superconductor with multiple Majorana cones — and the authors back it up with calculations and concrete experimental signatures you can test. If you work on topological superconductivity, Majorana physics or surface superconductivity, this is exactly the sort of result that could change how people design experiments and devices. If you don’t, it’s still neat: sharp ARPES + symmetry reasoning + accessible predictions = a tidy paper that saves you hours of digging.