Evidence of superconducting Fermi arcs

Abstract

An essential ingredient for the production of Majorana fermions for use in quantum computing is topological superconductivity^1,2. As bulk topological superconductors remain elusive, the most promising approaches exploit proximity-induced superconductivity³, making systems fragile and difficult to realize^4-7. Due to their intrinsic topology⁸, Weyl semimetals are also potential candidates^1,2, but have always been connected with bulk superconductivity, leaving the possibility of intrinsic superconductivity of their topological surface states, the Fermi arcs, practically without attention, even from the theory side. Here, by means of angle-resolved photoemission spectroscopy and ab initio calculations, we identify topological Fermi arcs on two opposing surfaces of the non-centrosymmetric Weyl material trigonal PtBi₂ (ref. ⁹). We show these states become superconducting at temperatures around 10 K. Remarkably, the corresponding coherence peaks appear as the strongest and sharpest excitations ever detected by photoemission from solids. Our findings indicate that superconductivity in PtBi₂ can occur exclusively at the surface, rendering it a possible platform to host Majorana modes in intrinsically topological superconductor-normal metal-superconductor Josephson junctions.

Fig. 1. 3D band structure of PtBi₂.

a, Crystal structure of PtBi₂. b, Fragment of the band structure. One Weyl point is included. c, Fermi surface, Weyl and high-symmetry points. Colour scale indicates Fermi velocity. d, ΓMK plane of the Brillouin zone with projections of the Weyl points. Magenta (blue) colours stand for positive (negative) chirality. e, Fermi surface maps taken using different photon energies and the corresponding results of the band structure calculations. We note that fixed photon energy probes a sphere of the large radius in the k-space, matching theoretical data formally only at one point in the centre. Theoretical Fermi maps were averaged over a range of 1/10 of the Brillouin zone size in the k_z direction to account for experimental uncertainties. The intensities of the theoretical Fermi maps were normalized to the density of states for different k_z points. f,g, Left, energy-momentum intensity distributions at 21 eV (f) and 19 eV (g) along the cuts indicated by blue dashed arrows in e. Right, corresponding energy-momentum spectra taken from the band structure calculation. Source Data

Fig. 2. Fermi arcs.

a, High-resolution Fermi surface maps (hν = 17 eV, T = 1.5 K) from both terminations. Arcs in the first Brillouin zone are indicated by the arrows. Note their presence in the equivalent positions in the first and repeated Brillouin zone. b, Fermi surface maps at different photon energies, all showing the presence of the arcs measured at 15 K. The sketch in the middle provides a visual reference for position of the arcs. c, Arcs as seen in the calculations. Blue dots show the projections of the Weyl points. d,e, Experimental and calculated energy-momentum intensity plots for terminations A (d) and B (e) along the cuts through the arcs highlighted by blue dashed arrows in a. Source Data

Fig. 3. Laser-ARPES.

a, Fermi surface map taken using hν = 5.9 eV at 3 K. Arcs are seen together with other bulk-originated features. b, Underlying dispersion along the momentum cuts indicated by arrows in a. c, Typical EDCs from b. Bulk EDC is taken close to zeroth momentum, while surface EDC corresponds to the arc. d, One of the narrowest and strongest EDCs detected in the present study. e, Arcs seen along the different cuts through the Brillouin zone in different experimental geometries. f, Intensity distribution taken using horizontally polarized light along the path crossing two arcs. g, The same momentum and energy range as in f, from the calculations. Note, the surface states at around 200 meV binding energies are also reproduced. h, Circular dichroism from the same region of the k-space. Colour bar in pannel a also applies to panels b,e,f, and g. Source Data

Fig. 4. Superconducting arcs.

a, Temperature dependence of the arcs’ dispersion from the terminations A and B. b, Zoomed-in datasets showing underlying dispersion of the arcs. c, EDCs corresponding to the coloured arrows in b. d, Leading edge and peak positions from b. e, Averaged values of the peak positions closest to the Fermi level as a function of temperature for different samples and terminations. Samples 1 and 3 correspond to termination A and Samples 2 and 4 correspond to termination B. f, Shift of the EDCs with temperature. g, Difference plots showing the changes of the intensity as a function of temperature. h, Results of the calculated spectral weight, taking into account the superconductivity at the surface. i, Schematics of the electronic structure of PtBi₂. Green contours represent the Majorana states suggested by the topological superconductivity at the surfaces. a.u., arbitrary units. Source Data

Extended Data Fig. 1. Fermi surface maps.

Photoemission intensity integrated within a small energy region around the Fermi level. Data were recorded using 16 different photon energies.

Extended Data Fig. 2. Photon energy dependence of the Fermi arcs.

a, Energy distribution curves (EDC) across the Fermi arc as a function of photon energy (upper panel), EDC across the Fermi arc measured with 5.9 eV laser (middle panel), theoretical EDC for fully integrated bulk (lower panel). b, Theoretical calculation for bulk (left) and bulk with surface (right) in ΓM direction.

Extended Data Fig. 3. 3D band structure.

a, Fermi surface maps taken using different photon energies and corresponding results of the band structure calculations. We note, that fixed photon energy probes a sphere of the large radius in the k-space, matching theoretical data formally only at one point in the centre. b,c, Energy-momentum intensity distributions at 21 eV and 19 eV respectively along the cuts indicated by blue dashed arrows in panel e.

Extended Data Fig. 4. EDC across the Fermi arc.

a, Energy distribution curves corresponding to sample # 3 from Fig. 4e of the main manuscript and normalized to the maximum intensity. The opening of the superconducting gap is clearly visible as a displacement of the peaks and leading edges with temperature. b, Energy distribution curves taken close to k_F of the arcs for different k, samples (S) and cleaves (C).

Extended Data Fig. 5. Theoretical calculations of gap opening in PtBi₂.

a The path in the BZ. b The surface-only superconducting spectral function of the (00-1)-surface for Δ = 2meV and penetration depth 30a_B (G_ee only). Note that the gap is only open around the surface state pocket. c the blow-up of this pocket. Note, that the gap is open for the surface state but closed for the bulk bands.

Extended Data Fig. 6. Polarization dependent datasets.

ARPES spectra measured with horizontal (left), circular left (middle) and circular right (right) polarization of the 5.9 eV laser at 3.5 K.