Fig. 2: Evidence of topological surface state.

a The calculated band structure projected onto the (001) surface. The topological surface state (TSS) along with the bulk valence band (BVB) and the bulk conduction band (BCB) are plotted. b ARPES spectral intensity plots along the Γ–M direction on undoped CaKFe₄As₄ at the photon energy of 76 eV and the temperature of 25 K; the blue line tracks the 3d_z²/4p_z dispersion by Lorentzian fitting on the peaks of MDCs of b. c Same as b, but the sample is under K-surface dosing with current I = 5.6 A for 40 s. Both b, c are divided by the Fermi–Dirac distribution. d–e The MDC second-derivative plot of b, c within the red boxes³². The red and yellow dashed lines plot the extracted band dispersions, by Lorentzian peaks fitting on the MDCs of the data in b, c, respectively. A Dirac-cone-like band structure is visible in e. The red and yellow solid lines display the linear-fitting results of extracted band dispersions (colored dashed lines). f The MDC plot of the data in c are normalized by the intensity at k_x = 0.15 π/a at the energy range from −35 to 40 meV, and the gray line are guides to the eye indicating the positions of peaks. g The energies of the Dirac points with the duration of K-adsorption. The error bar is from the uncertainty of the Dirac point, which comes from the different selected ranges of the linear fitting. h A laser-based ARPES spectral intensity plot along Γ–M, measured with a p-polarized laser (photoenergy 7 eV) at 8 K. i EDCs at 8 K. j, k The symmetrized EDCs at k_F ~ 0.03 π/a and 0.17 π/a (indicated by k₁, k₂ in h) measured at 8 K (blue) and 40 K (red). The superconducting gap values (5.9 meV in j, and 7.5 meV in k) can be estimated from the two sharp peaks in the symmetrized EDCs. We attribute the gap of 5.9 meV to the SC gap in the topological surface band.