Fig. 4: LiFeAs superconducting energy-gap symmetry from MAHAEM.

a The measured |g(q)| pattern recorded in the FOV with multiple atomic scattering sites. The hole-like to electron-like scattering as predicted in Fig. 3c is detected clearly and indicated by a brown circle at the same location as 3c. The features inside the circle do not appear identical because the intensity in real experimental data falls off at higher |q|, while the theoretical simulation is replicated about the q-space Brillouin zone boundary with the same intensity, creating a non-physical equal intensity reflected feature. A Gaussian mask of σ = 0.68 Å⁻¹ = 0.8π/a is used to suppress the |g(q)| data in the |q| ≈ 0 core region, to allow clearer presentation of the high-|q|- under study. Much of this |q| ≈ 0 signal intensity is believed to emanate from long-range disorder and is, moreover, unrelated to the scientific objectives of this paper. b The measured \(\rho _{{\mathrm{MA}}}^ - ({\mathbf{q}},E = 3.33\,{\mathrm{meV}})\) using Eq. (9); it is typical of all \(\rho _{{\mathrm{MA}}}^ - ({\mathbf{q}},E)\) between 1 and 6 meV. The circle indicates the hole-like to electron-like scattering in a. We integrate the \(\rho _{{\mathrm{MA}}}^ - ({\mathbf{q}},E)\) over the range of q within this region. The dashed lines are guide to eye to a feature which is consistent with intra h₃ scattering. Again, a Gaussian mask of \(\sigma = 0.68\,{{\mathrm{\AA}}}^{ - 1} = 0.8\pi /a\) is used to suppress the intense core emanating from long range disorder, to allow clearer presentation of the \(\rho _{{\mathrm{MA}}}^ - \left( {{\mathbf{q}},E} \right)\) information at high-|q|. This suppressed area corresponds to ~18% of the total area of the first q-space Brillouin zone, and the unprocessed \(\rho _{{\mathrm{MA}}}^ - ({\mathbf{q}},E)\) data for this figure are provided in its entirety at Supplementary Fig. S6a. c The resulting \(\rho _{{\mathrm{MA}}}^ - (E)\) calculated by summing over the oval enclosed region in b (black dots), and the theory curves (solid) for s_± (black) and s₊₊ (pink) overlaid. Clearly, this demonstrates using MAHAEM that the superconducting energy gap symmetry of LiFeAs is s_± (black).