LAUSR

Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α , for all momenta k on the Fermi surface of every band α . While there are a variety of techniques for determining $$|{\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha |$$ ∣ Δ k α ∣ , no general method existed to measure the signed values of $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α . Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting all k -space regions where $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α it generates to the $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α determined from single-atom scattering in FeSe where s ± energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α of opposite sign.