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Multi-Atom Quasiparticle Scattering Interference for Superconductor Energy-Gap Symmetry Determination

Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap $Δ_\mathbf{k}^α$, for all momenta $\mathbf{k}$ on the Fermi surface of every band $α$. While there are a variety of techniques for determining $|Δ_\mathbf{k}^α|$, no general method existed to measure the signed values of $Δ_\mathbf{k}^α$. Recently, however, a new 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 $Δ_\mathbf{k}^α$ 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 $Δ_\mathbf{k}^α$ it generates to the $Δ_\mathbf{k}^α$ determined from single-atom scattering in FeSe where $s_{\pm}$ 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 $Δ_\mathbf{k}^α$ of opposite sign.