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Complete theoretical understanding of the most complex superconductorsrequires a detailed knowledge of the symmetry of the superconducting energy-gap$\Delta_\mathbf{k}^\alpha$, for all momenta $\mathbf{k}$ on the Fermi surfaceof every band $\alpha$. While there are a variety of techniques for determining$|\Delta_\mathbf{k}^\alpha|$, no general method existed to measure the signedvalues of $\Delta_\mathbf{k}^\alpha$. Recently, however, a new technique basedon 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 theseimages identifies wavevectors connecting all k-space regions where$\Delta_\mathbf{k}^\alpha$ has the same or opposite sign. But use of a singleisolated impurity atom, from whose precise location the spatial phase of thescattering interference pattern must be measured is technically difficult. Herewe introduce a generalization of this approach for use with multiple impurityatoms, and demonstrate its validity by comparing the $\Delta_\mathbf{k}^\alpha$it generates to the $\Delta_\mathbf{k}^\alpha$ determined from single-atomscattering in FeSe where $s_{\pm}$ energy-gap symmetry is established. Finally,to exemplify utility, we use the multi-atom technique on LiFeAs and findscattering interference between the hole-like and electron-like pockets aspredicted for $\Delta_\mathbf{k}^\alpha$ of opposite sign.

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