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 $Delta_mathbf{k}^alpha$, for all momenta $mathbf{k}$ on the Fermi surface of every band $alpha$. While there are a variety of techniques for determining $|Delta_mathbf{k}^alpha|$, no general method existed to measure the signed values of $Delta_mathbf{k}^alpha$. 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 $Delta_mathbf{k}^alpha$ 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 $Delta_mathbf{k}^alpha$ it generates to the $Delta_mathbf{k}^alpha$ 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 $Delta_mathbf{k}^alpha$ of opposite sign.