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