Quasiparticle Interference and Symmetry of Superconducting Order Parameter in Strongly Electron-Doped Iron-based Superconductors

Motivated by recent experimental reports of significant spin-orbit coupling (SOC) and a sign-changing order-parameter in the Li$_{1-x}$Fe$_x$(OHFe)$_{1-y}$Zn$_y$Se superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states - $s$-wave, $d$-wave and helical $p$-wave - can have a fully gapped density of states (DOS) consistent with angle-resolved photoemission spectroscopy (ARPES) experiments and, due to spin-orbit coupling, are a mixture of spin singlet and triplet components leading to intra- and inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spin-triplet dominated even parity $A_{1g}$ (s-wave) and $B_{2g}$ (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments.