Theory for quasiparticle interference in the presence of spin-orbit coupling in strongly electron-doped iron-based superconductors

Motivated by recent experimental reports on sizable spin-orbit coupling (SOC) and a sign-changing order-parameter
in the Li_1-xFe_x(OHFe)_1-yZn_ySe superconductor with only electron Fermi surface 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 ARPES experimens 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 s- and d-wave pairing states with a dominant even parity triplet component can fit the experimental data with the two dominant peak positions in the DOS roughly correspond to the gap sizes at each pocket. Moreover we show that pairing states with dominant triplet component can be further verified using spin-resolved STM.