Robust measurement of superconducting gap sign changes via quasiparticle interference: an application to 111 compounds*

While quasiparticle interference (QPI) measurements based on scanning tunneling spectroscopy are often proposed as definitive tests of gap structure, the analysis typically relies on details of the model employed. Here using the simplified two-band model system we propose, that the temperature dependence of momentum-integrated QPI data can be used to identify gap sign changes in a qualitative way, and present an illustration for $s_{\pm}$ and $s_{++}$ states in a system with typical Fe-pnictide Fermi surface. Using ARPES derived band structures within 10 orbital model Hamiltonian we analyze the QPI spectra in LiFeAs and Co-doped NaFeAs compounds and show that the sign-changing gap can be clearly identified using non-magnetic impurity scattering.