Sign inversion in the superconducting order parameter of LiFeAs inferred from Bogoliubov quasiparticle interference

Quasiparticle interference (QPI) by means of scanning tunneling microscopy/spectroscopy (STM/STS), angle resolved photoemission spectroscopy (ARPES), and multi-orbital tight bind- ing calculations are used to investigate the band structure and superconducting order parameter of LiFeAs. Using this combination we identify intra- and interband scattering vectors between the hole (h) and electron (e) bands in the QPI maps. Discrepancies in the band dispersions inferred from previous ARPES and STM/STS are reconciled by recognizing a difference in the $k_z$ sensitivity for the two probes. The observation of both h-h and e-h scattering is exploited using phase-sensitive scattering selection rules for Bogoliubov quasiparticles. From this we infer an s$_\pm$ gap structure, where a sign change occurs in the superconducting order parameter between the e and h bands.