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Quasiparticle interference (QPI) by means of scanning tunnelingmicroscopy/spectroscopy (STM/STS), angle resolved photoemission spectroscopy(ARPES), and multi-orbital tight bind- ing calculations are used to investigatethe band structure and superconducting order parameter of LiFeAs. Using thiscombination we identify intra- and interband scattering vectors between thehole (h) and electron (e) bands in the QPI maps. Discrepancies in the banddispersions inferred from previous ARPES and STM/STS are reconciled byrecognizing a difference in the $k_z$ sensitivity for the two probes. Theobservation of both h-h and e-h scattering is exploited using phase-sensitivescattering selection rules for Bogoliubov quasiparticles. From this we infer ans$_\pm$ gap structure, where a sign change occurs in the superconducting orderparameter between the e and h bands.

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