Since the discovery of iron-based superconductors, a number of theories have been put forward to explain the qualitative origin of pairing, but there have been few attempts to make quantitative, material-specific comparisons to experimental results. The spin-fluctuation theory of electronic pairing, based on first-principles electronic structure calculations, makes predictions for the superconducting gap. Within the same framework, the surface wave functions may also be calculated, allowing, e.g., for detailed comparisons between theoretical results and measured scanning tunneling topographs and spectra. Here we present such a comparison between theory and experiment on the Fe-based superconductor LiFeAs. Results for the homogeneous surface as well as impurity states are presented as a benchmark test of the theory. For the homogeneous system, we argue that the maxima of topographic image intensity may be located at positions above either the As or Li atoms, depending on tip height and the setpoint current of the measurement. We further report the experimental observation of transitions between As and Li-registered lattices as functions of both tip height and setpoint bias, in agreement with this prediction. Next, we give a detailed comparison between the simulated scanning tunneling microscopy images of transition-metal defects with experiment. Finally, we discuss possible extensions of the current framework to obtain a theory with true predictive power for scanning tunneling microscopy in Fe-based systems.
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