  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.
