  Kondo systems ranging from the single Kondo impurity to heavy fermion
materials present us with a plethora of unconventional properties whose
theoretical understanding is still one of the major open problems in condensed
matter physics. Over the last few years, groundbreaking scanning tunneling
spectroscopy (STS) experiments have provided unprecedented new insight into the
electronic structure of Kondo systems. Interpreting the results of these
experiments -- the differential conductance and the quasi-particle interference
spectrum -- however, has been complicated by the fact that electrons tunneling
from the STS tip into the system can tunnel either into the heavy magnetic
moment or the light conduction band states. In this article, we briefly review
the theoretical progress made in understanding how quantum interference between
these two tunneling paths affects the experimental STS results. We show how
this theoretical insight has allowed us to interpret the results of STS
experiments on a series of heavy fermion materials providing detailed knowledge
of their complex electronic structure. It is this knowledge that is a conditio
sine qua non for developing a deeper understanding of the fascinating
properties exhibited by heavy fermion materials, ranging from unconventional
superconductivity to non-Fermi-liquid behavior in the vicinity of quantum
critical points.
