  Strong electron correlations in rare earth hexaborides can give rise to a
variety of interesting phenomena like ferromagnetism, Kondo hybridization,
mixed valence, superconductivity and possibly topological characteristics. The
theoretical prediction of topological properties in SmB$_{6}$ and YbB$_{6}$,
has rekindled the scientific interest in the rare earth hexaborides, and
high-resolution ARPES has been playing a major role in the debate. The
electronic band structure of the hexaborides contains the key to understand the
origin of the different phenomena observed, and much can be learned by
comparing the experimental data from different rare earth hexaborides. We have
performed high-resolution ARPES on the (001) surfaces of YbB$_{6}$, CeB$_{6}$
and SmB$_{6}$. On the most basic level, the data show that the differences in
the valence of the rare earth element are reflected in the experimental
electronic band structure primarily as a rigid shift of the energy position of
the metal 5$\textit{d}$ states with respect to the Fermi level. Although the
overall shape of the $\textit{d}$-derived Fermi surface contours remains the
same, we report differences in the dimensionality of these states between the
compounds studied. Moreover, the spectroscopic fingerprint of the 4$\textit{f}$
states also reveals considerable differences that are related to their
coherence and the strength of the $\textit{d}$-$\textit{f}$ hybridization. For
the SmB$_6$ case, we use ARPES in combination with STM imaging and electron
diffraction to reveal time dependent changes in the structural symmetry of the
highly debated SmB$_{6}$(001) surface. All in all, our study highlights the
suitability of electron spectroscopies like high-resolution ARPES to provide
links between electronic structure and function in complex and correlated
materials such as the rare earth hexaborides.
