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.
