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The localized-to-itinerant transition of $f$ electrons lies at the heart of heavy-fermion physics, but has only been directly observed in single-layer Ce-based materials. Here, we report a comprehensive study on the electronic structure and nature of the Ce $4f$ electrons in the heavy-fermion superconductor ${\mathrm{Ce}}_{2}{\mathrm{PdIn}}_{8}$, a typical $n=2 {\mathrm{Ce}}_{n}{\mathrm{M}}_{m}{\mathrm{In}}_{3n+2m}$ compound, using high-resolution and $4d\ensuremath{-}4f$ resonant photoemission spectroscopies. The electronic structure of this material has been studied over a wide temperature range, and hybridization between $f$ and conduction electrons can be clearly observed to form a Kondo resonance near the Fermi level at low temperatures. The characteristic temperature of the localized-to-itinerant transition is around 120 K, which is much higher than its coherence temperature ${T}_{\text{coh}}\ensuremath{\sim}30\phantom{\rule{0.28em}{0ex}}\mathrm{K}$.

Hidden order in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$ has remained a mystery that is now entering its fourth decade. The importance of resolving the nature of the hidden order has stimulated extensive research. Here we present a detailed characterization of different surface terminations in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$ by angle-resolved photoemission spectroscopy, in conjunction with scanning tunneling spectroscopy and dynamical mean-field theory calculations that may unveil a piece of this puzzle. The U-terminated surface is characterized by an electronlike band around the $\overline{X}$ point, while a holelike band characterizes the Si-terminated surface. We also investigate the temperature evolution of the electronic structure around the $\overline{X}$ point from 11 up to 70 K, and do not observe any abrupt change of the electronic structure around the coherence temperature (55 K). The $f$ spectral weight gradually weakens upon increasing temperature; still some $f$ spectral weight can be found above this temperature. Our results suggest that surface terminations in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$ are an important issue to be taken into account in future work.

A key issue to understand the driving force and underlying physics in the isostructural $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\alpha}$ transition in Cerium is the character of the $4f$ states, whether it is localized or itinerant. Here the surface topography and electronic structure of the well-ordered Ce metal films on a W(110) substrate were investigated by using scanning tunneling microscopy, angle-resolved photoemission spectroscopy and density functional theory, and single-site dynamical mean-field theory calculations. Three nearly flat $f$ bands can be observed, and a weakly dispersive quasiparticle band near the Fermi level has been directly observed at low temperature, indicating the hybridization between $f$ electrons and conduction electrons in the low-temperature $\ensuremath{\alpha}$ phase. The hybridization strength becomes weaker upon increasing temperature, and the $f$ electrons become almost fully localized at 300 K in the high-temperature $\ensuremath{\gamma}$ phase. The observed localized-to-itinerant transition of the $f$ electrons with decreasing temperature gives direct experimental proof for the changes of the $4f$ character in the isostructural $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\alpha}$ phase transition. Our results suggest that the character of the $f$ electrons plays a crucial role during the $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\alpha}$ phase transition.

The electronic structure of the Kondo lattice CeIn3 has been studied by on-resonant angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy. A weakly dispersive quasiparticle band has been observed directly with an energy dispersion of 4 meV by photoemission, implying the existence of weak hybridization between the f electrons and conduction electrons. The hybridization is further confirmed by the formation of the hybridization gap revealed by temperature-dependent scanning tunneling spectroscopy. Moreover, we find the hybridization strength in CeIn3 is much weaker than that in the more two-dimensional compounds CeCoIn5 and CeIrIn5. Our results may be essential for the complete microscopic understanding of this important compound and the related heavy-fermion systems.