Moiré superlattice on the surface of Sm filmsdriven by surface valence transition

Abstract Rare earth (RE) metals exhibit unique mixed-valence behavior due to their $4f$ electronic configurations. In this study, we investigate the surface electronic structure and valence-mixing phenomena in samarium (Sm) films using molecular beam epitaxy (MBE), scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), and density functional theory (DFT). A natural moiré superlattice emerges on the Sm film surface as a result of lattice mismatch between the surface divalent Sm$^{2+}$ and bulk trivalent Sm$^{3+}$ layers. ARPES reveals the flat $f$ electron bands corresponding to Sm$^{3+}$ and Sm$^{2+}$ states, particularly demonstrating the partial coexistence of bulk Sm$^{2+}$ flat bands. The dispersive $s$-$d$ electron bands and surface-condition-induced band shifts are observed and analyzed through both STM and ARPES measurements. Our work provides direct evidence for the formation of moiré pattern on the surface of Sm films due to its unique surface valence transition, therefore paving the way for a new method to generate moiré superlattice in correlated $4f$-electron systems.