Dichotomy of flat bands in the van der Waals ferromagnet Fe$_5$GeTe$_2$

Quantum materials with bands of narrow bandwidth near the Fermi level represent a promising platform for exploring a diverse range of fascinating physical phenomena, as the high density of states within the small energy window often enables the emergence of many-body physics. On one hand, flat bands can arise from strong Coulomb interactions that localize atomic orbitals. On the other hand, quantum destructive interference can quench the electronic kinetic energy. Although both have a narrow bandwidth, the two types of flat bands should exhibit very distinct spectral properties arising from their distinctive origins. So far, the two types of flat bands have only been realized in very different material settings and chemical environments, preventing a direct comparison. Here, we report the observation of the two types of flat bands within the same material system--an above-room-temperature van der Waals ferromagnet, Fe$_{5-x}$GeTe$_2$, distinguishable by a switchable iron site order. The contrasting nature of the flat bands is also identified by the remarkably distinctive temperature-evolution of the spectral features, indicating that one arises from electron correlations in the Fe(1) site-disordered phase, while the other geometrical frustration in the Fe(1) site-ordered phase. Our results therefore provide a direct juxtaposition of the distinct formation mechanism of flat bands in quantum materials, and an avenue for understanding the distinctive roles flat bands play in the presence of magnetism, topology, and lattice geometrical frustration, utilizing sublattice ordering as a key control parameter.