Three-dimensional flat bands in pyrochlore metal CaNi 2 .

Electronic flat-band materials host quantum states characterized by a quenched kinetic energy. These flat bands are often conducive to enhanced electron correlation effects and emergent quantum phases of matter 1 . Long studied in theoretical models 2-4 , these systems have received renewed interest after their experimental realization in van der Waals heterostructures 5,6 and quasi-two-dimensional (2D) crystalline materials 7,8 . An outstanding experimental question is if such flat bands can be realized in three-dimensional (3D) networks, potentially enabling new materials platforms 9,10 and phenomena 11-13 . Here we investigate the C15 Laves phase metal CaNi 2 , which contains a nickel pyrochlore lattice predicted at a model network level to host a doubly-degenerate, topological flat band arising from 3D destructive interference of electronic hopping 14,15 . Using angle-resolved photoemission spectroscopy, we observe a band with vanishing dispersion across the full 3D Brillouin zone that we identify with the pyrochlore flat band as well as two additional flat bands that we show arise from multi-orbital interference of Ni d-electrons. Furthermore, we demonstrate chemical tuning of the flat-band manifold to the Fermi level that coincides with enhanced electronic correlations and the appearance of superconductivity. Extending the notion of intrinsic band flatness from 2D to 3D, this provides a potential pathway to correlated behaviour predicted for higher-dimensional flat-band systems ranging from tunable topological 15 to fractionalized phases 16 .