Recipe for Flat Bands in Pyrochlore Materials: A Chemist's Perspective

Pyrochlore lattices have recently attracted attention as platforms for realizing flat-band physics. In theory, orbitals arranged on the pyrochlore lattice can form dispersionless bands; however, real materials often deviate from this ideal behavior. In this work, we investigate the structural and electronic conditions under which "pyrochlore bands" can appear near the Fermi level in real compounds. We show that the simple model used in the literature does not apply to the bands at the Fermi level in real pyrochlore materials, but surprisingly, a subset of oxide pyrochlores—with oxygen orbitals located inside the tetrahedra—exhibit nearly ideal flat bands close to the Fermi level. Using an extended tight-binding model that includes these oxygen orbitals, we explain their origin and classify known pyrochlore materials, identifying promising candidates for future experimental studies.