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

Materials in which atoms are arranged in a pyrochlore lattice have found renewed interest, as, at least theoretically, orbitals on that lattice can form flat bands. However, real materials often do not behave according to theoretical models, which is why there has been a dearth of pyrochlore materials exhibiting flat band physics. Here, we examine the conditions under which ideal "pyrochlore bands" can exist in real materials and how to have those close to the Fermi level. We find that the simple model used in the literature does not apply to the bands at the Fermi level in real pyrochlore materials. However, surprisingly, we find that certain oxide compounds that have oxygen orbitals inside the pyrochlore tetrahedra do exhibit near-ideal pyrochlore bands near the Fermi level. We explain this observation by a generalized tight-binding model, including the oxygen orbitals. We further classify all known pyrochlore materials based on their crystal structure, band structure, and chemical characteristics and propose materials to study in future experiments.