Site Symmetry and Multiorbital Flat Bands on Kagome and Pyrochlore Lattices

Flat bands in electronic band structures are intriguing platforms for strong correlation and topological physics, primarily due to the suppressed kinetic energy of electrons. Various methods have been developed to create flat bands, utilizing lattice geometry or finely tuned parameters. Despite this, the investigation of orbital symmetry in multiorbital materials is a relatively new area of focus. In this work, we propose a site symmetry based systematic approach to emerging multiorbital flat bands in lattices made of corner-connecting motifs such as the kagome and pyrochlore lattices. As a conceptual advance, the one-orbital flat bands are shown to originate as mutual eigenstates of isolated molecular motifs. Further developing the mutual eigenstate method for multiorbitals transforming differently under the site symmetries such as mirror and inversion, we derive multiorbital flat bands from the skew-symmetric interorbital Hamiltonian and introduce an isolated molecule enabled group-theoretic description of the flat band wavefunctions. Realizations of the multiorbital flatbands in relevant materials are shown to be possible under the Slater-Koster formalism. Our findings provide new directions for exploring flatband electronic structures for novel correlated and topological quantum states.