Symmetry breaking-induced split-off flat bands in quantum materials

Electronic structures of traditional compounds are described by using principal crystallographic structures as input to electronic property calculations. However, “quantum materials” such as transition-metal oxides, possess additional microscopic degrees of freedom (m-DOF) nested within crystallographic phases. Such internal energy lowering m-DOF can encompass configuration of local magnetic or dipole moments, octahedral tilting, Jahn-Teller distortion, bond disproportionation or dimerization, defining local symmetries that are often ignored in XRD-defined global crystallographic “average structures”. Hence using XRD configurations as input to calculate properties can be misleading. Here we study the manner where the introduction of m-DOF into density functional electronic structure calculations of ABO₃ oxides can lead to symmetry breaking (SB), resulting in splitting of narrow flat bands from broad principal bands, which differ from those induced by topological geometry. Inclusion of such m-DOF can transform “false metals” into real insulators with flat bands trapping electrons (LaTiO₃, LaVO₃, CaCrO₃, LaMnO₃) or holes (YNiO₃, CaMnO₃, LaFeO₃, SrBiO₃). We will discuss different m-DOF that induce flat bands with distinct band-edge orbital characters in different quantum materials. Our research enriches the fundamental physics of quantum materials.