Three-dimensional flat band evolution between pyrochlore and perovskite lattices with enhanced anomalous Hall effect

Distinct from the flat band in two dimensions, the three-dimensional (3D) flat band and the corresponding physics have been relatively unexplored. Here, based on tight-binding models, we present a theoretical study of the evolution of the 3D flat band between pyrochlore and perovskite lattices, which are structurally interconvertible through diagonal strain and host double-degenerate flat bands. We discovered the presence of a persistent 3D flat band during the transition, which is stabilized by a robust compact localized state within the preserved kagome plane perpendicular to the diagonal direction. Furthermore, under the influence of spin-orbit coupling and Zeeman field, we can consistently achieve a magnetic Weyl semimetal state during this transition process due to the unique 3D flat band nature. Pairs of Weyl points form near the conserved flat band, leading to a large anomalous Hall conductivity (AHC) peak right at the energy of the flat band. Interestingly, we also observe an enhanced AHC during the transition from pyrochlore to perovskite lattice due to the enlarged momentum separation between Weyl points and the superimposition with another AHC peak from the dispersive Dirac bands.