  We propose a novel approach to achieve giant AHE in materials with flat bands
(FBs). FBs are accompanied by small electronic bandwidths, which consequently
increases the momentum separation ($K$) within pair of Weyl points and thus the
integrated Berry curvature. Starting from a simple model with a single pair of
Weyl nodes, we demonstrated the increase of $K$ and AHE by decreasing
bandwidth. It is further expanded to a realistic pyrochlore lattice model with
characteristic double degenerated FBs, where we discovered a giant AHE while
maximizing the $K$ with nearly vanishing band dispersion of FBs. We identify
that such model system can be realized in both pyrochlore and spinel compounds
based on first-principles calculations, validating our theoretical model and
providing a feasible platform for experimental exploration.
