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We propose a novel approach to achieve giant AHE in materials with flat bands(FBs). FBs are accompanied by small electronic bandwidths, which consequentlyincreases the momentum separation ($K$) within pair of Weyl points and thus theintegrated Berry curvature. Starting from a simple model with a single pair ofWeyl nodes, we demonstrated the increase of $K$ and AHE by decreasingbandwidth. It is further expanded to a realistic pyrochlore lattice model withcharacteristic double degenerated FBs, where we discovered a giant AHE whilemaximizing the $K$ with nearly vanishing band dispersion of FBs. We identifythat such model system can be realized in both pyrochlore and spinel compoundsbased on first-principles calculations, validating our theoretical model andproviding a feasible platform for experimental exploration.

Giant Anomalous Hall Effect due to Double-Degenerate Quasi Flat Bands