Gate-controllable giant anomalous Hall effect from flat bands in kagome metal CsV3Sb5 nanoflakes.

The giant anomalous Hall effect (AHE) and its correlation with chiral charge order and unconventional superconductivity in topological kagome metals AV3Sb5 (A= K, Rb, and Cs) have attracted great interest. However, the underlying mechanism for the giant AHE remains poorly understood. Here, we show that gate-induced proton intercalations can largely modulate the carrier density of CsV3Sb5 nanoflakes and change the Fermi surface topology from a hole pocket to an electron pocket. Moreover, we first observed the very large AHEs in both hole and electron pockets under the protonic gate, and the giant anomalous Hall conductivity (AHC, above 10^4 ohm^-1 cm^-1) is mainly constrained in a narrow hole-carrier-density window around p=(2.5+/-1.2)*10^22 cm^-3 within the charge density wave (CDW) gap. Meanwhile, shifting the Fermi level across the CDW gap, the AHC can be tuned over more than a decade and exhibits a clear extrinsic-to-intrinsic transition. Assisted by first-principles calculations, we suggest the extrinsic skew scattering of holes in the nearly flat bands with the ferromagnetic fluctuation of V atoms accounts for the giant AHE in CsV3Sb5. Our work enables a global understanding of the giant AHE and further reveals its correlation with chiral charge order in the AV3Sb5 family.