Berry-Curvature Activation by Orbital Flux in a Kagome Altermagnet

Abstract

We investigate topological electronic responses in a kagome altermagnetic metal hosting a compensated coplanar $120^\circ$ magnetic texture. Using a minimal tight-binding model containing nearest-neighbor hopping, noncollinear exchange coupling, intrinsic spin--orbit coupling, and a time-reversal-odd loop-current order, we disentangle the magnetic, orbital, and relativistic mechanisms governing the electronic response. The exchange field produces pronounced momentum-dependent spin splitting and spin-polarized Fermi surfaces without generating a net magnetization. Nevertheless, in the absence of loop-current order, a hidden antiunitary symmetry $\mathcal{T}C_{2z}$ enforces vanishing Berry curvature and intrinsic anomalous Hall conductivity, even for finite spin--orbit coupling. A directed imaginary bond order breaks this protection and activates finite Berry curvature and a sizable, strongly filling-dependent Hall response already in the nonrelativistic limit. Spin--orbit coupling subsequently reconstructs the avoided crossings and redistributes the Berry curvature, enhancing or suppressing the Hall response depending on filling. For sufficiently strong loop-current order and spin--orbit coupling, a global gap opens at $n_e=3$, and the Hall conductivity approaches $2e^2/h$, consistent with an occupied-band Chern number of magnitude two. Parameter-space and filling-dependent calculations further demonstrate that the Hall-active regime extends over broad ranges of exchange coupling, spin--orbit coupling, and chemical potential and remains robust against symmetry-preserving longer-range hopping. These results identify orbital-current order as an independent route for converting a Hall-silent kagome altermagnet into an anomalous Hall metal or a gapped topological phase without net magnetization, noncoplanar spin order, or scalar spin chirality.