Direct determination of layer anomalous Hall conductivity using uniaxial Wannier functions

We propose a method for computing layer anomalous Hall conductivity (LAHC) in real space by integrating the Fukui-Hatsugai-Suzuki method with hybrid Wannier functions localized along a single axis. To validate the method, we calculated the LAHC of axion-insulating MnBi${}_2$Te${}_4$ and confirmed the agreement between the sum of LAHC on the surface and the surface AHC previously reported. We further applied the method to antiferromagnetic Mn${}_2$Bi${}_2$Te${}_5$ and examined the dependence on the magnetic structure of LAHC, identifying cases with and without axion insulating behavior. This layer-resolved analysis offers a powerful tool for studying topological transport in complex materials, including heterostructures, and may guide the design of future devices based on the anomalous Hall effect with precise layer control.