$\textit{PY-BerryAHC}$: An $\textit{ab-initio}$ python 3 code to calculate Berry Curvature dependent Anomalous Hall Conductivity in any material

Abstract

The anomalous Hall conductivity (AHC) in materials has long been a topic of debate. Studies reveal that AHC originates from the Berry curvature ($\boldsymbol\Omega$) of Bloch states. Accurate computation of AHC is crucial for predicting material properties and guiding experimental studies in topological and spintronic applications. Traditional approaches often rely on wannier interpolation, which can introduce inaccuracies and computational overhead. Also, reliability of the wannierization technique becomes questionable when the bands are highly entangled and dispersive. This demands the calculation of AHC using the $\textit{first-principle}$ approach. Here, we present $\textit{PY-BerryAHC}$, a Python 3 based code that directly computes $\boldsymbol\Omega$ and AHC using WIEN2k output. Since, WIEN2k employs an all-electron full-potential linearized augmented plane wave method, $\textit{PY-BerryAHC}$ provides highly accurate AHC results. The code efficiently handles large $\textbf{k}$-grids by parallelizing $\boldsymbol\Omega$ computations over $\textbf{k}$-points. Also, it stores band-resolved $\boldsymbol\Omega$ in a binary file, thereby greatly reducing the required storage memory and allowing fast post-processing to compute AHC. $\textit{PY-BerryAHC}$ has been validated on well-known materials exhibiting AHC. These include- Fe, Fe$_3$Ge & Co$_2$FeAl. At 300 K, the calculated magnitude of $\sigma_{xy}$ for Fe & Fe$_3$Ge is found to be 744 $S/cm$ & 311 $S/cm$, respectively. For Co$_2$FeAl, the magnitude of $\sigma_{xy}$ is obtained to be $\sim$56 $S/cm$ and is found to be constant with the change in temperature from 0-300 K. These results are in good agreement with previously reported theoretical and experimental data. This ensures the accuracy, reliability and efficiency of the code. The code is also provided with a post-processing tool to visualize $\boldsymbol\Omega$.