C-BerryTrans: A C++ code for first-principles calculation of Berry-curvature-driven anomalous Hall and Nernst conductivities

Abstract

We present C-BerryTrans, a C++ code designed for first-principles calculations of Berry-curvature-driven transverse transport properties, namely the anomalous Hall conductivity (AHC) i.e., $\sigma_{\mu \nu}^{AHC}$ and anomalous Nernst conductivity (ANC) i.e., $\alpha_{\mu \nu}^{ANC}$. The code directly extracts eigenvalues and momentum-matrix elements from WIEN2k calculations and evaluates the Berry curvature ($\boldsymbol\Omega$) using a Kubo-like formalism. For computational efficiency, C-BerryTrans parallelizes $\boldsymbol\Omega$ evaluation over k-points using OpenMP and stores band-resolved curvature in binary format. This design enables rapid post-processing of AHC and ANC over a wide range of temperatures and chemical potentials ($\mu$) in a single run. The code has been benchmarked on well-studied ferromagnetic materials (Fe, Fe$_3$Ge, Pd, Fe$_3$Al, and Co$_2$FeAl). For Fe, the $\sigma_{xy}^{AHC}$ is obtained to be $\sim$775 ($\sim$744) $S/cm$ at 0 (300) K. In case of Fe$_3$Ge, the calculated value of $\sigma_{xy}^{AHC}$ is found to be 311 $S/cm$ at the room temperature. Nextly, for Co$_2$FeAl, the magnitude of computed value of $\sigma_{xy}^{AHC}$ at 2 K is found to be $\sim$56 $S/cm$. Next, magnitude of $\alpha_{xy}^{ANC}$ for Pd is obtained to be $\sim$0.97 $AK^{-1}m^{-1}$ at 300 K. For Fe$_3$Al, the maximum magnitude of $\alpha_{xy}^{ANC}$ for $T\leq$500 K is computed as $\sim$2.83 $AK^{-1}m^{-1}$. Lastly, for Co$_2$FeAl, the value of $\alpha_{xy}^{ANC}$ is obtained to be $\sim$0.10 $AK^{-1}m^{-1}$ at 300 K. These results show good agreement with previously reported data. With its accuracy, scalability, and user-friendly workflow, C-BerryTrans provides a powerful tool for exploring $\boldsymbol\Omega$-driven transport phenomena and is well suited for high-throughput materials discovery.