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

TL;DR

The paper presents C-BerryTrans, a C++ tool that directly computes Berry-curvature–driven transport properties from WIEN2k outputs via a Kubo-like framework to obtain $σ_{μν}^{\mathrm{AHC}}$ and $α_{μν}^{\mathrm{ANC}}$. It emphasizes an interpolation-free, first-principles approach with OpenMP parallelization and binary storage of band-resolved $Ω$, enabling rapid post-processing over ranges of temperature $T$ and chemical potential $μ$ for high-throughput materials screening. The method is validated on Fe, Fe$_3$Ge, Pd, Fe$_3$Al, and Co$_2$FeAl, with results for AHC and ANC in good agreement with literature, demonstrating accuracy and scalability. Overall, C-BerryTrans provides a practical, high-accuracy workflow for exploring $Ω$-driven transverse transport phenomena directly from DFT outputs, augmenting materials discovery pipelines.

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., $σ_{μν}^{AHC}$ and anomalous Nernst conductivity (ANC) i.e., $α_{μν}^{ANC}$. The code directly extracts eigenvalues and momentum-matrix elements from WIEN2k calculations and evaluates the Berry curvature ($\boldsymbolΩ$) using a Kubo-like formalism. For computational efficiency, C-BerryTrans parallelizes $\boldsymbolΩ$ 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 ($μ$) 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 $σ_{xy}^{AHC}$ is obtained to be $\sim$775 ($\sim$744) $S/cm$ at 0 (300) K. In case of Fe$_3$Ge, the calculated value of $σ_{xy}^{AHC}$ is found to be 311 $S/cm$ at the room temperature. Nextly, for Co$_2$FeAl, the magnitude of computed value of $σ_{xy}^{AHC}$ at 2 K is found to be $\sim$56 $S/cm$. Next, magnitude of $α_{xy}^{ANC}$ for Pd is obtained to be $\sim$0.97 $AK^{-1}m^{-1}$ at 300 K. For Fe$_3$Al, the maximum magnitude of $α_{xy}^{ANC}$ for $T\leq$500 K is computed as $\sim$2.83 $AK^{-1}m^{-1}$. Lastly, for Co$_2$FeAl, the value of $α_{xy}^{ANC}$ 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 $\boldsymbolΩ$-driven transport phenomena and is well suited for high-throughput materials discovery.

Figures (6)

• Figure 1: Workflow of the C-BerryTrans code showing the sequence of input preparation, $\boldsymbol\Omega$ calculation, and post-processing.
• Figure 2: The screenshots of the various files obtained from the WIEN2k calculations that are needed by the C-berryTrans code for computing the $\boldsymbol\Omega$-driven transverse transport properties.
• Figure 3: $\alpha^{ANC}_{xy}$ as a function of $\omega$ for the respective materials at 300 K. The value of $\omega$ is scaled with respect to Fermi energy.
• Figure 4: The black (red) curve represents the $\sigma_{xy}^{AHC}$ vs $\omega$ for respective materials at 0 K (300 K). The $\omega$ is scaled with respect to Fermi energy.
• Figure 5: $\sigma_{xy}^{AHC}$ vs $\omega$ for Co$_2$FeAl at 2 K. The $\omega$ is scaled with respect to Fermi energy.