BoltzTraP2, a program for interpolating band structures and calculating semi-classical transport coefficients

Abstract: BoltzTraP2 is a software package for calculating a smoothed Fourier expression of periodic functions and the Onsager transport coefficients for extended systems using the linearized Boltzmann transport equation. It uses only the band and $k$-dependent quasi-particle energies, as well as the intra-band optical matrix elements and scattering rates, as input. The code can be used via a command-line interface and/or as a Python module. It is tested and illustrated on a simple parabolic band example as well as silicon. The positive Seebeck coefficient of lithium is reproduced in an example of going beyond the constant relaxation time approximation.

• The paper introduces a novel interpolation method that combines quasi-particle energies with intra-band momentum matrix elements to boost accuracy in transport coefficient calculations.
• The tool employs Fourier expansions and derivative information to achieve smoother band structure interpolations compared to earlier approaches.
• BoltzTraP2 features a modular design with a user-friendly API and high-performance C++ backend, facilitating integration into advanced material science simulations.

BoltzTraP2: A Tool for Interpolating Band Structures and Calculating Semi-Classical Transport Coefficients

The paper presents the development and application of BoltzTraP2, a computational tool designed to calculate transport coefficients by solving the linearized Boltzmann transport equation. This tool implements a method to interpolate band structures using Fourier expansions, a critical element for accurately determining electronic properties in solid-state materials. The primary novelty of BoltzTraP2 rests in its ability to utilize both quasi-particle energies and intra-band momentum matrix elements to achieve interpolation, thereby enhancing the program's accuracy over its predecessors.

Core Methodology

BoltzTraP2 builds upon the original BoltzTraP's interpolation scheme instantiated by minimizing roughness functions subject to constraints ensuring calculated quasi-particle energies are exactly reproduced. This approach is refined in BoltzTraP2 by including derivative information from intra-band momentum matrix elements, which allows for a smoother and more precise interpolation of band structures. These enhancements are targeted towards making the program more suitable for beyond-Kohn-Sham methods that usually require finer gradients for accurate results.

Numerical Implementations and Interfaces

The software is constructed using Python 3, with core computational functionalities written in C++11 to optimize performance. High-level operations are powered by standard numerical libraries such as NumPy and SciPy, while computationally expensive tasks leverage fast Fourier transform (FFT) libraries like FFTW. Its user-friendly design offers both a command-line interface for standalone computations and a modular Python API for integration into automated workflows or custom simulations.

Applications and Performance

BoltzTraP2 has been applied to several canonical materials to verify its efficacy. The paper demonstrates calculations on silicon and lithium, showcasing the program's ability to recreate transport properties using finer interpolation grids for quasi-particle energies. For instance, the capability to incorporate state-dependent relaxation times in bcc-lithium calculations demonstrates how BoltzTraP2 can move beyond the constant relaxation time approximation, which had previously limited similar computational frameworks.

Implications and Future Prospects

The ability to finely interpolate band structures and calculate transport properties reliably opens numerous avenues for the application of BoltzTraP2 in material science, particularly in developing thermoelectric materials where electronic transport plays a pivotal role. Additionally, the flexibility to utilize various DFT outputs broadens its usability across different computational material science platforms.

In the theoretical domain, BoltzTraP2 provides a robust framework for testing and verifying predictions from advanced electronic structure methods, contributing to the deeper understanding of solid-state transport phenomena. Future iterations could focus on integrating machine learning techniques to accelerate convergence and enhance prediction accuracy, or expanding functionality to cover more complex scattering mechanisms inherent in advanced materials.

In conclusion, BoltzTraP2 represents a significant step forward in computational tools for material science, providing researchers with an adaptable and efficient method for determining semi-classical transport coefficients necessary for the development of next-generation materials.