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First-principles calculations of transport coefficients in Weyl semimetal TaAs

This paper presents first-principles calculations of charge and heat transport coefficients in the Weyl semimetal TaAs using density functional perturbation theory and an iterative Boltzmann Transport Equation approach, demonstrating excellent agreement with experimental electrical conductivity while highlighting the method's capability to handle time-reversal symmetry breaking and the strong dependence of transport properties on carrier concentration.

Original authors: Guillaume E. Allemand, Matteo Giantomassi, Matthieu J. Verstraete

Published 2026-10-30

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CC BY 4.0

Original authors: Guillaume E. Allemand, Matteo Giantomassi, Matthieu J. Verstraete

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast landscape of modern materials science, there exists a special class of crystals where electrons do not behave like the heavy, sluggish particles we encounter in ordinary wires. Instead, these electrons act as if they have no mass at all, zipping through the material with extraordinary speed and agility. This unusual behavior occurs in a group of substances known as Weyl semimetals. To understand why this matters, imagine a highway where cars can move without ever hitting a bump or slowing down for traffic; in these materials, the electrons flow with similarly high efficiency. This property makes them fascinating for fundamental physics, but also incredibly promising for future technology, particularly in the field of thermoelectrics. Thermoelectric devices are capable of turning waste heat directly into electricity, or using electricity to create cooling, offering a way to power sensors or recover energy from hot surfaces. The challenge for scientists has always been to predict exactly how well these exotic materials perform in real-world conditions, a task that requires peering into the quantum mechanical rules that govern how electrons interact with the vibrating atoms of the crystal.

A team of researchers set out to solve this puzzle for a specific material called tantalum arsenide, which was the first of these Weyl semimetals to be confirmed in a laboratory. Rather than relying on simplified guesses or approximations that often fail for metals, the team performed a rigorous, first-principles calculation. This means they started with nothing but the fundamental laws of physics and the known arrangement of atoms in the crystal, then used powerful computers to simulate how the electrons and the vibrating atoms interact. They mapped out the energy levels of the electrons and the frequencies at which the atoms vibrate, creating a detailed digital twin of the material. With this foundation, they calculated how heat and electricity move through the crystal, specifically looking at how the electrons scatter off the vibrating atoms, a process that determines how easily current can flow.

The researchers compared three different ways of solving the complex equations that describe this movement. Two of these methods are standard shortcuts that assume the electrons relax back to a calm state at a single, average speed. The third method, which the team refined and applied here, is a more demanding, step-by-step approach that accounts for the messy reality of electrons constantly bumping into one another and the lattice. They found that for tantalum arsenide, the simpler shortcuts actually work quite well, provided the chemical environment is described accurately. However, the more rigorous method offered a crucial advantage: it allowed them to calculate two specific properties, the Seebeck coefficient and the Peltier coefficient, without forcing them to be mathematically identical, a constraint that usually applies only when the material is not magnetic. This flexibility is vital for studying materials that break time-reversal symmetry, opening the door to understanding magnetic versions of these exotic crystals.

When the team compared their simulation results to actual measurements taken from real samples of tantalum arsenide, the results were a mix of striking success and instructive discrepancy. For the ability to conduct electricity along the horizontal direction of the crystal, their calculations matched the experimental data almost perfectly. However, for the vertical direction, their model predicted a conductivity that was higher than what was measured in the lab. The researchers suspect this difference arises because the real samples they compared against likely had a different concentration of extra electrons than the perfect, idealized crystal in their simulation. This highlights a common challenge in the field: the tiny, unintentional variations in how a crystal is grown can significantly alter its electrical properties.

The study also shed light on how the material handles heat and voltage. The calculated ability to generate a voltage from a temperature difference, known as the Seebeck coefficient, was found to be of the same general size as what experiments show, but the precise behavior at low temperatures depended heavily on how many extra electrons were present in the sample. Perhaps most notably, the team discovered that a long-standing rule of thumb in physics, which usually links electrical conductivity to thermal conductivity, breaks down in this material. Between temperatures of roughly 150 Kelvin and 350 Kelvin, the relationship between how well the material carries electricity and how well it carries heat is severed. This finding suggests that Weyl semimetals like tantalum arsenide possess unique thermal properties that could be exploited for more efficient energy conversion devices, provided scientists can better control the precise doping levels in the crystals they create.

Technical Summary: First-Principles Calculations of Transport Coefficients in Weyl Semimetal TaAs

Problem Statement
The transport properties of topologically non-trivial materials, specifically Weyl semimetals (WSMs), are of significant interest for both fundamental physics and thermoelectric applications. While experimental signatures of topology, such as the chiral anomaly, have been observed, theoretical characterization often relies on approximations that fail to capture the subtleties of low-energy scattering near the Fermi level. Previous theoretical studies on the prototypical WSM, Tantalum Arsenide (TaAs), have either neglected transport entirely or utilized the constant relaxation time approximation (cRTA) to solve the Boltzmann Transport Equation (BTE). The cRTA is known to be inadequate for metals as it assumes a momentum-independent scattering time, failing to account for the detailed electron-phonon coupling (EPC) and specific band dispersion effects inherent to WSMs.

Methodology
This study presents a fully first-principles investigation of charge and heat transport in TaAs using the ABINIT software suite. The approach integrates Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) to determine the equilibrium geometry, ground-state electronic structure, and phonon dispersion. Crucially, the authors calculate electron-phonon coupling matrix elements ( $g_{mn\nu}$ ) to derive transport coefficients by solving the linearized BTE without the cRTA.

Three distinct methodologies are compared:

Self-Energy Relaxation Time Approximation (SERTA): Calculates scattering rates using Fermi's golden rule, corresponding to the imaginary part of the Fan-Migdal self-energy. This approach ignores most back-scattering processes.
Momentum Relaxation Time Approximation (MRTA): A refinement of SERTA that partially accounts for back-scattering by weighting the scattering rate with a factor dependent on the velocity change.
Iterative Boltzmann Transport Equation (IBTE): A more rigorous approach that explicitly includes both "in" and "out" electron-phonon scattering terms. The authors implement an extension of the IBTE formalism to solve for transport under simultaneous thermal and electrical potential gradients. This involves deriving additional equations to determine the distribution function corrections ( $\delta f$ ) linear in the electric field ( $E$ ) and temperature gradient ( $\nabla T$ ).

The calculations employ fully-relativistic norm-conserving GGA-PBE pseudopotentials with spin-orbit coupling. To ensure accuracy in the transport coefficients, the authors utilize a star-function interpolation method to generate dense $q$ -point grids (up to $64 \times 64 \times 64$ ) for scattering potentials and filter the $k$ -point grid to focus on states within a 0.25 eV window around the Fermi level.

Key Contributions

First-Principles Transport in TaAs: The paper provides a comprehensive calculation of electrical conductivity ( $\sigma$ ), Seebeck coefficient ( $S$ ), electronic thermal conductivity ( $\kappa_{el}$ ), and the Peltier coefficient ( $\Pi$ ) for TaAs, moving beyond the limitations of the cRTA.
Methodological Extension: The authors derive and implement an additional equation within the IBTE framework necessary to fully solve for transport under both thermal and electrical gradients. This allows for the explicit calculation of both $S$ and $\Pi$ without imposing Onsager reciprocity ( $L_{12} = L_{21}$ ) a priori, a feature particularly relevant for systems breaking time-reversal symmetry (e.g., magnetic materials).
Validation of Approximations: The study demonstrates that for TaAs, provided the chemical potential is treated accurately, the SERTA and MRTA approximations yield results similar to the more computationally expensive iterative IBTE solution.
Doping Sensitivity Analysis: The work highlights the strong dependence of transport coefficients, particularly the Seebeck coefficient, on carrier concentration (doping levels), explaining discrepancies between theory and experiment.

Results

Electrical Conductivity: The calculated in-plane conductivity ( $\sigma_{xx}$ ) shows excellent agreement with experimental data from Xiang et al. and Huang et al. However, the out-of-plane conductivity ( $\sigma_{zz}$ ) is overestimated by the theory, particularly at low temperatures. The authors attribute this discrepancy likely to differences in experimental carrier concentrations rather than a failure of the theoretical model, noting that the intrinsic anisotropy predicted by the band structure is insufficient to explain the magnitude of the experimental anisotropy.
Seebeck Coefficient: The theoretical Seebeck coefficients are of the same order of magnitude as experimental values. The study finds that the low-temperature behavior of $S$ is highly sensitive to the doping level. The calculated $S$ becomes negative below $\sim 200$ K, a feature dependent on the specific carrier concentration assumed.
Onsager Reciprocity and Wiedemann-Franz Law: The iterative method reveals that Onsager reciprocity is not automatically imposed in the full IBTE solution, serving as a test for numerical convergence in time-reversal symmetric systems like TaAs. Furthermore, the results indicate that the Wiedemann-Franz relation is strongly broken in TaAs within the temperature range of approximately 150 K to 350 K.
Hall Coefficient: Calculations of the Hall coefficient ( $R_H$ ) using the IBTE and cRTA (via BoltzTrap2) suggest that TaAs is relatively isotropic in both $\sigma$ and $R_H$ within the GGA framework. The strong anisotropy observed in experiments is likely due to natural doping variations or specific band structure details not fully captured by the current GGA-DFT approach.

Significance
The paper establishes a robust first-principles framework for predicting thermoelectric transport in topological semimetals, demonstrating that accurate treatment of electron-phonon scattering is essential for quantitative agreement with experiment. By validating that simpler approximations (SERTA/MRTA) can suffice for TaAs when chemical potential is accurate, the work offers a pathway for efficient screening of thermoelectric materials. Additionally, the ability to decouple $S$ and $\Pi$ calculations and handle time-reversal symmetry breaking extends the applicability of these methods to magnetic topological materials. The findings underscore that discrepancies between theory and experiment in WSMs often stem from sample-specific doping levels rather than fundamental flaws in the transport theory.

Technical Summary: First-Principles Calculations of Transport Coefficients in Weyl Semimetal TaAs

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