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Model for charge carrier spectra in topological semimetals of the TaAs family

¹B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine, Kharkiv 61103, Ukraine
²Institute of Low Temperature and Structure Research, Polish Academy of Sciences, 50-422 Wrocław, Poland

Phys. Rev. B 113, 045111 – Published 6 January, 2026

DOI: https://doi.org/10.1103/j554-xyky

Abstract

We propose a four-band model describing the electron energy spectra near the Weyl points in the topological semimetals of the TaAs family (TaAs, TaP, NbAs, NbP). This model takes into account the fact that these Weyl points result from the band-contact lines which would exist in the mirror-reflection planes of these materials if the spin-orbit interaction were absent in them. Within this model, we obtain conditions for the existence of the Weyl points, determine their positions in the Brillouin zone, and derive the explicit formula for dispersion of the bands along the straight line connecting the two close Weyl points with opposite topological charges. Using NbP as an example, the values of the parameters defining the model spectrum are found. The obtained results show that for the semimetals of the TaAs family, the charge-carriers spectrum in the vicinity of the two close Weyl points can be analyzed without complex band-structure calculations.

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References (24)

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An analysis shows that the condition $m_{1}^{2} + m_{5}^{2} + m_{6}^{2} = m_{2}^{2}$ , which vanishes $Y_{min}$ , does not lead to the appearance of the Weyl points.
Equations (5)– (7) are invariant under the following two transformations of $m_{i}$ : (i) $m_{4} \to - m_{4}$ and $m_{6} \to - m_{6}$ , (ii) $m_{6} \to - m_{6}, m_{3} \to - m_{3}, m_{2} \to - m_{2}$ , and $m_{1} \to - m_{1}$ . Therefore, without the loss in generality, we may set $m_{6} > 0, m_{4} > 0$ .
Equations (5)– (7) remain invariant if the signs of $m_{1}$ and $d_{z}$ (i.e., $a^{'}$ ) change simultaneously, and so without the loss in generality, we assume below that $a^{'}$ is always positive, whereas $m_{1}$ can have either sign.
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If $p_{y} = p_{y}^{w}, p_{⊥} = p_{⊥}^{W}$ , then Eq. (B1) fails for the crossing bands ( $i = 2$ , 3), since one has $(\partial F / \partial ε) = 0$ for these bands. In this case, Eq. (A6) has to be used for the calculation of $Δ ε_{i}$ with $i = 2$ , 3.

Phys. Rev. B 113, 045111– Published 6 January, 2026

Vol. 113, Iss. 4 — 15 January 2026

Received 14 October 2025
Accepted 9 December 2025

DOI: https://doi.org/10.1103/j554-xyky

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Model for charge carrier spectra in topological semimetals of the TaAs family

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