Optical signature of Weyl electronic structures in tantalum pnictides $\mathrm{Ta}Pn$ ($Pn=$ P, As)

Optical signature of Weyl electronic structures in tantalum pnictides $Ta P n$ ( $P n =$ P, As)

Shin-ichi Kimura, Hiroko Yokoyama, Hiroshi Watanabe, Jörg Sichelschmidt, Vicky Süß, Marcus Schmidt, and Claudia Felser

Phys. Rev. B 96, 075119 – Published 10 August 2017

Abstract

To investigate the electronic structure of Weyl semimetals $Ta P n$ ( $P n =$ P, As), optical conductivity $[σ (ω)]$ spectra are measured over a wide range of photon energies and temperatures, and these measured values are compared with band calculations. Two significant structures can be observed: a bending structure at $ℏ ω \sim 85$ meV in TaAs, and peaks at $ℏ ω \sim$ 50 meV (TaP) and $\sim 30$ meV (TaAs). The bending structure can be explained by the interband transition between saddle points connecting a set of $W_{2}$ Weyl points. The temperature dependence of the peak intensity can be fitted by assuming the interband transition between saddle points connecting a set of $W_{1}$ Weyl points. Owing to the different temperature dependence of the Drude weight in both materials, it is found that the Weyl points of TaAs are located near the Fermi level, whereas those of TaP are further away.

Received 24 May 2017

DOI:https://doi.org/10.1103/PhysRevB.96.075119

Physics Subject Headings (PhySH)

Dielectric properties Electrical conductivity Electronic structure Semimetals Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shin-ichi Kimura^1,2,*, Hiroko Yokoyama², Hiroshi Watanabe^1,2, Jörg Sichelschmidt^3,1, Vicky Süß³, Marcus Schmidt³, and Claudia Felser³

¹Graduate School of Frontier Biosciences, Osaka University, Suita 565-0871, Japan
²Department of Physics, Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan
³Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany

^*kimura@fbs.osaka-u.ac.jp

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Vol. 96, Iss. 7 — 15 August 2017

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Figure 1
Temperature-dependent reflectivity $[R (ω)]$ spectra of TaP and TaAs in the energy region of 5–500 meV. The inset shows the $R (ω)$ spectrum of TaAs at 300 K in the whole measured region up to 30 eV.
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Figure 2
(a) Experimentally obtained optical conductivity $[σ (ω)]$ spectra of TaP and TaAs at the temperature of 9 K compared with the spectra obtained from band calculations. The arrows indicate the corresponding peaks between experimental and calculated $σ (ω)$ spectra. (b) Calculated density of states (DOS) of TaP and TaAs. The zero energy corresponds to the Fermi energy ( $E_{F}$ ). The inset shows an enlargement near $E_{F}$ .
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Figure 3
Temperature-dependent optical conductivity $[σ (ω)]$ spectra of TaP and TaAs in the photon energy $ℏ ω$ range below 200 meV. The baseline of each spectrum is shifted by $10^{3} Ω^{- 1} {cm}^{- 1}$ . For TaAs, the dashed lines denote two $ω$ -linear components at $T = 9$ and 300 K, and the dot-dashed line is a guide for the temperature dependence of the bending point. For TaP, the dashed lines are fitted Drude functions and two $ω$ -linear components at $T = 9 K$ . In the figure, the energy of the bending point is assumed to be the same as that of TaAs. Hatched peaks show the remaining $σ (ω)$ spectra given by subtracting the dashed lines from the $σ (ω)$ spectra at 9 K. The sharp peak of TaP (indicated by an arrow) is caused by an optical phonon; this is not discussed in the present paper [31].
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Figure 4
(a) Temperature-dependent Drude parameters of effective carrier density (Drude weight, $N_{D}$ ) and damping factor (inverse relaxation time, $Γ$ ) obtained by the fitting of the $σ (ω)$ spectra of Fig. 3. The solid, dashed, and dot-dashed lines are the calculated carrier densities ( $N_{0}$ ) of TaAs, TaP with $E_{F} = 0 eV$ , and TaP with $E_{F} = - 20 meV$ , respectively, using the calculated DOS in Fig. 2. (b) Temperature-dependent effective mass ( $m_{D} / m_{0} = N_{0} / N_{D}$ ) of TaAs (solid square—solid line), TaP with $E_{F} = 0 meV$ (solid circle—dashed line), and TaP with $E_{F} = - 20 meV$ (open circle—dot-dashed line), derived from the comparison of experimental $N_{D}$ with calculated $N_{0}$ in (a).
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Figure 5
Temperature dependence of peak intensities [effective electron number ( $N_{p}$ )] of TaP and TaAs at around 50 and 30 meV, respectively. The error of $N_{p}$ is less than the symbol size. The dashed and dot-dashed lines are fitting curves assuming the temperature dependence of interband transition expressed by Eq. (3). The obtained parameters are listed in Table 1. Inset: Schematic electronic structure near a set of Weyl points. There are two bands connecting a set of Weyl points, namely, the upper Weyl band (UWB) and the lower Weyl band (LWB). $E_{F}$ and $E_{g}$ are the Fermi energy and the energy difference between LWB and UWB, respectively.
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Figure 6
Band dispersions near the $W_{1}$ (a) and $W_{2}$ (b) Weyl points of TaP (solid lines) and TaAs (dashed lines) along the $k_{x}$ axis. The horizontal axis is normalized by the distance between the $Γ$ and $Σ$ points. The zero energy is $E_{F}$ evaluated from the summation of the electron number. The center coordinates of the figures for TaP and TaAs are (0, $0.9510 (Γ - Σ)$ , 0) and (0, $0.9413 (Γ - Σ)$ , 0) for $W_{1}$ , and (0, $0.5057 (Γ - Σ), 0.5855 (Γ - Z)$ ) and (0, $0.5195 (Γ - Σ), 0.5915 (Γ - Z)$ ) for $W_{2}$ .
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Physical Review B

covering condensed matter and materials physics

Optical signature of Weyl electronic structures in tantalum pnictides $Ta P n$ ( $P n =$ P, As)

Shin-ichi Kimura, Hiroko Yokoyama, Hiroshi Watanabe, Jörg Sichelschmidt, Vicky Süß, Marcus Schmidt, and Claudia Felser

Phys. Rev. B 96, 075119 – Published 10 August 2017

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Physical Review B

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Optical signature of Weyl electronic structures in tantalum pnictides TaPn (Pn= P, As)

Shin-ichi Kimura, Hiroko Yokoyama, Hiroshi Watanabe, Jörg Sichelschmidt, Vicky Süß, Marcus Schmidt, and Claudia Felser

Phys. Rev. B 96, 075119 – Published 10 August 2017

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Optical signature of Weyl electronic structures in tantalum pnictides $Ta P n$ ( $P n =$ P, As)