Optical conductivity of the Weyl semimetal NbP

David Neubauer, Alexander Yaresko, Weiwu Li, Anja Löhle, Ralph Hübner, Micha B. Schilling, Chandra Shekhar, Claudia Felser, Martin Dressel, and Artem V. Pronin

Phys. Rev. B 98, 195203 – Published 7 November 2018

Abstract

The optical properties of (001)-oriented NbP single crystals have been studied in a wide spectral range from 6 meV to 3 eV from room temperature down to 10 K. The itinerant carriers lead to a Drude-like contribution to the optical response; we can further identify two pronounced phonon modes and interband transitions starting already at rather low frequencies. By comparing our experimental findings to the calculated interband optical conductivity, we can assign the features observed in the measured conductivity to certain interband transitions. In particular, we find that transitions between the electronic bands spilt by spin-orbit coupling dominate the interband conductivity of NbP below 100 meV. At low temperatures, the momentum-relaxing scattering rate of itinerant carriers in one of the conduction channels is very small, leading to mesoscopic (hundreds of nanometers) characteristic length scales for momentum relaxation.

Received 26 March 2018

DOI:https://doi.org/10.1103/PhysRevB.98.195203

Physics Subject Headings (PhySH)

Optical conductivity Topological phases of matter

Topological materials Weyl semimetal

Reflectivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

David Neubauer¹, Alexander Yaresko², Weiwu Li¹, Anja Löhle¹, Ralph Hübner^1,3, Micha B. Schilling¹, Chandra Shekhar⁴, Claudia Felser⁴, Martin Dressel¹, and Artem V. Pronin¹

¹1. Physikalisches Institut, Universität Stuttgart, 70569 Stuttgart, Germany
²Max-Planck-Institut für Festkörperforschung, Heisenbergstr. 1, 70569 Stuttgart, Germany
³Biomedical Chemistry, Department of Clinical Radiology and Nuclear Medicine, Medical Faculty Mannheim of Heidelberg University, 68167 Mannheim, Germany
⁴Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany

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Vol. 98, Iss. 19 — 15 November 2018

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Images

Figure 1
Temperature-dependent (001)-plane dc resistivity of the NbP sample used in the optical measurements. The inset shows dc conductivity.
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Figure 2
(a) Optical reflectivity, real parts of the (b) optical conductivity and (c) dielectric permittivity of NbP at selected temperatures between $T = 10$ and 300 K; note the logarithmic frequency scale. The inset (d) shows a simple fit of the low-energy $σ (ν)$ at $T = 10 K$ by the sum of two Drude terms (narrow and broad) and two Lorentzians centered at 250 and $500 {cm}^{- 1}$ , which mimic interband transitions. The inset (e) displays the phonon modes in $σ (ν)$ on an enlarged frequency scale. The dashed red line corresponds to a fit of the features at $T = 10 K$ by two narrow Lorentzians centered at 336 and $370 {cm}^{- 1}$ , respectively.
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Figure 3
Interband optical conductivity of NbP calculated with (red line) and without (blue line) SOC and the total experimental NbP conductivity at 10 K (black line). Intraband (Drude) contributions to the conductivity are not included in the computations. Inset shows same sets of data on a broader photon energy scale (0–3 eV). All spectra are for the (001)-plane response.
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Figure 4
(a), (b) Band structure of NbP along selected lines in the BZ with allowed transitions shown as colored vertical lines. The thickness of the lines is proportional to the transition probability. (c) Calculated contributions to the interband conductivity from transitions between different pairs of bands crossing $E_{F}$ , as indicated, and the total calculated interband conductivity of NbP. (d) Contribution to $σ_{20 \to 21} (ω)$ from the transitions within the small volumes in $k$ -space, enclosing the W2 Weyl points (red solid line, see text for details), in comparison with the total $σ_{20 \to 21} (ω)$ (dashed green line). The arrow indicates a kink, which corresponds to the point, where the chiral Weyl bands merge.
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Figure 5
(a) Fermi surface cross sections by $k_{y} = 0$ plane. Small black circles illustrate integration volumes around Weyl points. (b) BZ of NbP. Weyl points from the W1 set are situated near the S point, while the points from the W2 set are close to the N–M line.
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Figure 6
Low-frequency portion of the real part of NbP optical conductivity at 10 K and assignment of the observed features to different absorption mechanisms, as discussed in the course of this paper. Note that the contributions of these mechanisms are shown schematically; for example, the scattering rate of the broad Drude mode is ill defined.
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