Fermi surface of the Weyl type-II metallic candidate ${\mathrm{WP}}_{2}$

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Fermi surface of the Weyl type-II metallic candidate ${WP}_{2}$

R. Schönemann, N. Aryal, Q. Zhou, Y.-C. Chiu, K.-W. Chen, T. J. Martin, G. T. McCandless, J. Y. Chan, E. Manousakis, and L. Balicas

Phys. Rev. B 96, 121108(R) – Published 11 September 2017

Abstract

Weyl type-II fermions are massless quasiparticles that obey the Weyl equation and which are predicted to occur at the boundary between electron and hole pockets in certain semimetals, i.e., the $({W, Mo) (Te, P)}_{2}$ compounds. Here, we present a study of the Fermi surface of ${WP}_{2}$ via the Shubnikov-de Haas (SdH) effect. Compared to other semimetals, ${WP}_{2}$ exhibits a very low residual resistivity, i.e., $ρ_{0} ≃ 10 n Ω cm$ , which leads to perhaps the largest nonsaturating magnetoresistivity $[ρ (H)]$ reported for any compound. For the samples displaying the smallest $ρ_{0}, ρ (H)$ is observed to increase by a factor of $2.5 \times 10^{7} %$ under $μ_{0} H = 35$ T at $T = 0.35$ K. The angular dependence of the SdH frequencies is found to be in excellent agreement with the first-principles calculations when the electron and hole bands are shifted by 30 meV with respect to the Fermi level. This small discrepancy could have implications for the predicted topological character of this compound.

Received 13 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.121108

Physics Subject Headings (PhySH)

Electrical conductivity First-principles calculations Hall effect Landau levels Metals Spin-orbit coupling Surface states Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

R. Schönemann^1,*, N. Aryal^1,2, Q. Zhou¹, Y.-C. Chiu¹, K.-W. Chen¹, T. J. Martin³, G. T. McCandless³, J. Y. Chan³, E. Manousakis^1,2, and L. Balicas^1,†

¹National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA
²Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
³The University of Texas at Dallas, Department of Chemistry and Biochemistry, Richardson, Texas 75080, USA

^*schoenemann@magnet.fsu.edu
^†balicas@magnet.fsu.edu

Large magnetoresistance in the type-II Weyl semimetal ${WP}_{2}$

Aifeng Wang (王爱峰), D. Graf, Yu Liu (刘育), Qianheng Du (杜乾衡), Jiabao Zheng (郑佳宝), Hechang Lei (雷和畅), and C. Petrovic

Phys. Rev. B 96, 121107(R) (2017)

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Vol. 96, Iss. 12 — 15 September 2017

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Figure 1
(a) Crystallographic structure and orthorhombic unit cell of $β − {WP}_{2}$ . The W and P atoms are depicted in grey and in red, respectively. (b) Fermi surface of ${WP}_{2}$ , which consists of two pairs of electron (blue) and hole pockets (red) within the first Brillouin zone. (c) Resistivity $ρ$ , from a ${WP}_{2}$ single-crystal having a RRR of 4750, as a function of the temperature $T$ under several field values. The arrows indicate the “turn-on” temperature given by the minimum in $ρ (μ_{0} H, T)$ . (Inset) For this particular sample, $ρ (μ_{0} H)$ exceeds $6 \times 10^{6}$ % under $T = 2$ K and $μ_{0} H = 9$ T. (d) Angular-dependence of the magnetoresistivity at $T = 2 K$ . The field is rotated in a plane perpendicular to the crystallographic $a$ axis where $θ = 0^{\circ}$ corresponds to $H ∥ b axis$ .
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Figure 2
$ρ$ as a function of $μ_{0} H$ for a ${WP}_{2}$ single crystal at $T = 0.35 K$ and for several angles between $θ = 0^{\circ}$ (or $H ∥ b axis)$ and $90^{\circ}$ $(H ∥ a)$ . The amplitude of the oscillatory component superimposed onto $ρ (H)$ , or the SdH-effect, is most pronounced for $μ_{0} H ∥ b$ axis, whereas no oscillation can be resolved for $μ_{0} H ∥ a$ . $ρ (μ_{0} H)$ can be described by a single power law $ρ (H) \propto H^{λ}$ for $μ_{0} H > 0.5 T$ , with $λ = 1.8$ for $H ∥ b$ (red line) and $λ \approx (1.85 \pm 0.05)$ for $θ \neq 0^{\circ}$ .
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Figure 3
(a) $ρ$ as a function of $μ_{0} H ∥ b axis$ for several temperatures. (b) Oscillatory component superimposed onto $ρ$ , after subtraction of the background magnetoresistivity, as a function of ${(μ_{0} H)}^{- 1}$ . (c) Fast Fourier transform (FFT) of the SdH oscillations/signal shown in (b). The observed peaks and their second harmonics are labeled upon identification of the associated Fermi surface sheets. $α$ and $β$ peaks result from cyclotronic orbits on the hole pockets, while $γ$ and $δ$ results from orbits on the electron sheets. Electron and hole sheets are split by the spin-orbit coupling. (d) and (e) Amplitude of the FFT peaks as a function of $T$ where solid lines represent fits to the Lifshitz-Kosevich formalism from which one extracts the effective cyclotron masses.
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Figure 4
SdH frequencies $F$ observed in ${WP}_{2}$ as a function of the angle $θ$ . Markers indicate the position of the peaks observed in the FFT spectra while solid lines depict the angular dependence of the frequencies predicted by the DFT calculations. In (a), the predicted frequencies are shown without a displacement of the Fermi level. (b) Predicted $F (θ)$ after the Fermi level has been shifted to improve the agreement with the experiments, see main text. Colors of markers and lines indicate the associated Fermi surface pockets (shown to the right). Black and red $(α$ and $β)$ represent the frequencies associated with the spin-orbit split electron pockets. Magenta and blue $(γ$ and $δ)$ represent orbits on the hole pockets.
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Physical Review B

covering condensed matter and materials physics

Fermi surface of the Weyl type-II metallic candidate ${WP}_{2}$

R. Schönemann, N. Aryal, Q. Zhou, Y.-C. Chiu, K.-W. Chen, T. J. Martin, G. T. McCandless, J. Y. Chan, E. Manousakis, and L. Balicas

Phys. Rev. B 96, 121108(R) – Published 11 September 2017

Abstract

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Large magnetoresistance in the type-II Weyl semimetal ${WP}_{2}$

Aifeng Wang (王爱峰), D. Graf, Yu Liu (刘育), Qianheng Du (杜乾衡), Jiabao Zheng (郑佳宝), Hechang Lei (雷和畅), and C. Petrovic

Phys. Rev. B 96, 121107(R) (2017)

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Physical Review B

covering condensed matter and materials physics

Fermi surface of the Weyl type-II metallic candidate WP2

R. Schönemann, N. Aryal, Q. Zhou, Y.-C. Chiu, K.-W. Chen, T. J. Martin, G. T. McCandless, J. Y. Chan, E. Manousakis, and L. Balicas

Phys. Rev. B 96, 121108(R) – Published 11 September 2017

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

See Also

Large magnetoresistance in the type-II Weyl semimetal WP2

Aifeng Wang (王爱峰), D. Graf, Yu Liu (刘育), Qianheng Du (杜乾衡), Jiabao Zheng (郑佳宝), Hechang Lei (雷和畅), and C. Petrovic

Phys. Rev. B 96, 121107(R) (2017)

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Fermi surface of the Weyl type-II metallic candidate ${WP}_{2}$

Large magnetoresistance in the type-II Weyl semimetal ${WP}_{2}$