Stable Weyl points, trivial surface states, and particle-hole compensation in ${\mathrm{WP}}_{2}$

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Stable Weyl points, trivial surface states, and particle-hole compensation in ${WP}_{2}$

E. Razzoli, B. Zwartsenberg, M. Michiardi, F. Boschini, R. P. Day, I. S. Elfimov, J. D. Denlinger, V. Süss, C. Felser, and A. Damascelli

Phys. Rev. B 97, 201103(R) – Published 4 May 2018

Abstract

A possible connection between extremely large magnetoresistance and the presence of Weyl points has garnered much attention in the study of topological semimetals. Exploration of these concepts in transition-metal diphosphides ${WP}_{2}$ has been complicated by conflicting experimental reports. Here we combine angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations to disentangle surface and bulk contributions to the ARPES intensity, the superposition of which has plagued the determination of the band structure in ${WP}_{2}$ . Our results show that while the hole- and electronlike Fermi surface sheets originating from surface states have different areas, the bulk-band structure of ${WP}_{2}$ is electron-hole compensated in agreement with DFT. Furthermore, the ARPES band structure is compatible with the presence of at least four temperature-independent Weyl points, confirming the topological nature of ${WP}_{2}$ and its stability against lattice distortions.

Received 11 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.201103

Physics Subject Headings (PhySH)

Magnetoresistance Weyl fermions

Weyl semimetal

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

E. Razzoli^1,2,*, B. Zwartsenberg^1,2, M. Michiardi^1,2,3, F. Boschini^1,2, R. P. Day^1,2, I. S. Elfimov^1,2, J. D. Denlinger⁴, V. Süss³, C. Felser³, and A. Damascelli^1,2,†

¹Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada V6T 1Z4
²Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada V6T 1Z1
³Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
⁴Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*razzoli@physics.ubc.ca
^†damascelli@physics.ubc.ca

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Vol. 97, Iss. 20 — 15 May 2018

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Figure 1
DFT calculations and ARPES intensity maps at $T = 25$ K of ${WP}_{2}$ . (a) Fermi surface sheets from DFT were plotted using xcrysden visualization package [20]. (b) Bulk DFT calculations at $E_{F}$ in the $k_{x} - k_{z}$ plane. Black squares indicate the $k_{F} s$ extracted from the MDC peak position of the ARPES data in (c). (c) ARPES intensity maps at $E_{F}$ in the $k_{x} - k_{z}$ plane at $h ν = 50$ eV. (d) DFT band structure in the $k_{x} - k_{z}$ plane of a ${WP}_{2}$ slab of 18 W planes and 36 P layers, for the relaxed structure. The color scale represents the contribution from the top W layer (surface contribution) and from the layers below (bulk contribution). (e) Bulk band structure along high-symmetry lines [red path in panel (b)]. Black squares indicate the $k_{F}$ extracted from the MDC peak position of the data in (f). (f),(g) ARPES intensity maps along high-symmetry lines for $p$ - and $s$ -polarized light, respectively. MDCs at the $E_{F}$ are shown in the inset. Red (black) vertical lines identify surface (bulk) peaks in the MDCs. (h) Slab DFT band structure along high-symmetry lines.
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Figure 2
(a) ARPES intensity maps at $E_{F}$ in the $k_{x} - k_{y}$ plane measured by tuning the photon energy from 50 to 120 eV. (b) MDC second derivative intensity plot, MDC peak positions for bulk (azure hexagons), and surface bands (pink crosses) of the ARPES data in (a). Bulk-DFT calculations (black lines) are superimposed with the data. Red lines denote the boundaries of the BZ.
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Figure 3
ARPES intensity maps. (a) ARPES intensity map at one of the Weyl points. (a),(b) ARPES intensity maps along $(k_{x}, 4.344, 0)$ for $p$ - and $s$ -polarized incident light, respectively. Inset in (b) is the MDC second derivative intensity plot. (c),(d) ARPES intensity map at the Weyl point along $(0.19, 4.344, k_{z})$ for $p$ - and $s$ -polarized incident light, respectively. (e) ARPES intensity map at the Weyl point along $(0.19, k_{y}, 0)$ for $p$ -polarized incident light. Bulk-DFT calculations at the Weyl point superimposed with the data. (f) ARPES intensity maps at $E_{b} = 400$ meV in the $k_{x} - k_{y}$ plane obtained by tuning the photon energy from 50 to 120 eV. DFT calculations (black and orange lines) are superimposed with the data. Red lines denote the boundaries of the BZ.
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Figure 4
Temperature dependence of ARPES band structure. (a) ARPES intensity maps at $E_{F}$ in the $k_{x} - k_{z}$ plane at $h ν = 50$ eV collected at $T = 150$ K. (b) $T$ -dependent dispersion of bulk-band $μ$ [defined in Fig. 1] close to $\bar{X}$ extracted from MDC peaks. (c)–(g) ARPES intensity maps along $\bar{Γ} - \bar{X}$ for $s$ -polarized light at various temperatures. (h) EDCs at $\bar{Γ}$ as a function of temperature. (i) MDCs along $\bar{Γ} - \bar{X}$ at $E_{F}$ as a function of temperature.
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Physical Review B

covering condensed matter and materials physics

Stable Weyl points, trivial surface states, and particle-hole compensation in ${WP}_{2}$

E. Razzoli, B. Zwartsenberg, M. Michiardi, F. Boschini, R. P. Day, I. S. Elfimov, J. D. Denlinger, V. Süss, C. Felser, and A. Damascelli

Phys. Rev. B 97, 201103(R) – Published 4 May 2018

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Physical Review B

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Stable Weyl points, trivial surface states, and particle-hole compensation in WP2

E. Razzoli, B. Zwartsenberg, M. Michiardi, F. Boschini, R. P. Day, I. S. Elfimov, J. D. Denlinger, V. Süss, C. Felser, and A. Damascelli

Phys. Rev. B 97, 201103(R) – Published 4 May 2018

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Stable Weyl points, trivial surface states, and particle-hole compensation in ${WP}_{2}$