Direct observation of nonequivalent Fermi-arc states of opposite surfaces in the noncentrosymmetric Weyl semimetal NbP

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Direct observation of nonequivalent Fermi-arc states of opposite surfaces in the noncentrosymmetric Weyl semimetal NbP

S. Souma, Zhiwei Wang, H. Kotaka, T. Sato, K. Nakayama, Y. Tanaka, H. Kimizuka, T. Takahashi, K. Yamauchi, T. Oguchi, Kouji Segawa, and Yoichi Ando

Phys. Rev. B 93, 161112(R) – Published 20 April 2016

Abstract

We have performed high-resolution angle-resolved photoemission spectroscopy (ARPES) on noncentrosymmetric Weyl semimetal candidate NbP, and determined the electronic states of both Nb- and P-terminated surfaces. We revealed a drastic difference in the Fermi-surface topology between two types of surfaces, whereas the Fermi arcs on both surfaces are likely terminated at the surface projection of the same bulk Weyl nodes. A comparison of the ARPES data with our first-principles band calculations suggests a notable difference in the electronic structure at the Nb-terminated surface between theory and experiment. The present result opens a platform for realizing exotic quantum phenomena arising from the unusual surface properties of Weyl semimetals.

Received 6 October 2015
Revised 5 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.161112

Physics Subject Headings (PhySH)

Weyl fermions

Semimetals Topological materials

Angle-resolved photoemission spectroscopy First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Souma¹, Zhiwei Wang², H. Kotaka², T. Sato³, K. Nakayama³, Y. Tanaka³, H. Kimizuka³, T. Takahashi^1,3, K. Yamauchi², T. Oguchi², Kouji Segawa⁴, and Yoichi Ando^2,5

¹WPI Research Center, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
²Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan
³Department of Physics, Tohoku University, Sendai 980-8578, Japan
⁴Department of Physics, Kyoto Sangyo University, Kyoto 603-8555, Japan
⁵Institute of Physics II, University of Cologne, Köln 50937, Germany

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Vol. 93, Iss. 16 — 15 April 2016

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Images

Figure 1
(a) Schematics of the Dirac-cone and Fermi-arc surface states at opposite surfaces of the topological insulator (top) and WSM (bottom), respectively. (b) Left: Crystal structure of NbP with two possible cleaving planes (arrows). Right: Side view of the crystal structure. (c) Bulk and surface BZs of NbP. The green shaded area is a mirror plane which is projected onto the $\bar{Γ} \bar{X}$ line, and red and green dots highlight the Weyl nodes (W1, W2). (d), (e) Calculated bulk-band dispersion along cuts crossing W1 and W2, respectively. (f), (g) ARPES spectrum measured at $h ν = 200$ eV for the Nb- and P-terminated surfaces, respectively. (h), (i) Second derivative of ARPES intensity along $\bar{Γ} \bar{X}$ cut for the Nb- and P-terminated surfaces, respectively. (j), (k) Calculated band structure for a slab of 7-unit-cell NbP, for Nb- and P-terminated surfaces, respectively. The radius of circles represents the surface spectral weight. The projection of bulk bands is shown by the yellow shade. The gray shaded area is outside of the band plots in (h) and (i).
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Figure 2
(a) Experimental FS around $\bar{X}$ for the P-terminated surface. Fermi wave vectors ( $k_{F}$ 's) are plotted with gray dots. The projection of Weyl nodes estimated from the present experiment is also indicated by circles and diamonds. (b) Second-derivative intensity of the EDCs at $E_{B} = E_{F}$ , 0.1 and 0.2 eV, measured with vertically polarized 21-eV photons. The polarization vector of lights is indicated by the arrow. Experimental FSs are overlaid for $E_{B} = E_{F}$ . (c) Same as (b) but measured with circularly polarized 50-eV photons. (d) Second-derivative intensity in cuts A–C, measured with $h ν = 21$ eV (top) and 50 eV (bottom). The dashed curves are a guide to the eyes to trace the band dispersions. (e) Second-derivative intensity at $E_{B} = 0.1$ eV measured with horizontally polarized lights of $h ν = 21$ eV. (f) Calculated FS for the P-terminated surface around $\bar{X}$ . The surface weight is reflected by the gradual color scale. The $k$ window is the same as (a).
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Figure 3
(a), (b) ARPES-intensity mapping at $E_{F}$ and second-derivative intensity of the EDCs for the Nb-terminated surface, respectively, plotted as a function of $k_{x}$ and $k_{y}$ measured with $h ν = 50$ eV. (c) Experimental FS for the Nb-terminated surface. $k_{F}$ points extracted by tracing the band dispersion are plotted with gray dots. The projection of Weyl nodes estimated from the present experiment is also indicated by circles and diamonds. (d) Second-derivative intensity plots of the EDCs at $E_{B} = 0.1$ and 0.3 eV. (e) Second-derivative intensity along cuts A–H in (c). (f) Calculated FS for the Nb-terminated surface.
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Figure 4
(a) (Left) crystal structure of NbP and (right) schematics of experimental FS around $\bar{X}$ for the opposite surfaces. Bulk Weyl nodes are illustrated by circles. The arrows indicate the Berry curvature. (b) Direct comparison of experimental FS between Nb-terminated (blue) and P-terminated (red) surfaces. The projection of Weyl nodes W2 at the intersection of FSs for opposite surfaces is overlaid by solid circles, whereas other intersections are shown by open circles. Possible Weyl pairs W1 are also indicated with diamonds. (c), (d) Schematics of Fermi arcs (solid curves) and trivial FSs (gray dashed curves) for the P- and Nb-terminated surfaces, respectively. The closed loop enclosing three Weyl nodes is indicated by a green dashed rectangle. The arrows indicate the crossing points of Fermi arcs and trivial FSs.
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