Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide

Journal name:
Nature Physics
Volume:
11,
Pages:
748–754
Year published:
DOI:
doi:10.1038/nphys3437
Received
Accepted
Published online

Abstract

Three types of fermions play a fundamental role in our understanding of nature: Dirac, Majorana and Weyl. Whereas Dirac fermions have been known for decades, the latter two have not been observed as any fundamental particle in high-energy physics, and have emerged as a much-sought-out treasure in condensed matter physics. A Weyl semimetal is a novel crystal whose low-energy electronic excitations behave as Weyl fermions. It has received worldwide interest and is believed to open the next era of condensed matter physics after graphene and three-dimensional topological insulators. However, experimental research has been held back because Weyl semimetals are extremely rare in nature. Here, we present the experimental discovery of the Weyl semimetal state in an inversion-symmetry-breaking single-crystalline solid, niobium arsenide (NbAs). Utilizing the combination of soft X-ray and ultraviolet photoemission spectroscopy, we systematically study both the surface and bulk electronic structure of NbAs. We experimentally observe both the Weyl cones in the bulk and the Fermi arcs on the surface of this system. Our ARPES data, in agreement with our theoretical band structure calculations, identify the Weyl semimetal state in NbAs, which provides a real platform to test the potential of Weyltronics.

At a glance

Figures

  1. Topological electronic structure of NbAs: Weyl nodes and Fermi arcs.
    Figure 1: Topological electronic structure of NbAs: Weyl nodes and Fermi arcs.

    a, Body-centred tetragonal structure of NbAs, shown as stacks of Nb and As layers. b, Scanning tunnelling microscopy (STM) topographic images of cleaved surfaces of NbAs used in our studies. c, First-principles band structure calculation of the bulk NbAs without spin–orbit coupling. d, (Left) Schematics of the distribution of the Weyl nodes in the three-dimensional Brillouin zone (BZ) of NbAs. The red and blue lines represent the nodal lines without considering spin–orbit coupling. (Right) Schematic cartoon (not to scale) showing the projected Weyl nodes and their chiral charges on the (001) Fermi surface of NbAs. The projected Weyl nodes are denoted by black and white circles whose colour indicates opposite chiral charges. e, First-principles band structure calculated (left) and the ARPES-measured Fermi surface (right) of the (001) Fermi surface of NbAs. The Fermi arcs are clearly resolved in our ARPES measurements in agreement with the theoretical prediction.

  2. Weyl cones in NbAs.
    Figure 2: Weyl cones in NbAs.

    a, First-principles calculated Fermi surface map at ky = 0 in the kzkx plane. b, Soft X-ray ARPES Fermi surface map at ky = 0 in the kzkx plane, which agrees well with the theoretical prediction in a. The measurements were conducted using photon energies (∝kz) of 518–800eV. c, First-principles calculations of the energy–momentum dispersions of the two types of Weyl nodes (W1 and W2) in NbAs, which show that these nodes are offset in energy by 36meV relative to each other. d, Soft X-ray ARPES Fermi surface map at kz = W2 in the kxky plane, revealing the locations of the W2 Weyl nodes. e, Schematics corresponding to d indicating the locations of the W2 Weyl nodes (black and white circles marked as ‘2) and other trivial bulk bands (red dots). fh, Soft X-ray ARPES spectra (f), its zoomed-in version close to the Fermi level (g) and its curvature plot (h) along the Cut 1 direction shown in d that goes through the twin Weyl nodes marked as ‘2 in e. The photon energy of the measurements in d, f and g is 651eV. i, Soft X-ray ARPES spectra along the Cut 2 direction shown in d (normal to the plane), which again reveals the existence of two Weyl cones along the kz direction. j, First-principles calculations of the energy–momentum dispersions of the W2 Weyl nodes along kz corresponding to the ARPES measurements in i. k, Soft X-ray ARPES Fermi surface map at kz = W1 in the kxky plane, revealing the locations of the W1 Weyl nodes. The photon energy here is 611eV. l, Schematics corresponding to k, indicating the locations of the W1 Weyl nodes (black and white circles marked as ‘1) and other trivial bulk bands (red dots). m,n Soft X-ray ARPES spectra (m) and its zoomed-in version (n) close to the Fermi level along the Cut 3 direction shown in k that goes through the Weyl nodes marked as ‘1 in l. As can be seen in n, the energy of the W1 Weyl node is below the Fermi level and W2, in agreement with the calculations in c.

  3. Observation of Fermi arc surface states on the (001) surface of NbAs.
    Figure 3: Observation of Fermi arc surface states on the (001) surface of NbAs.

    a, High-resolution ARPES Fermi surface map and constant binding energy contours of the band structure of NbAs along the (001) direction at various energies. The square BZ and C4 rotational symmetry at higher binding energies both clearly indicate that the sample is cleaved on the (001) surface. The C4 violation by certain bands at shallow binding energies is consistent with C4 screw axis symmetry broken by the (001) surface and clearly shows that the C4 asymmetric states are surface states. b, High-resolution ARPES Fermi surface map, with the soft X-ray ARPES map from Fig. 2d overlaid on top of it to scale (greyscale region), showing the relative positions of the Fermi arcs and the Weyl nodes. c, Schematics of the locations of the W2 Weyl nodes in the bulk BZ of NbAs and the unusual topology of the Fermi arcs on the (001) surface Fermi surface in this compound. The pseudo-spin texture near the Weyl nodes with positive and negative chiral charges resembles the magnetic field around magnetic monopoles and antimonopoles. d, ARPES Fermi surface map of the tadpole Fermi arcs along and the corresponding Weyl nodes. e, First-principles calculated Fermi surface map of the tadpole Fermi arcs along which shows the qualitative agreement with the ARPES data. f, Schematics of the connectivity of the Fermi arcs in the first BZ. g, ARPES Fermi surface, and a constant binding energy contour at a binding energy of 120meV, of the Fermi arcs along .

  4. Visualization of the co-propagating chiral modes and the structure of the tadpole Fermi arcs in NbAs.
    Figure 4: Visualization of the co-propagating chiral modes and the structure of the tadpole Fermi arcs in NbAs.

    a, Bottom panel: a circular pipe through the bulk BZ of NbAs, enclosing two Weyl nodes of chiral charge +1. The pipe extends through the entire bulk BZ in the kz direction, forming a closed manifold. Because it encloses two Weyl nodes of chiral charge +1, the Chern number on this manifold is +2. Middle panel: by cleaving an NbAs sample on the (001) surface, we introduce a boundary on this manifold corresponding to a circle in the surface BZ. Top panel: the Chern number of +2 requires that the band structure on this circle in the surface BZ have two gapless co-propagating chiral edge modes. b, Our direct experimental observation by ARPES of the way in which Fermi arcs connect Weyl nodes on the (001) surface of NbAs places strong constraints on the dispersion of the Fermi arcs. To be consistent with a chiral charge of ±2 for the projections of the Weyl nodes on the surface BZ, the tadpole Fermi arcs must disperse as shown by the red and blue sheets. The Weyl cones are shown in green. c, Constant-energy contours of the tadpole Fermi arc surface states at binding energies ε above the energy of the Weyl nodes εW, near the energy of the Weyl nodes and below the energy of the Weyl nodes. For the Fermi arcs to be co-propagating, the red sheet must grow with binding energy, whereas the blue sheets must disperse towards each other.

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Author information

  1. These authors contributed equally to this work.

    • Su-Yang Xu,
    • Nasser Alidoust &
    • Ilya Belopolski

Affiliations

  1. Laboratory for Topological Quantum Matter and Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

    • Su-Yang Xu,
    • Nasser Alidoust,
    • Ilya Belopolski,
    • Guang Bian,
    • Tay-Rong Chang,
    • Hao Zheng,
    • Daniel S. Sanchez &
    • M. Zahid Hasan
  2. Princeton Center for Complex Materials, Princeton Institute for Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA

    • Su-Yang Xu,
    • Nasser Alidoust,
    • Ilya Belopolski &
    • M. Zahid Hasan
  3. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China

    • Zhujun Yuan,
    • Chenglong Zhang &
    • Shuang Jia
  4. Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan

    • Tay-Rong Chang &
    • Horng-Tay Jeng
  5. Paul Scherrer Institute, Swiss Light Source, CH-5232 Villigen PSI, Switzerland

    • Vladimir N. Strocov
  6. Centre for Advanced 2D Materials and Graphene Research Centre National University of Singapore, 6 Science Drive 2 Singapore 117546, Singapore

    • Guoqing Chang,
    • Chi-Cheng Lee,
    • Shin-Ming Huang,
    • BaoKai Wang &
    • Hsin Lin
  7. Department of Physics, National University of Singapore, 2 Science Drive 3 Singapore 117542, Singapore

    • Guoqing Chang,
    • Chi-Cheng Lee,
    • Shin-Ming Huang,
    • BaoKai Wang &
    • Hsin Lin
  8. Division of Materials Science and Engineering, Ames Laboratory, US DOE Ames, Iowa 50011, USA

    • Daixiang Mou,
    • Yun Wu,
    • Lunan Huang &
    • Adam Kaminski
  9. Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

    • Daixiang Mou,
    • Yun Wu,
    • Lunan Huang &
    • Adam Kaminski
  10. Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

    • BaoKai Wang &
    • Arun Bansil
  11. Institute of Physics, Academia Sinica, Taipei 11529, Taiwan

    • Horng-Tay Jeng
  12. Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA

    • Titus Neupert
  13. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

    • Shuang Jia

Contributions

S.-Y.X., N.A., I.B., G.B. and D.S.S. conducted the ARPES experiments with assistance from H.Z., V.N.S., D.M., Y.W., L.H., A.K. and M.Z.H.; Z.Y., C.Z. and S.J. grew the single-crystal samples; H.Z. conducted the STM measurements with assistance from G.B., S.-Y.X. and D.S.S.; T.-R.C., G.C., C.-C.L., S.-M.H., B.W., A.B., H.-T.J. and H.L. performed first-principles band structure calculations; T.N. did theoretical analyses; M.Z.H. was responsible for the overall direction, planning and integration among different research units.

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The authors declare no competing financial interests.

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