Research ArticlePHYSICS

Experimental discovery of a topological Weyl semimetal state in TaP

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Science Advances  13 Nov 2015:
Vol. 1, no. 10, e1501092
DOI: 10.1126/sciadv.1501092

Figures

  • Fig. 1 Electronic band structure of the Weyl semimetal TaP.

    (A) Body-centered tetragonal structure of TaP, shown as stacks of Ta and P layers. (B) First-principles band structure calculation of the bulk TaP without SOC. (C) Same as (B) but with SOC. Schematic of the distribution of Weyl nodes in the three-dimensional BZ of TaP. (D) Bulk BZ and (001) surface BZ of TaP, with certain high-symmetry points labeled. (E) Calculation of the positions of the Weyl nodes, with opposite chiralities indicated by the white and black circles. The mirror planes are blue and the kz = 2π/c plane is red. (F) Band structure on the kx = 0 mirror plane, E(kx = 0, ky, kz), in the vicinity of the ring-like crossing, in yellow, which we find in calculation when SOC is ignored. (G) Calculation showing the ring-like crossings in the kx = 0 plane, with the Weyl nodes indicated by green dots. The distribution of chiralities of the projected W1 nodes in the first surface BZ depends on whether the ring-like crossing is large enough that the W1 nodes spill over the edge of the first surface BZ, marked by the dotted line through the bulk N point. (H) To more clearly understand the distribution of chiralities, we show cartoons (not to scale) of the projected Weyl nodes and their chiral charges on the (001) Fermi surface of TaP (TaAs) and NbP (NbAs), respectively. The projected Weyl nodes are denoted by black and white circles; their color indicates their opposite chiralities and the number in the circle indicates the projected chiral charge. We find that the chiralities of the W1 points are swapped in TaP (TaAs) with respect to NbP (NbAs).

  • Fig. 2 Bulk Weyl fermion cones in TaP.

    (A) SX-ARPES Fermi surface (FS) map at ky = 0 in the kzkx plane. (B) SX-ARPES Fermi surface map at kz = W2 in the kxky plane, showing the W2 Weyl nodes. EXP, experimental. (C) Theoretical calculation of the same slice of the BZ at the same energy shows complete agreement with the SX-ARPES measurement. THY, theoretical. (D) First-principles calculations of the energy-momentum dispersion of the two sets of Weyl nodes, W1 and W2, in TaP. The two nodes are offset in energy by 64 meV. (E and F) Energy dispersion maps, Ek//, for W1 and W2, respectively. (G and H) ARPES measured and theoretically calculated out-of-plane dispersion, Ekz, for W2, which shows the linear dispersion of the Weyl cone along the out-of-plane direction. All data in (A) to (G) are obtained from Batch I. (I) Energy dispersion of the W2 Weyl cones from a sample in Batch II. We see the ± Weyl nodes more clearly for Batch II TaP, as labeled in (I).

  • Fig. 3 Fermi arc surface states in TaP.

    (A and B) ARPES-measured Fermi surface and first-principles band structure calculation of the (001) Fermi surface of TaP, respectively. (C) High-resolution ARPES Fermi surface map in the vicinity of the Embedded Image high-symmetry line. (D) Theoretical calculated surface Fermi surface along Embedded Image. The calculation used the Green function technique to obtain the spectral weight from the top two unit cells of a semi-infinite TaP system. SSs, surface states. (E) Schematic showing the Fermi arcs and the trivial surface states that correspond to our data in (C). This configuration is obtained by analyzing our ARPES data and comparing it with calculations (see the main text). (F) ARPES dispersion along the Embedded Image high-symmetry line. The six Fermi crossings are numbered 1 to 6. We see four states (1 to 4) with one sign of Fermi velocity and the other two (5 and 6) with the opposite sign. This is consistent with the projected chiral charge ±2 for the W2. These six states are also labeled in (E), where the arrows represent their corresponding Fermi velocity direction.

  • Fig. 4 Bulk-boundary correspondence and topological nontrivial nature of TaP.

    (A) ARPES energy-momentum dispersion map along the Embedded Image high-symmetry line, which shows six band crossings at the Fermi level. (B) Calculated energy dispersion along the Embedded Image line. The calculation uses the Green function technique to obtain the spectral weight from the top unit cell of a semi-infinite TaP system. (C) Similar to (B) but for the top two unit cells. (D) Schematic examples of closed paths (green and magenta triangles) that enclose both W1 and W2 Weyl nodes. The bigger black and white circles represent the projected W2 nodes, whereas the smaller ones correspond to the W1 nodes. The red lines denote the Fermi arcs and the blue lines show the trivial surface states. The specific configuration of the surface states in this cartoon is not intended to reflect the Fermi arc connectivity in TaP. It simply provides an example of one configuration of the surface states that is allowed by the projected Weyl nodes and their chiral charges by the bulk-boundary correspondence. (E) Zoomed-in ARPES spectra near the W2 nodes along Embedded Image. The white dashed line marks a rectangular loop that encloses a projected W2 Weyl node. The circles are added by hand on the basis of the calculated locations of the projected W2 nodes. (F to I) ARPES dispersion data as one travels around the k-space rectangular loop shown in (E) in a counterclockwise way from I to IV. The closed path has edge modes with a net chirality of 2, showing that the path must enclose a projected chiral charge of 2 using no first-principles calculations, assumptions about the crystal lattice or band structure, or ARPES spectra of the bulk bands.

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