Experimental Discovery of Weyl Semimetal TaAs

Weyl semimetals are a class of materials that can be regarded as three-dimensional analogs of graphene upon breaking time-reversal or inversion symmetry. Electrons in a Weyl semimetal behave as Weyl fermions, which have many exotic properties, such as chiral anomaly and magnetic monopoles in the crystal momentum space. The surface state of a Weyl semimetal displays pairs of entangled Fermi arcs at two opposite surfaces. However, the existence of Weyl semimetals has not yet been proved experimentally. Here, we report the experimental realization of a Weyl semimetal in TaAs by observing Fermi arcs formed by its surface states using angle-resolved photoemission spectroscopy. Our first-principles calculations, which match remarkably well with the experimental results, further confirm that TaAs is a Weyl semimetal.

Popular Summary

Hermann Weyl proposed in 1929 that a massless solution of the Dirac equation can represent a new type of particle—the Weyl fermion, which apparently breaks left-right symmetry. However, the Weyl fermion has remained elusive in particle physics for more than 80 years; the neutrino was regarded as a Weyl fermion until it was found to have mass. Recently, significant advances in topological materials have provided an alternative way to realize Weyl fermions in condensed matter as an emergent phenomenon. Weyl semimetals are predicted to be a class of topological materials that can be thought of as three-dimensional analogs of graphene upon breaking time-reversal or inversion symmetry. Some electrons in a Weyl semimetal can behave exactly like Weyl fermions. When these Weyl fermions are projected onto a surface, they will exhibit Fermi arcs connecting two Weyl fermions with opposite chirality. We use angle-resolved photoemission spectroscopy measurements to clearly observe Fermi arcs on the (001) surface of noncentrosymmetric crystal TaAs; we also study the shape and connectivity of these Fermi arcs.

We develop a mathematically rigorous method to confirm the existence of Fermi arcs, namely, by counting the crossing number of Fermi surfaces through an arbitrary closed momentum loop in the two-dimensional surface Brillouin zone. Furthermore, based on first-principles calculations, we are able to clearly resolve the pattern of these Fermi arcs connecting the projected Weyl fermions; separated Weyl nodes are a characteristic of a Weyl semimetal. Observations of Fermi arcs are a direct and distinguished exhibition of Weyl fermions or magnetic monopoles in a crystal, which is one of the hallmarks of a Weyl semimetal. We have accordingly shown that TaAs is a Weyl semimetal, which has stimulated intensive studies. The negative magnetoresistance of the semimetal due to the chiral anomaly has also been reported, and the Weyl nodes in the bulk states have been observed via soft x-ray photoemission.

Possible superconductivity in Weyl semimetals is currently being pursued for realizing exotic topological superconductivity and Majorana fermions.

Figure 1

Weyl semimetal and TaAs single crystal. (a) A 3D Dirac-cone point (DCP) can be driven into Weyl nodes with opposite chirality by either time-reversal symmetry breaking (TRB) or inversion-symmetry breaking (ISB). (b) A Weyl semimetal has Fermi arcs on its surface connecting projections of two Weyl nodes with opposite chirality. A Weyl node behaves as a magnetic monopole (MMP) in momentum space and its chirality corresponds to the charge of the MMP. (c) Crystal structure of TaAs. The arrow indicates that the cleavage occurs between the As and Ta atomic layers, producing two kinds of (001) surfaces with either As- or Ta-terminated atomic layers. (d) Bulk and projected (001) surface BZs are shown, with high-symmetry points indicated. (e) The core-level photoemission spectrum measured with a photon energy $h\nu =70\mathrm{eV}$ shows the characteristic As $3d$, Ta $5p$, and Ta $4f$ peaks. Panels (f) and (g) are pictures taken by metallographic microscopy of the cleaved surface of one TaAs sample used in our ARPES measurements. (h) ARPES spectra along $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ showing highly dispersive and well-defined quasiparticle peaks.

Figure 2

Electronic structure of the (001) surface state. (a)–(d) Curvature intensity plots of ARPES data along $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ at $h\nu =30$, 36, 42, and 48 eV, respectively. Dashed lines represent the extracted band dispersions. (e) Extracted band dispersions from the experimental data in (a)–(d). (f) Curvature intensity plot of ARPES data at $E_{\mathrm{F}}$ along $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ as a function of momentum and photon energy, for which the kz range at the BZ center is estimated to be $6.1-8.1\pi /c^{\prime }$ with the inner potential of 15 eV, where $c^{\prime }$ is one half of the $c$-axis lattice constant of TaAs. (g) Calculated band structure along $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ for a seven-unit-cell-thick (001) slab with As and Ta terminations on the top and bottom surfaces, respectively. The intensity of the red color scales with the wave-function spectral weight projected to one unit cell at the top surface with As termination. (h) Same as (g), but the spectral weight is projected to the bottom surface with Ta termination. (i,j) Intensity plot of ARPES data and corresponding curvature intensity plot along the high-symmetry lines $\overline{M}\text{−}\overline{X}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{Y}\text{−}\overline{M}\text{−}\overline{\mathrm{\Gamma }}$, respectively. For comparison, the calculated surface bands on the As-terminated surface are plotted on top of the experimental data in (j). (k) Calculated band structure along $\overline{M}\text{−}\overline{X}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{Y}\text{−}\overline{M}\text{−}\overline{\mathrm{\Gamma }}$. The red color indicates the surface bands on the As-terminated surface.

Figure 3

Fermi surface on the TaAs (001) surface. (a) Photoemission intensity plot at $E_F$ in the (001) surface recorded at $h\nu =54$ (outside the green box) and 36 eV (inside the green box). Larger and smaller circles indicate the locations of W1 and W2 projected onto the (001) surface BZ, respectively. Black and red colors represent opposite chirality. (b) Theoretical Fermi surface in the (001) surface BZ. (c) Schematic of a closed Fermi surface pocket and an open Fermi arc crossing an arbitrary $k$ loop in the two-dimensional case. (d) Blue and magenta circles indicate the locations where the surface bands cross the enclosed $k$ loop $\overline{\mathrm{\Gamma }}\text{−}\overline{X}\text{−}\overline{M}\text{−}\overline{\mathrm{\Gamma }}$ and $\overline{\mathrm{\Gamma }}\text{−}\overline{Y}\text{−}\overline{M}\text{−}\overline{\mathrm{\Gamma }}$ at $E_F$, respectively. (e,f) Photoemission intensity map and energy distribution curves along $\overline{X}\text{−}\overline{M}$ [$C1$ indicated in (a)], respectively. (g,h) Same as (e,f), respectively, but recorded along $C2$. (i,j) Same as (e,f), respectively, but recorded along $\overline{Y}\text{−}\overline{M}$ [$C3$ indicated in (a)]. The calculated-surface-state bands along $\overline{X}\text{−}\overline{M}$ and $\overline{Y}\text{−}\overline{M}$ are plotted on top of the experimental data in (e) and (i), respectively. The dashed lines in (h) and (j) track the band dispersions.

Figure 4

Surface Fermi arcs on the TaAs (001) surface. (a,b) Fine $k$-point sampling calculations of surface states at $E_F$ around W2 and W1 along $\overline{\mathrm{\Gamma }}\text{−}\overline{Y}$, respectively. W1 are indicated by dashed circles since the chemical potential is slightly away from the nodes. $a1\text{−}a5$ represent the arclike lines connecting to W1. (c) Schematic of the Fermi-arc connecting pattern. Solid and hollow circles represent the projected Weyl nodes with opposite chirality, and numbers inside indicate the total chiral charge. (d,e) Photoemission intensity plot at $E_{\mathrm{F}}$ around W1 and extracted Fermi arcs, respectively. (f) Same as (b) but near $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$. $b1\text{−}b5$ represent the arclike lines connecting to W1. (g,h) Photoemission intensity plot and calculated-surface-state bands along $C4$ [indicated in (b)], respectively. (i,j) Same as (g) and (h), respectively, but recorded along $C5$ [indicated in (f)]. (k) Schematic of the locations of the cuts $C6$ and $C7$ near W2. (l,m) Curvature intensity plots of ARPES data along $C6$ ($k_y=0.95\pi /\mathrm{a}$) and $C7$ ($k_y=\pi /a$), respectively.

Figure 5

(a)–(e) Curvature intensity plots of ARPES data along $D1\text{−}D5$, respectively. (f) ARPES intensity plot at $E_F$ around the Weyl-node projection W1. Red lines represent the momentum locations of cuts $D1\text{−}D5$ sliding through W1.