Spin Polarization and Texture of the Fermi Arcs in the Weyl Fermion Semimetal TaAs

A Weyl semimetal is a new state of matter that hosts Weyl fermions as quasiparticle excitations. The Weyl fermions at zero energy correspond to points of bulk-band degeneracy, called Weyl nodes, which are separated in momentum space and are connected only through the crystal’s boundary by an exotic Fermi arc surface state. We experimentally measure the spin polarization of the Fermi arcs in the first experimentally discovered Weyl semimetal TaAs. Our spin data, for the first time, reveal that the Fermi arcs’ spin-polarization magnitude is as large as 80% and lies completely in the plane of the surface. Moreover, we demonstrate that the chirality of the Weyl nodes in TaAs cannot be inferred by the spin texture of the Fermi arcs. The observed nondegenerate property of the Fermi arcs is important for establishing its exact topological nature, which reveals that spins on the arc form a novel type of 2D matter. Additionally, the nearly full spin polarization we observed ($\sim 80\%$) may be useful in spintronic applications.

Figure 1

Theoretically calculated surface band structure and spin texture. (a) Body-centered tetragonal structure of TaAs, shown as stacks of Ta (blue) and As (silver) layers. The screwlike pattern along the $z$ direction leads to a nonsymmorphic $C_4$ rotation symmetry that includes a translation along the $z$ direction by $c/4$. The lattice of TaAs lacks space-inversion symmetry. (b) First-principles band-structure calculation of the (001) surfaces states of TaAs. The black and white circles indicate the projected Weyl nodes with opposite chirality. (c) Corresponding theoretical spin texture of the Fermi arc surface states. The $k$-space range is defined by the white dotted box in (b). (d) The bulk and (001) surface Brillouin zone of TaAs. High symmetry points are noted. (e) Experimental geometry of the spin-resolved ARPES instrument.

Figure 2

Spin-texture measurement of the outer Fermi arc. (a) High-resolution ARPES Fermi surface map of the crescent Fermi arcs measured with incident photon energy of 90 eV. The numbers 1, 2, 3, 4, and 5 indicate the $k$ locations where spin-resolved ARPES measurements were performed on the outer arc. (b) Schematic illustration of the spin texture. The arrows show the direction of spin polarization on selective $k$ points on the Fermi arcs based on our calculations. (c)–(g) Measured in-plane spin polarizations at 1–5 correspond to panels denoted by $k_1$, $k_2$, $k_3$, $k_4$, and $k_5$, respectively.

Figure 3

Spin-texture measurement of the inner Fermi arc. (a) High-resolution ARPES Fermi surface map of thecrescent Fermi arcs. The numbers 6, 7, and 8 indicate the $k$ locations where spin-resolved ARPES measurements were performed on the inner arc. (b) Schematic illustration of the spin texture. The arrows show the direction of spin polarization on selective $k$ points on the Fermi arcs based on our calculations. (c)–(g) Measured in-plane spin polarizations at 6–8 correspond to panels denoted by $k_6$, $k_7$, and $k_8$, respectively. (f) Spin-polarization measurements at $k_1$ using different polarizations of the incident light polarization.

Figure 4

Lack of out-of-plane spin polarization, large spin-polarization magnitude, and deviation between spin textures of the Fermi arc and Weyl cones. (a) Spin-polarization measurements along the out-of-plane direction for $k_1$, $k_4$, and $k_6$. No out-of-plane spin polarization is measured in our experimental resolution. (b) Theoretically calculated surface-energy dispersion along $\overline{\mathrm{\Gamma }}-\overline{X}$. (c) The magnitude of spin polarization for the two bands that form a Kramers pair near the Fermi level at the $\overline{\mathrm{\Gamma }}$ point in panel (b). These two bands arise from the two Fermi arcs of one crescent-shaped feature. The range of the $x$ axis is from the $\overline{\mathrm{\Gamma }}$ point to the white dotted lines in panel (b). (d) A zoomed-in calculation near a projected Weyl node slightly above the Fermi level. The two Fermi arcs are seen to merge into the bulk band projection, which is noted by the white contour. The black contour shows the projection of the Weyl cones only. We see that the total projection (white contour) is larger than the Weyl cone projection (black contour). This demonstrates that there are additional irrelevant (non-Weyl) bulk Fermi surfaces contributing to the bulk projection. (e) The spin-texture calculation for (d), which shows the spin polarization of the Fermi arc surface states with white arrows; the red arrows are for the bulk pocket around the Weyl node. (f) A schematic showing crescent-shaped Fermi arcs (blue curve) connecting to projected Weyl nodes. (g) An illustration of the band structure along the black dotted circle.