Experimental Observation and Spin Texture of Dirac Node Arcs in Tetradymite Topological Metals

We report the observation of a nontrivial spin texture in Dirac node arcs, i.e., novel topological objects formed when Dirac cones of massless particles extend along an open one-dimensional line in momentum space. We find that such states are present in all the compounds of the tetradymite ${\mathrm{M}}_2{\mathrm{Te}}_2\mathrm{X}$ family ($\mathrm{M}=\mathrm{Ti}$, Zr, or Hf and $\mathrm{X}=\mathrm{P}$ or As) regardless of the weak or strong character of the topological invariant. The Dirac node arcs in tetradymites are thus the simplest possible textbook example of a type-I Dirac system with a single spin-polarized node arc.

Figure 1

(a) Constant energy maps at various binding energies. A linear feature appears at an approximate binding energy of 850 meV. The dashed blue hexagon marks the borders of the surface-projected Brillouin zone. The dashed red square indicates the area with saturated contrast shown in the inset above the top left panel. (b) Energy-momentum dispersion showing a persistent Dirac-like dispersion along various $k$ paths marked by dashed lines in (a). All data were collected using photons of 50 eV and linear horizontal polarization. The temperature was 6 K.

Figure 2

(a) In-plane Fermi surface map of ${\mathrm{Ti}}_2{\mathrm{Te}}_2\mathrm{P}$ showing a sixfold symmetry. (b),(c) Near-$E_F$ band structure of ${\mathrm{Ti}}_2{\mathrm{Te}}_2\mathrm{P}$ along the $\overline{\mathrm{KMK}}$ high-symmetry line with spin-integrated, (b), and spin-resolved, (c), ARPES, showing a Dirac-like dispersion with clear spin polarization. The color scale in (c) represents the sign and value of the in-plane spin polarization along $\overline{\mathrm{\Gamma }\mathrm{M}}$ with blue (red) pointing toward (away from) the reader. (d) Near-$E_F$ band structure of ${\mathrm{Hf}}_2{\mathrm{Te}}_2\mathrm{P}$ along the $\overline{\mathrm{KMK}}$ high-symmetry line. Blue (red) squares indicate branches of the Dirac cone with spin polarization pointing toward (away from) the reader. (e) Energy dependent spin polarization of ${\mathrm{Hf}}_2{\mathrm{Te}}_2\mathrm{P}$ at the constant momenta indicated by the vertical light blue and magenta dashed lines in (c). (f) Spin-resolved momentum distribution curves (blue, red) and momentum dependent spin polarization (green) at the constant energy indicated by the horizontal green dashed line in (d). Spin up and spin down means parallel and antiparallel to $\overline{\mathrm{\Gamma }\mathrm{M}}$. The Dirac point at energy $E_D$ is shown by a red arrow in panels (b)–(e). All data were collected with LH polarized photons of 55 eV. The temperature was 25 K.

Figure 3

(a),(b) Spin-integrated ARPES results obtained at synchrotron SOLEIL with LH polarized photons of 50 eV at a temperature of 6 K showing the Fermi surface contours of ${\mathrm{Ti}}_2{\mathrm{Te}}_2\mathrm{P}$ (a) and the existence of linear features at a binding energy of 0.85 eV (b). (c) Same as panel (b) but measured with LH photons of 55 eV at the ESPRESSO spin-resolved ARPES setup of beamline 9B at HiSOR. Path (1) corresponds to data shown in panels (d) and (g), path (2) to panels (e) and (f), and path (3) to panels (f) and (i). (d)–(f) Spin-resolved EDCs (red, blue) and energy dependent in-plane spin polarization parallel to $\overline{\mathrm{\Gamma }\mathrm{M}}$ (green) measured at the left branch of the Dirac cones [panels (g)–(i)], themselves obtained at different $k\text{locations}$ along the Dirac node arc. (g)–(i) Energy-momentum dispersion along the $k$ paths indicated in panel (c), with overlaid vertical dashed lines showing the $k\text{locations}$ of the spin-resolved EDCs shown in panels (d)–(f). Panels (c)–(f) were all measured with LH photons of 55 eV at a temperature of 25 K.