Coexistence of Strong and Weak Topological Orders in a Quasi-One-Dimensional Material

Topological materials have broad application prospects in quantum computing and spintronic devices. Among them, dual topological materials with low dimensionality provide an excellent platform for manipulating various topological states and generating highly conductive spin currents. However, direct observation of their topological surface states still lacks. Here, we reveal the coexistence of the strong and weak topological phases in a quasi-one-dimensional material, ${\mathrm{TaNiTe}}_5$, by spin- and angle- resolved photoemission spectroscopy. The surface states protected by weak topological order forms Dirac-node arcs in the vicinity of the Fermi energy, providing the opportunity to develop spintronics devices with high carrier density that is tunable by bias voltage.

Figure 1

Crystal structure and calculated bulk bands of ${\mathrm{TaNiTe}}_5$: (a) Crystal structure of ${\mathrm{TaNiTe}}_5$ with its two cleaved planes, indicated by different colors. (b) Bulk Brillouin zone (BZ) and projected surface BZ for the two cleaved planes. (c),(d) Calculated band structures without and with SOC. The band inversion around the $Y$ point between $\alpha$ and $\beta$ is indicated by red rectangles.

Figure 2

Band structures for side-cleaved plane of ${\mathrm{TaNiTe}}_5$: (a),(b) Calculated bulk bands along the $\mathrm{\Gamma }\text{−}\mathrm{Y}$ direction without and with SOC. (c) Calculated (left) and measured (right, $h\nu =70\mathrm{eV}$, $T_{\text{sample}}=15\mathrm{K}$) electronic states along the $\overline{\mathrm{\Gamma }}\text{−}\overline{Y}\text{−}\overline{\mathrm{\Gamma }}$ direction, respectively. (d) Magnified view of the area indicated by a black rectangle in (c), showing the TSS1 in the bulk band gap between $\alpha$ and $\beta$ (plotted by green and yellow dashed lines, respectively). (e) Corresponding 2nd derivative spectrum in the same region of (d), where TSS 1 are guided by red dashed lines. (f) Band dispersions and (g) spin texture obtained from calculations corresponding to (d).

Figure 3

Band structures for the top-cleaved plane of ${\mathrm{TaNiTe}}_5$: (a),(b) Calculated bulk bands along the $T\text{−}Y$ direction without and with SOC. (c) Band structures along $\overline{Z}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{Z}$ direction measured with various photon energy from 50–100 eV (high-symmetry points are marked in red). (d),(f) Calculated band structures and spin texture along the $\overline{Z}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{Z}$ direction (colored lines mark the bulk bands and the black arrow indicates TSS2). (e),(g) Spin-integrated and spin-resolved band structures along the $\overline{Z}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{Z}$ direction obtained in laser-based SARPES measurement.

Figure 4

Dirac-node arcs on side-cleaved plane: (a) Constant energy contour at different binding energy obtained at the side-cleaved plane by ARPES measurements ($h\nu =70\mathrm{eV}$, red arrows indicate the Dirac-node arcs). (b) Experimentally measured band structures along the $\overline{X}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction on the side-cleaved plane (left, $h\nu =65\mathrm{eV}$) and the top-cleaved plane (right, $h\nu =86\mathrm{eV}$), respectively. (c) Magnified momentum distribution curves of the area indicated by the black rectangle in (b). The shape of the Dirac cone is fitted by red dots and the curve where the intersection lies is colored in orange. (d) The same $\mathrm{\Gamma }\text{−}\mathrm{\Sigma }$ direction projected onto different cleaved surfaces. (e),(f) Calculated bulk bands along the $\mathrm{\Gamma }\text{−}\mathrm{\Sigma }$ direction without and with SOC.