Layer-locked spin states revealed in the centrosymmetric nodal-line semimetal HfSiS

The spin-polarized bulk states in the centrosymmetric nodal-line semimetal HfSiS were observed by spin- and angle-resolved photoelectron spectroscopy. Combining with density functional theory calculations and the tight-binding model, the layer-locked spin states' nature of the observed $\mathrm{\Lambda }$-shaped bulk bands was revealed and the tight-binding model shows the importance of the next-nearest-neighbor term of spin-orbit coupling in the spin reversal of the bands along the $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathit{M}}$ direction. Furthermore, the topological essence of attractive Dirac node arc states was confirmed.

Figure 1

(a) Crystal structure of HfSiS. (b) Bulk tetragonal Brillouin zone and projection to the (001) surface (green plane). (c) Measured spin-integrated Fermi surface.

Figure 2

Experimental band structure and spin polarization along the $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathit{M}}$ direction of HfSiS. (a) Spin-integrated ARPES image along the $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathit{M}}$ high-symmetry direction. (b) A high-resolution view of the spin-integrated band structure near the Fermi edge and the inset calculation results describe the structure of the observed bands. (c) Spin-resolved ARPES image in the region indicated by the red rectangle in (a) and the measured spin direction is in plane and perpendicular to momentum. (d) MDC spin polarization of the cut in (c).

Figure 3

Calculated bulk band structure of HfSiS and elaborate spin structure along the $\mathrm{\Gamma }\text{−}\mathit{M}$ direction. (a) vasp calculated bulk band structure along several high-symmetry directions. (b) vasp calculated components of $\mathrm{\Lambda }$-shaped bulk bands along the $\mathrm{\Gamma }\text{−}\mathit{M}$ ($k_z=0$) and $\mathit{Z}\text{−}\mathit{A}$ ($k_z=\pi$) direction in (a). (c) vasp calculated in-plane spin polarization perpendicular to the momentum direction contributed by the upper layers. (d) Schematic diagram of the local dipole field at the upper and lower Hf layers. The direction of the dipole field is indicated by red and blue triangles. (e) Schematic of the spin texture located at the upper and lower Hf layers calculated by the tight-binding model, with the sizes of arrows representing the numerical values of spin polarization.

Figure 4

Dirac node arc SSs in HfSiS. (a) Band structure along the $\overline{\mathit{X}}\overline{\mathit{X}}$ direction of HfSiS, with a crossing that could be seen near ${\mathrm{E}}_{\mathrm{F}}$. (b), (c) Schematic diagrams of the Fermi surface and the location of the Dirac node arc surface states in the $E\text{−}k$ space, respectively, with the crossing of the Fermi surface and Dirac node arc surface states indicated by the red dots. (d), (e) Measured spin-resolved ARPES images of cut 1 and cut 2 indicated in (b) with Dirac node arc SSs indicated by red and blue solid guidelines and bulk states denoted by dotted lines.