Band splitting and Weyl nodes in trigonal tellurium studied by angle-resolved photoemission spectroscopy and density functional theory

We have performed high-resolution angle-resolved photoemission spectroscopy (ARPES) on trigonal tellurium consisting of helical chains in the crystal. Through the band-structure mapping in the three-dimensional Brillouin zone, we found a definitive evidence for the band splitting originating from the chiral nature of crystal. A direct comparison of the band dispersion between the ARPES results and the first-principles band-structure calculations suggests the presence of Weyl nodes and tiny spin-polarized hole pockets around the H point. The present result opens a pathway toward studying the interplay among crystal symmetry, band structure, and exotic physical properties in chiral crystals.

Figure 1

(a), (b) Three-dimensional and top views of trigonal Te, respectively, consisting of right-handed helical chains. Dashed line in (b) represents mesomeric chain [16]. Cleaving plane is parallel to this chain. (c) LEED pattern of a cleaved surface measured with a primary electron energy of 80 eV. (d) Bulk BZ of trigonal Te. (e) EDC in a wide energy region measured with $h\nu =80$ eV. (f) Photon-energy dependence of normal-emission EDCs in the VB region measured at $\mathit{T}=40$ K. (g) ARPES intensity in the VB region along the $\mathrm{\Gamma }\mathrm{M}$ line plotted as a function of wave vector $\left(k_x\right)$ and binding energy, together with the calculated band dispersions (red and blue curves for lone-pair and bonding $5p$ bands, respectively).

Figure 2

(a) BZ of trigonal Te, which is rotated with respect to Fig. 1. Shaded areas (yellow and blue) represent the $k_y\text{−}{k}_z$ planes where the Fermi-surface-mapping data in (b) and (c) were obtained, respectively. (b), (c) ARPES-intensity mapping at $E_{\mathrm{F}}$ on the ($11\overline{2}0)$ surface for $k_x\sim 0$ $(h\nu =90$ eV; $\mathrm{\Gamma }\mathrm{KHA}$ plane) and $k_x\sim -\pi$ $(h\nu =62$ eV; MKHL plane), respectively. (d), (e) ARPES intensity and corresponding second derivative plots in the VB region, respectively, measured along cut $1(\mathrm{\Gamma }\mathrm{K}$ cut) in (b). (f), (g) Calculated band dispersions for cut 1 with and without SOC, respectively. (h)–(k) Same as (d)–(g) but along cut 2 (AH cut) in (b).

Figure 3

(a)–(c) Second derivative of the near-$E_{\mathrm{F}}$ ARPES intensity crossing the H point, measured along cuts 2–4 (HA, HL, and HK cuts, respectively) in Figs. 2 and 2, compared with (d)–(f) the calculated band dispersions incorporating the SOC. Arrows in (a)–(c) represent the magnitude of the band splitting between ${\alpha }_1$ and ${\alpha }_2$ bands at the H point. Blue solid and dashed circles in (f) represent Weyl nodes with negative and positive monopole charges, respectively. (g) Schematic Fermi surface of top lone-pair band $\left({\alpha }_1\right)$ around the H point. Red arrows indicate calculated spin vectors. (h) Schematic Fermi surface and spin vectors of the ${\alpha }_1$ band under applying an electronic field along the horizontal direction.