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

Abstract

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. PACS numbers: 74.25.Jb, 74.70.Xa, Chirality, the asymmetry of an object upon its mirroring, is ubiquitous in nature. In the standard model of particle physics, quantum vacuum state is regarded to be chiral and the characteristic of elementary particles (quarks and leptons) is essentially different between lefthanded and right-handed counterparts. Chirality also emerges as chiral molecules, ions, and crystals, playing an important role in a wide variety of subjects such as chemistry, biology, and solid-state physics [1,2]. Chiral crystals are recently attracting a great deal of attention, since they are known to be useful for advanced applications such as polarization optics [3][4][5], multiferroics [6,7], and spintronics [8][9][10]. Also, they are predicted to host peculiar optical and transport properties, essentially owing to the spin splitting of electronic energy bands originating from the space-inversion-symmetry (SIS) breaking of the crystal [11][12][13][14][15]. The chiral crystals belong to the non-symmorphic space group, and are characterized by the screw symmetry (translational plus rotational symmetry), which is currently discussed to be one of key ingredients for the realization of novel topological semimetals [13,16,17].Amongst various chiral crystals, trigonal tellurium (Te) is recently attracting particular attention due to its simple crystal structure suitable for the band engineering [13,16,[18][19][20][21][22][23][24][25]. As shown in Figs. 1(a) and 1(b), trigonal Te consists of three atoms in a unit cell with infinite helical chains arranged in a hexagonal array, which spiral around axes parallel to c ([001] axis). Depending on the right-handed or left-handed screw axis, the space group is P3 1 21 or P3 2 21 (D 4 3 or D 6 3 ) [note that the right-handed case is displayed in Figs. 1(a) and 1(b)], in which the SIS is broken. Trigonal Te is a semiconductor with a band gap of 0.32 eV [18,19] in which the valence-band (VB) maxima and conduction-band (CB) minima are located at around the H point of the bulk Brillouin zone (BZ) [13,16,20,22], and it shows intriguing physical properties such as high efficiency thermoelectricity [24], circular photon drag effect [14], and current-induced spin polarization [11,12]. Under pressure, it undergoes complex structural changes and semiconductor to metal transition [21]. Ab in...

Radial Spin Texture in Elemental Tellurium with Chiral Crystal Structure

“…1f) is reached at h = 63 eV as shown in Fig. 1g, which is consistent with a previous study using h = 62 eV 28 . The hole-like band near the Fermi level is further examined in (Fig.…”

“…The highest and second-highest bands are described by double group representations (H4, and H5, respectively) 18,21,22 , and thus the spin degeneracy of these is lifted. While the D3 symmetry requires no net spin polarization at the highly symmetrical H-point, non-zero spin polarization should appear off the H-point 25,28,30 .…”

Composite Weyl nodes stabilized by screw symmetry with and without time-reversal invariance

“…Since their presence anywhere in the BZ requires broken P * T symmetry, we assume this to be the case for our crystal. Examples include ferromagnetic metals such as body-centered cubic Fe [12] and hcp Co, nonmagnetic acentric semiconductors such as trigonal Te [13,14], and polar conductors such as TaAs, a Weyl semimetal [15,16]. In the first two examples T symmetry is broken and P symmetry is present, while the reverse is true for the others.…”

“…which together with Eqs. (14) and (15) constrains the form of f (q + , q − , 0). Turning to g(q + , q − , 0) and setting m 3 = 0 in Eq.…”

Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines

“…In this structure the Te atoms form helical chains along the z direction, which are arranged in a hexagonal array [74]. Recent first principles calculation have shown that the valence and conduction bands of Te at the H point exhibit several Weyl points [75,76]. Moreover, it was found that hydrostatic or uniaxial strain leads to a band inversion at the H point, thereby transforming Te into a strong topological insulator [77].…”