First-principles calculation of electronic and topological properties of low-dimensional tellurium

TL;DR

This work addresses how reducing dimensionality in tellurium affects its electronic and topological properties. Using first-principles DFT with SOC and hybrid functionals, tight-binding models from MLWFs, and WannierTools for topological invariants, the authors analyze bulk Te-I, 2D tellurene (α-Te, β-Te), and 1D Te-h nanowires. Key findings include Weyl nodes and Weyl phonons in Te-I, a hedgehog spin texture, and Weyl-like states in Te-h, while several 2D lattices are topologically trivial under preserved symmetries, with some topological exceptions under specific conditions; external perturbations can induce Weyl phases in monolayers. The results position tellurium as a versatile platform for engineered Weyl physics in nanoscale electronics and optoelectronics, with tunable topology through strain, passivation, or doping.

Abstract

We employ first-principles density-functional theory to investigate the structural, thermodynamic, electronic, and topological properties of tellurium in its various dimensional forms: bulk trigonal tellurium (Te-I), two-dimensional (2D) monolayers $α$-Te, $β$-Te and one-dimensional helical nanowire (Te-h). A softening of the acoustic phonon modes is seen in most of the 2D phases, suggesting a tendency to structural distortions or phase transitions under small perturbations. The trigonal 3D Te-I structure is characterized as a narrow-gap semiconductor hosting Weyl nodes at high-symmetry locations in the Brillouin zone, which is supported by the characteristic spin texture seen in momentum space, where spins align radially, forming Berry monopoles. This topological feature, along with the observation of Weyl phonons is attributed to inversion symmetry breaking and strong SOC. Ultrathin Te-h nanowires also exhibit signatures of Weyl nodes and presents a considerable energy gap under SOC. On the other hand, the two-dimensional monolayers $α$-Te, $β$-Te, are classified as topologically trivial, as indicated by their topological invariants, which arises from the preservation of both spatial inversion and time-reversal symmetries in these systems. The potential for inducing topological phase transitions via external perturbations suggest that these monolayers are promising candidates for engineered Weyl phases or other topological states. We demonstrate that tellurium and its low-dimensional derivatives are versatile materials that exhibit a broad range of electronic and phononic phenomena intrinsically linked to chirality and symmetry breaking. The tunability of their electronic and topological properties places tellurium as a promising material platform for the exploration and application of Weyl physics in next-generation electronic and optoelectronic technologies.

Figures (18)

• Figure 1: Relaxed geometry of trigonal Te-I: (a) top view projected along $\vec{c}$; (b) along $\vec{a}$; (c) perpendicular to $\vec{b}$.
• Figure 2: Vibrational and thermodynamic properties of trigonal tellurium (Te-I). a) Phonon dispersion curve and density of states and b) free energy, entropy and heat capacity.
• Figure 3: Selected phonon modes in Te-I: (a-c) projected along the $\vec{c}$-axis and (d) is viewed along the $\vec{a}$ axis.
• Figure 4: Relaxed crystal structures of 2D tellurium phases: a) $\alpha$-Te, b) $\beta$-Te, c) buckled pentagonal, d) buckled kagome, e) buckled square, f) planar hexagonal, g) Lieb-like, h) planar kagome and i) planar square.
• Figure 5: Phonon dispersion curves of 2D tellurene phases: a) $\alpha$-Te, b) $\beta$-Te, c) buckled pentagonal and d) buckled kagome and e) buckled square.