${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$: A possible one-dimensional topological insulator

Using the first-principles calculations, we present a prediction of the nontrivial topological phase in one-dimensional (1D) ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ with high stability further verified by the molecular dynamics simulation and phonon spectrum. In this material, the band inversion intrinsically occurs between $\mathrm{Ta}\text{−}d$ and $\mathrm{Te}\text{−}p$ orbitals without the spin-orbit coupling effect. As a novel topological insulator, protected by time-reversal symmetry Tˆ and inversion symmetry Pˆ, we explicitly demonstrate the existence of nontrivial topological invariants and the protected edge states in it with a large bulk band gap of $\sim 163\mathrm{meV}$, which could facilitate the experimental verification at the room temperature. In addition, we find its topological states are robust against the external pressure. Our results uncover a potential 1D topological-insulating ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ and promote it as a concrete material platform for exploring the intriguing physics of low-dimensional topological phases.

Figure 1

(a) Top view of ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ bulk and (b) side view of 1D freestanding ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire. The blue, yellow, and black balls represent Ta, Te, and Si atoms, respectively. The $a$, $b$, and $c$ represent the corresponding lattice constants. (c) The schematic of a Ta atom bonding with four nearest Te atoms and the bond angles of Te1-Ta-Te1 and Te2-Ta-Te2. (d) The phonon spectrum and (e) the evolution of energies from AIMD simulations of 1D freestanding ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire. Inset in (e): The side view of 1D freestanding ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire after 5 ps AIMD simulation.

Figure 2

(a) Calculated band structures with (red solid line) and without (blue dashed line) the SOC effect for 1D ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire. The $E_g$ and $2\delta$ represent the bulk and inverted band gaps, respectively. Element-orbital-projected band structures without (b) and with (c) the SOC effect, in which the relative size of cyan, red, and blue solid balls represents the contribution of $\mathrm{Ta}\text{−}{d}_{z^2}$, $\mathrm{Te}\text{−}{p}_{x,y}$, and $\mathrm{Ta}\text{−}{d}_{xz,yz}$ atomic orbitals, respectively. (d) Band structures with the SOC effect. The size of red and blue solid balls represents the contribution of $\mathrm{Ta}\text{−}d$ and $\mathrm{Te}\text{−}p$ atomic orbitals, respectively. (e) The schematic diagram of band inversion mechanism from $\mathrm{Ta}\text{−}5d$ and $\mathrm{Te}\text{−}5p$ orbitals of atomic limit with (I) distorted tetrahedron field and (II) bonding between them. (f) The projected density of states (PDOS). The Fermi level is set to 0 eV with black dashed line.

Figure 3

(a) Bulk band gaps ($E_g$) of 1D Ta4SiTe4 nanowires under various relative SOC strengths $\chi$. The ${\chi }_0$ represents the normal (physical) SOC strength. Inset: Band structures with strengths $\chi =0.2{\chi }_0$ and $1.9{\chi }_0$. (b) The band structures of 1D ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire with SOC from individual elements, Ta, Si, and Te.

Figure 4

(a) The discrete energy level of the 1D finite-size ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire based on DFT. (b) The band structures of 1D ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire based on DFT calculations (red solid lines) and MLWFs (blue dashed lines). (c) The discrete energy level of 1D finite-size ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire based on MLWFs. The red and black solid balls represent the edge and the bulk states, respectively. (d) The distribution of zero-energy states (upper panel) and bulk states (lower panel) of the 1D finite-size ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire based on DFT.

Figure 5

The band structures of 1D ${\mathrm{Ta}}_4{\mathrm{SiTe}}_4$ nanowire without (upper panel) and with (lower panel) the SOC effect under strain effect of $-6\%$, $-2\%$, and $6\%$. The Fermi level is set to 0 eV with black dashed line. The gap of Dirac point $E_D$, the global gap $E_g$, and the inverted gap $2\delta$ induced by the SOC effect are highlighted by blue arrows.