Realization of tunable Dirac cone and insulating bulk states in topological insulators (Bi(1-x)Sb(x))(2)Te(3)

Abstract

The bulk-insulating topological insulators with tunable surface states are necessary for applications in spintronics and quantum computation. Here we present theoretical evidence for modulating the topological surface states and achieving the insulating bulk states in solid-solution (Bi(1-x)Sb(x))(2)Te(3). Our results reveal that the band inversion occurs in (Bi(1-x)Sb(x))(2)Te(3), indicating the non-triviality across the entire composition range, and the Dirac point moves upwards till it lies within the bulk energy gap accompanying the increase of Sb concentration x. In addition, with increasing x, the formation of prominent native defects becomes much more difficult, resulting in the truly insulating bulk. The solid-solution system is a promising way of tuning the properties of topological insulators and designing novel topologically insulating devices.

Figure 1. Crystal structure.

(a) The hexagonal conventional unit cell of (Bi_1−xSb_x)₂Te₃, and (b) side view of the quintuple layer structure of perfect bulk, (c) Te1 vacancy, and (d) Te_Bi antisite. Numbers in panel (a) are the possibility sites of native point defects.

Figure 2. Cohesive energies, lattice parameters, and projection of the lowest-conduction band.

Cohesive energies per formula unit of the most stable configurations of (a) 15-atom and (b) 40-atom (Bi_1−xSb_x)₂Te₃ at each x, and the lattice parameters of (Bi_1−xSb_x)₂Te₃ with (c) 15-atom and (d) 40-atom plotted as a function of the Sb content x. The solid lines represent the lattice parameters calculated from Vegard's law. (e) and (f) Projection of the lowest-conduction band at Γ point on Te and Sb (Bi) p_z orbital as functions of the SOC strength (λ₀ is the actual SOC strength) with x = 1 and the Sb content x, respectively.

Figure 3. Surface states.

The band structures calculated for the 5QLs (Bi_1−xSb_x)₂Te₃ with (a) x = 0 and (b) x = 1. (c) and (d) The evolution of the Dirac cone with different SOC strength λ/λ₀ (λ₀ is the actual SOC strength) for (Bi₁Sb₀)₂Te₃. The highest occupied and the lowest unoccupied bands are plotted to clearly show the evolutions. The bottom of the conduction band at Γ point is explicitly aligned to 0 eV in panel (c). The inset in panel (a) shows the zoomed-in view of band for (Bi₁Sb₀)₂Te₃ with the lattice parameters of (Bi₀Sb₁)₂Te₃. The Fermi level is indicated by the dashed line at 0 eV.

Figure 4. Comparison of the Dirac cone around the Γ point for (Bi_1−xSb_x)₂Te₃ with x = 0 and x = 1.

(a) and (b) the upper Dirac cone for x = 0 and x = 1, and (c) and (d) the lower Dirac cone for x = 0 and x = 1, respectively. The constant-energy contour plots are given at the bottom.

Figure 5. Formation energies and relative formation energies.

(a) Formation energies of the lowest-energy vacancy (V_Te1) and antisite (Te_Bi and Sb_Te) defects in (Bi_1−xSb_x)₂Te₃ under various Te chemical potential (μ_Te), and (b) that of Vse1 in (Bi_1−xSb_x)₂Se₃ under various μ_Se. (c) and (d) Relative formation energies of V_Te1 and Te_Bi in (Bi₁Sb₀)₂Te₃ as a function of the SOC strength. The formation energy for the actual SOC strength (λ/λ₀ = 1) is set to zero. (e) Strain dependence of relative formation energy of Sb_Te in (Bi₀Sb₁)₂Te₃. c₀ refers to the lattice constants of the unstrained (Bi₀Sb₁)₂Te₃, and Δc to the difference of that between strained and unstrained systems.