Functionalized Thallium Antimony Films as Excellent Candidates for Large-Gap Quantum Spin Hall Insulator

Abstract

Group III-V films are of great importance for their potential application in spintronics and quantum computing. Search for two-dimensional III-V films with a nontrivial large-gap are quite crucial for the realization of dissipationless transport edge channels using quantum spin Hall (QSH) effects. Here we use first-principles calculations to predict a class of large-gap QSH insulators in functionalized TlSb monolayers (TlSbX2; (X = H, F, Cl, Br, I)), with sizable bulk gaps as large as 0.22~0.40 eV. The QSH state is identified by Z2 topological invariant together with helical edge states induced by spin-orbit coupling (SOC). Noticeably, the inverted band gap in the nontrivial states can be effectively tuned by the electric field and strain. Additionally, these films on BN substrate also maintain a nontrivial QSH state, which harbors a Dirac cone lying within the band gap. These findings may shed new light in future design and fabrication of QSH insulators based on two-dimensional honeycomb lattices in spintronics.

Figure 1

(a) Top and side views of the geometrical structures of TlSbX₂ (X = H, F, Cl, Br, I). Blue, red, and gray balls denote hydrogen & halogen, Sb, and Tl atoms, respectively. Shadow area in (a) presents a unit cell. (b) Phonon band dispersion for TlSbH₂.

Figure 2

The calculated band structures for (a) TlSbH₂ and (d) TlSbF₂ with and without SOC. The red lines correspond to band structures without SOC, and the blue lines correspond to band structures with SOC. (b,c) Orbital-resolved band structures of TlSbH₂, as well as (e,f) TlSbF₂, respectively. The blue dots represent the contributions from the s atomic orbital, and the red dots represent contributions from the p_x,y atomic orbitals of Tl and Sb atoms.

Figure 3

Total (left panel) and spin (right panel) edge density of states for (a,b) TlSbH₂, (d,e) TlSbF₂. In the spin edge plot, red/blue lines denote the spin up/down polarization. Evolutions of Wannier centers along k_y are presented in (c) TlSbH₂ and (f) TlSbF₂. The evolution lines (blue dot lines) cross the arbitrary reference line (red dash line parallel to k_y) with an odd number of times, thus yielding Z₂ = 1.

Figure 4

The evolution of atomic s and p_x,y orbitals without SOC and with SOC of (a) TlSbH₂ and (b) TlSbF₂. The horizontal blue dashed lines indicate the Fermi level. (c) The ratio of Sb-p_x,y to X-p_x,y component in the p_x,y orbital at the Fermi level. (d) The ratio of TI-p_x,y to X-p_x,y component in the p_x,y orbital at the Fermi level.

Figure 5

The dependence of band gap of the strain (a) TlSbH₂ and (b) TlSbF₂, and the electric field (c) TlSbH₂ and (d) TlSbF₂, respectively.

Figure 6

Crystal structures of TlSbX₂ grown on BN substrate from the top and side view for (a) TlSbH₂ and (b) TlSbF₂. (c) TlSbH₂ and (d) TlSbF₂ correspond to the orbital-resolved band structures with SOC.