Large gap Quantum Spin Hall Insulators of Hexagonal III-Bi monolayer

Abstract

In the present work, we demonstrate that both GaBi₃ and InBi₃ monolayers are Quantum Spin Hall insulators. Here, the electronic band structures and edge states of the two novel monolayers are systematically investigated by first principle calculation. Our analysis of the band inversion and Z₂ number demonstrate that both GaBi₃ and InBi₃ are promising 2D TIs with large gaps of 283meV and 247meV, respectively. Taking GaBi₃ as example, it is illustrated that the edge states are impacted by SOC and finite size effect. In addition, it is found that the compression and tension totally affect differently on the edge states. Finally, the electron velocity is studied in detail, which is highly important in the manufacturing of spintronics device.

Figure 1

(a) Geometric structure of XBi₃ monolayer. The purple balls represent Bi atoms and the green balls represent X (X = Ga, In, Tl) atoms. (b) First Brillioun zone of XBi₃. (c,d) Top and side view of geometric structure of XBi₃ primitive cell. (e) Phonon spectrum of GaBi₃ and InBi₃ (TlBi₃ is omitted for its metallic character).

Figure 2. Upper part: The electronic bulk band structures of GaBi₃, InBi₃, TlBi₃.

The blue lines and red lines represent the band structures without and with SOC, respectively. The horizontal purple dashed line indicates the Fermi level. Lower part: The evolution from atomic p-orbit of Ga and Bi to VBM and CBM at Γ point for XBi₃, fermi level (E_f) is indicated by the red dashed line. The parities of the states at Γ point are denoted by + and −.

Figure 3

(a) The geometric structure of XBi₃(X = Ga, In) nanoribbon. (b,c) Electronic band structures of GaBi₃ and InBi₃ nanoribbon. The blue or green shadow part represent the bulk energy spectrum, the red line represent the edge states. The widths are 9.8 nm and 12.0 nm for GaBi₃ and InBi₃ respectively.

Figure 4

(a) Nanoribbon of GaBi₃ (b) Electronic band structures for the GaBi₃ zigzag nanoribbons of 2.4 nm, 3.6 nm. 6.4 nm, 7.9 nm and 9.8 nm, respectively (c) Real space charge density distribution of the edge states at Γ points.

Figure 5

GaBi₃ monolayers under strain from −8% to +8% for (a) bulk energy spectrums according to strain (b) edge states according to strain. (c) The variation of the bulk direct gap E_g(Γ) at the Γ point and the indirect band gap E_g as a function of external strain. (d) Variation of the ribbon edge gap as a function of external strain. (e) Electron velocity near Fermi level at Γ point with the strain from −8% to 2%.