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Rashba spin splitting and quantum spin Hall effect have attracted enormous interest due to their great significance in the application of spintronics. According to the first-principles calculation, we propose a two-dimensional hexagonal lattice material H-Pb-Cl, which realizes the coexistence of giant Rashba spin splitting and quantum spin Hall effect. Owing to the break of space inversion symmetry and the existence of intrinsic electric field, H-Pb-Cl has a huge Rashba spin splitting phenomenon (αR = 3.78 eV·Å), and the Rashba spin splitting of H-Pb-Cl(–16%—16%) can be adjusted by changing the biaxial stress. By analyzing the electronic properties of H-Pb-Cl, we find that H-Pb-Cl has a huge band gap near the Fermi surface (1.31 eV), and the topological invariant Z2 = 1 of the system is caused by the inversion of s-p orbit, which indicates that H-Pb-Cl is a two-dimensional topological insulator with a huge topological band gap, and the gap is large enough to observe the topological edge states at room temperature. In addition, we further consider the effect of BN and graphane substrates on the topological band gap of H-Pb-Cl by using the H-Pb-Cl (111)-(1×1) /BN (111)-(2×2) and H-Pb-Cl(1×1)/ graphane (2×2) system, and find that the lattice mismatch between H-Pb-Cl (5.395 Å) and BN (2.615 Å) and between H-Pb-Cl (5.395 Å) and graphane (2.575 Å) are about 3% and 4.5%, respectively. According to our calculation results, H-Pb-Cl still retains the properties of topological insulator under the effect of spin orbit coupling, and is not affected by BN nor graphane. Our results show that the nontrivial topological band gap of H-Pb-Cl can be well preserved under both biaxial stress effect and substrate effect. In addition, H-Pb-Cl can well retain the nontrivial topological band gap under the stress of –16%–16%, and thus there are many kinds of substrate materials used to synthesize this material, which is very helpful in successfully realizing preparation experimentally. Our research provides a promising candidate material for exploring and realizing the coexistence of Rashba spin splitting and quantum spin Hall effect. And the coexistence of giant Rashba spin splitting and quantum spin Hall effect greatly broadens the scope of potential applications of H-Pb-Cl in the field of spintronic devices.
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Keywords:
- two dimensional topological insulator /
- Rashba spin splitting /
- spatial inversion symmetry /
- spin orbit coupling
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图 1 (a) 2D层状材料H-Pb-Cl结构的侧视图和俯视图; (b) H-Pb-Cl结构在布里渊区沿高对称点的声子谱
Figure 1. (a) Side and top view of the crystal structure H-Pb-Cl; (b) phonon dispersion of 2D H-Pb-Cl along the high symmetry points in Brillouin zone.
图 2 采用PBE和HSE06的2D H-Pb-Cl的能带结构 (a), (c) 不考虑SOC; (b), (d)考虑SOC. 蓝点、红点和绿点分别表示Pb原子的s, px, y和pz轨道的投影权重. 图(b)中的插图表示的是费米面附近的能带劈裂现象
Figure 2. The band structure of 2D H-Pb-Cl using PBE and HSE06: (a), (c) Without SOC; (b), (d) with SOC. Blue, red and green dots represent the contribution of s, px, y, pz orbitals of Pb atoms, respectively. The illustration in Figure (b) shows the band splitting near the Fermi surface.
图 3 (a) 沿着ky方向的瓦尼尔中心演化, 得到Z2 = 1; (b) H-Pb-Cl沿着锯齿形边缘的边缘态; (c) H-Pb-Cl在Γ点的能级演化
Figure 3. (a) The evolutions of Wannier centers along ky, yielding Z2 = 1; (b) edge states of H-Pb-Cl on the zigzag edges; (c) evolution of energy bands at Γ for H-Pb-Cl.
图 4 (a) 无双轴应力作用下H-Pb-Cl的功函数, ∆Φ表示的是静电势差; (b) H-Pb-Cl的静电势差在双轴应力从–16% 到16%作用下的变化图
Figure 4. (a) Work functions of H-Pb-Cl under 0 biaxial stress, where ∆Φ represents the electrostatic potential difference under different biaxial stresses; (b) the variations of electrostatic potential difference ∆Φ of H-Pb-Cl with the biaxial stress of –16% to 16%.
图 5 (a) 在双轴应力(–16%到16%)作用下H-Pb-Cl体系内的Rashba自旋劈裂系数αR的变化图; (b) H-Pb-Cl (1×1)/BN (2×2)的能带结构, 其中红色部分代表的是基底BN在能带中的贡献情况; (c) H-Pb-Cl (1×1)/石墨烷 (2×2), 其中紫色点线代表的是石墨烷在能带中的贡献情况
Figure 5. (a) The variations of Rashba spin splitting αR of H-Pb-Cl with the biaxial stress of –16% to 16%; (b) band structure of H-Pb-Cl (1×1)/BN (2×2), with the red stars-lines contributed by BN substrate; (c) band structure of H-Pb-Cl (1×1)/graphane (2×2), with the purple dotted line contributed by graphane substrate.
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[1] Moore J E 2010 Nature 464 194
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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