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Strain-Induced Large Band-Gap Topological Insulator in a New Stable Silicon Allotrope: Dumbbell Silicene

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Strain-Induced Large Band-Gap Topological Insulator in a New Stable Silicon Allotrope: Dumbbell Silicene Strain-induced large band-gap topological insulator in a new stable silicon allotrope: dumbbell silicene Tian Zhang1, Yan Cheng1,∗ Xiang-Rong Chen1,† and Ling-Cang Cai2 1Institute of Atomic and Molecular Physics, College of Physical Science and Technology, Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610065, China 2National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, China (Dated: Oct. 30, 2015) By the generalized gradient approximation in framewok of density functional theory, we investigate a 2D topological insulator of new silicon allotrope (call dumbbell silicene synthesized recently by Cahangirov et al) through tuning external compression strain, and find a topological quantum phase transition from normal to topological insulator, i.e., the dumbbell silicene can turn a two-dimensional topological insulator with an inverted band gap. The obtained maximum topological nontrivial band gap about 12 meV under isotropic strain is much larger than that for previous silicene, and can be further improved to 36 meV by tuning anisotropic strain, which is sufficiently large to realize quantum spin Hall effect even at room-temperature, and thus is beneficial to the fabrication of high- speed spintronics devices. Furthermore, we confirm that the boron nitride sheet is an ideal substrate for the experimental realization of the dumbbell silicene under external strain, maintaining its nontrivial topology. These properties make the two-dimensional dumbbell silicene a good platform to study novel quantum states of matter, showing great potential for future applications in modern silicon-based microelectronics industry. PACS numbers: 73.22.-f, 73.43.-f, 71.70.Ej, 85.75.-d Two-dimensional (2D) materials have been a focus of mobility24,25. Unfortunately, its tiny band gap (about intense research in recent years1–7. As opposed to three- 8×10−4 meV26) opened by spin-orbit coupling (SOC) ef- dimensional (3D) one, the optical, electronic, mechanical fect seriously limits its device applications. Subsequently, and thermal properties of the 2D materials are easily ad- silicene with a low buckled honeycomb lattice was syn- justed by external strains, defects, electric field, or stack- thesized and predicted quickly to be a new 2D TI with a ing orders8–11, and thus its realistic performance can be relatively large spin-orbit gap of 1.55 meV27,28. Almost readily improved through current microfabrication tech- every striking property of graphene can be transferred to nology. More fascinatingly, 2D modes12,13 was first pre- this innovative material. Indeed, these features together dicted with quantum spin Hall (QSH) effect, and recently with the natural compatibility with current silicon-based more and more 2D materials have been confirmed as 2D microelectronics industry make silicene a promising can- topological insulators (TIs)14–18, also known as QSH in- didate for future nanoelectronics application. However, sulators. 2D TIs are novel materials characterized by its topological nontrivial band gap is still small and limits a bulk energy gap and gapless spin-filtered edge states. its room-temperature application in spintronics. Hence, Different from surface states of 3D TIs, which is only free there is great interest in searching for room temperature from exact 1800-backscattering and suffers from scatter- 2D TI (topological band gap about 26 meV), especially ing of other angles, the special edges of 2D TIs are topo- for silicon-based 2D TI. logically protected by the time reversal symmetry and In this work, we will investigate a 2D topological insu- can immune to nonmagnetic scattering and geometry lator of new silicon allotrope (call dumbbell silicene syn- perturbations, thus open new ways for backscattering- thesized recently by Cahangirov et al29) through tuning free transport. Clearly, 2D TIs is better than 3D TIs external strain, then find a topological quantum phase for coherent nondissipative spin transport related appli- transition from normal to topological insulator, accompa- arXiv:1510.08338v1 [cond-mat.mtrl-sci] 28 Oct 2015 cations. nied by a band inversion at Γ point that changes Z2 num- The 2D TIs have stimulated enormous research ac- ber from 0 to 1. Isotropic strain can induce the quantum tivities in condensed matter physics due to their novel topological phase transition in the dumbbell silicene and QSH effect and the potential application in quan- modulate its topological nontrivial band gap regularly. tum computation and spintronics19,20. Well-known The maximum topological nontrivial band gap about 12 2D TI graphene, a monolayer of carbon atoms form- meV under isotropic strain can be further improved to ing a similar honeycomb lattice, hosts a miraculous 35 meV by tuning anisotropic strain, which is sufficiently electronic system, and thus becomes perfect breeding large to realize QSH effect of the dumbbell silicene even ground for a variety of exotic quantum phenomena, such at room temperature. The pristine dumbbell silicene also as quantum anomalous Hall effect (QAHE), Majorana owns a Dirac cone at K point originated from pz orbital, fermions and superconductor21–23. Furthermore, mass- like in previous silicene, but the Dirac zone can be easily less Dirac fermions endow graphene with superior carrier destroyed as a result of spatial symmetry breaking under 2 (a)a1 (b) dumbbell silicene silicene (a) (b) 16 16 a1 14 14 12 12 2 10 10 a2 a 8 8 6 6 s = 4.29 Å s = 2.58Å Frequency(THz) Frequency(THz) 4 4 Si(α) h= 0.44Å 2 2 h= 2.71Å Si(β) Si 0 0 dumbbell silicene silicene Γ M K Γ Γ M K Γ (c) 3 (c) (d) 4.46 5.94 7.43 8.92 10.40 (d) 3 b1 -2.5 2 2 dumbbell silicene M Γ -3.0 silicene 1 1 K -3.5 0 0 -4.0 Energy(eV) HB -1 Energy(eV) -1 E nergy (eV/atom) E nergy -4.5 L B -5.0 b2 -2 -2 2.30 3.07 3.84 4.61 5.38 -3 -3 L attice constant (angstrom) M Γ K M M Γ K M FIG. 1: (Color online) (a) Top and side view of the dumbbell FIG. 2: (Color online) Vibrational band structure ω(~k) of (a) silicene structure. (b) Top and side view of the silicene struc- the dumbbell silicene and (b) the silicene. The slope of the red ture. Pink dashed lines mark the hexagonal lattice; ~a1 and dashed lines along the longitudinal acoustic branches near Γ ~a2 are the lattice unit vectors. (c) The first Brillouin zone. corresponds to the speed of sound and the in-plane stiffness. ~b1 and ~b2 are the reciprocal lattice unit vectors. Γ, M and K Electronic band structure of (c) the dumbbell silicene and refer to special points in the first Brillouin zone. (d) Total (d) the silicene without SOC. Dirac cone is marked by black energies of the dumbbell silicene and silicene with different rectangular box. The green dots corresponding to Si-pz. The lattice constants. Fermi level is set to zero. anisotropic strain. It implies that the hexagonal symme- ditional, we calculated the phonon vibration spectra by try is the main precondition for the present of Dirac cone using the frozen phonon method as implemented in the in the dumbbell silicene. In additional, we further show PHONOPY code37. that the boron nitride (BN) substrate is suitable to sup- Crystal structure of the dumbbell silicene is presented port the dumbbell silicen under external strain, and the in Fig. 1(a). Different from silicene [see Fig. 1(b)], in the topologically nontrivial properties of the strained dumb- dumbbell silicene there are two types of Si atoms: one is bell silicene can be retained well in the realistic growth fourfold coordinated [denoted by Si(α)], and the other on the boron nitride (BN) substrate. one is only threefold coordinated with a dangling bond The first-principle calculations based on the density [denoted by Si(β)]. It is easy to find that all the Si(α) functional theory were performed using the Vienna ab atoms keep on the same plane, like in graphene, which simulation package (VASP)30,31. We use the general- is surrounded by the Si(β) atoms to form the dumbbell ized gradient approximations (GGA) of Perdew-Burke- structure. The optimized dumbbell silicene has a hexag- 32 Ernzerhof (PBE) for electron-electron interactions onal structure with space group D6h (P 6/mmm) and ten and the projector-augmented-wave (PAW)33 pseudo- Si atoms in one unit cell, which is different from the op- potentials in the plane-wave basis with an energy cutoff timized silicene with space group D3d (P 3m1) and only of 700 eV. The Brillouin zone (BZ) was sampled using two Si atoms in one unit cell. The buckling height of the an 13×13×1 gamma-centered Monkhorst-Pack grid34. A dumbbell silicene [h in Fig. 1(a) and (b)] about 2.71 A˚ is slab model, together with a vacuum layer larger than 30 much larger than that in the silicene about 0.44 A,˚ which A, was employed to avoid spurious interactions due to may result in the larger SOC strength for the dumbbell the nonlocal nature of the correlation energy35. The lat- silicene. The obtained lattice constant and the distance tice constants are relaxed until the residual force on each between the neighboring dumbbell units (s in Fig. 1(a)) atom is less than 0.01 eV/A˚ and the total energy is less for the dumbbell silicene are 7.43 A˚ and 4.29 A,˚ respec- than 1×10−6 eV. Spin-orbit coupling (SOC)36 is included tively. These results including those for the silicene are in in the calculations after the structural relaxations.
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