Tunability of the Quantum Spin Hall Effect in Bi(110 ... - ACS Publications

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Tunability of the Quantum Spin Hall Effect in Bi(110) Films: Effects of Electric Field and Strain Engineering Sheng-shi Li,† Wei-xiao Ji,‡ Ping Li,‡ Shu-jun Hu,† Li Cai,† Chang-wen Zhang,*,‡ and Shi-shen Yan*,† †

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, Shandong 250100, P. R. China School of Physics and Technology, University of Jinan, Jinan, Shandong 250022, P. R. China

‡

S Supporting Information *

ABSTRACT: The quantum spin Hall (QSH) effect is promising for achieving dissipationless transport devices due to their robust gapless edge states inside insulating bulk gap. However, the currently discussed QSH insulators usually suffer from ultrahigh vacuum or low temperature due to the small bulk gap, which limits their practical applications. Searching for large-gap QSH insulators is highly desirable. Here, the tunable QSH state of a Bi(110) films with a black phosphorus (BP) structure, which is robust against structural deformation and electric field, is explored by first-principles calculations. It is found that the two-monolayer BPBi(110) film obtains a tunable large bulk gap by strain engineering and its QSH effect shows a favorable robustness within a wide range of combinations of in-plane and out-of-plane strains, although a single in-plane compression or out-of-plane extension may restrict the topological phase due to the self-doping effect. More interestingly, in view of biaxial strain, two competing physics on band topology induced by bonding−antibonding and px,y−pz band inversions are obtained. Meanwhile, the QSH effect can be persevered under an electric field of up to 0.9 V/Å. Moreover, with appropriate in-plane strain engineering, a nontrivial topological phase in a four-monolayer BP-Bi(110) film is identified. Our findings suggest that these twodimensional BP-Bi(110) films are ideal platforms of the QSH effect for low-power dissipation devices. KEYWORDS: Bi(110) film, topological insulator, quantum spin Hall effect, strain engineering, electric field, first-principles calculations

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were first established in HgTe/CdTe quantum wells in 2007.6,14 Experimental confirmation of the quantum spin Hall (QSH) effect is reported successively in inverted InAs/ GaSb15,16 quantum wells. However, the drawback of small bulk gap makes the observation of the QSH effect in these quantum well structures require a harsh experimental conditions. Thus, there is an urgent need to identify 2-D TIs with a large bulk gap and experimental feasibility. Following the first proposal of QSH effect in graphene,5 extensive efforts have been devoted to honeycomb lattices to stimulate the above-mentioned goal, such as the bilayer of group IV,17−20 group V,21−25 groups III−V,26−29 groups II− VI,30,31 and so on. In addition to those of the hexagonal structure, topological properties are also identified in tetragonal,32 pentagonal,33 and dumbbell structures34,35 as well as in metal-organic frameworks.36,37 However, these results are still confined to the scope of theoretical analysis, and the experimental synthesis suffers many challenges and difficulties. It is worth mentioning that the Bi(111) bilayer, which was predicted as a 2-D TI with a large bulk gap, has been fabricated on Bi2Te3 and Bi(111) substrates38−43 experimentally. Unfortunately, according to experimental identification, its

INTRODUCTION Over the last few decades, spintronics, as a new subject, has arisen in condensed matter physics, devoted to effectively controlling the spin configuration and spin current.1,2 This objective has made a breakthrough with the generation of spin current in magnetic conductors. In 2008, the proposal of spingapless semiconductors3 further promoted its development, in which both electrons and holes are fully spin-polarized. Recently, topological insulators (TIs)4−6 have attracted quite intensive research enthusiasm because they provide an alternative platform to realize helical-Fermion dispersions. Different from those of normal insulators (NIs), the timereversal symmetry (TRS)-protected gapless surface or edge states in TIs span the insulating bulk gap,5,7−9 which are robust against nonmagnetic perturbations, providing a channel for spin-current transport, with low-power dissipation, which guarantees significant applications in energy-efficient spintronics devices and quantum computing. On comparison, two-dimensional (2-D) TIs are preferable in transport applications than three-dimensional (3-D) TIs, as the electrons can only move along edges with opposite spins. Nevertheless, to date, a vast majority of fabricated TIs in experiments are 3-D materials,10 in which the compounds containing bismuth (Bi) element are the most representative ones due to their strong spin−orbit coupling (SOC), for example, Bi2Se3 (Bi2Te3),11 BaBiO3,12 and BiTeI.13 For 2-D TIs, the helical edge states © 2017 American Chemical Society

Received: February 26, 2017 Accepted: June 5, 2017 Published: June 15, 2017 21515

DOI: 10.1021/acsami.7b02818 ACS Appl. Mater. Interfaces 2017, 9, 21515−21523

ACS Applied Materials & Interfaces

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RESULTS AND DISCUSSION First, we revisit the structural and electronic properties of the 2ML BP-Bi(110) film. Figure 1a,b presents the geometric

edge states are hybridized with the surface states of the substrate. Very recently, an ultrathin Bi(110) film with a black phosphorus (BP) structure has been grown on a Si(111) substrate or a highly oriented pyrolytic graphite by selfassembly.44−47 The gapless edge states of the Bi(110) film are experimentally detected by scanning tunneling microscopy/ spectroscopy,44 indicating a great breakthrough in 2-D TIs. We all know that interfacial strain and charge transfer (equivalent to an internal electric field), which are caused by lattice mismatch and chemical heterogeneity between film and substrate, are essential for the growth of a film. These two non-negligible factors generally result in drastic effects on the quantum states of the 2-D films.42,43,48 On the other hand, strain engineering also plays a significant role in the regulation of the topological state,49 whereas the electric field can drive the transition between the nontrivial and trivial phase,50 which provides the feasibility of a topological field-effect transistor. Consequently, for the Bi(110) film, which is one of the few 2-D TIs that has been prepared in experiments, from the point of view of practical devices application, a question is raised: Can the bulk gap be tuned and the QSH state be robust against the effects of strain and electric field? In this work, by means of first-principles calculations, we report that the two-monolayer (2ML) BP-Bi(110) film shows a favorable robustness under isolated or combined strain engineering and the tunability of the bulk gap can be realized easily as well. In particular, under the effect of in-plane biaxial strain, competition between two kinds of band topologies is demonstrated, which originate from bonding−antibonding and px,y−pz band inversions, respectively. Additionally, the QSH state can withstand an external electric field of up to 0.9 V/Å, with the bulk gap decreasing monotonically. Our results give a better understanding of the QSH effect in 2-D BP-Bi(110) films against strain engineering and the external electric field, which can be useful for further experimental investigation and possible applications in spintronic devices.

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Figure 1. Top view (a) and side view (b) of the puckered 2ML BPBi(110) film. (c) The corresponding 2-D Brillouin zone with highsymmetry points. (d) Side view of the 4ML BP-Bi(110) film.

structure of the 2ML BP-Bi(110) film, which respectively shares a hexagonal lattice and puckered bilayer structure from the top (Figure 1a) and side (Figure 1b) views. As depicted in the dotted box, the primitive cell consists of four Bi atoms, among which each Bi atom forms strong covalent bonds with the three nearest neighboring atoms. The corresponding rectangular 2-D Brillouin zone is presented in Figure 1c. After structural optimizations, the orthogonal lattice constants are a = 4.74 Å and b = 4.43 Å, which are in good agreement with previous experimental results.44 For simplicity, the inplane bond length and bond angle are denoted as l1 and α, whereas the interplanar bond length and bond angle are labeled as l2 and β. The calculated results are summarized in Table 1. One can see that β is close to 90°, revealing a little deviation along the x direction between the two atomic layers. The calculated puckered height (h) between two atomic layers is demonstrated to be 3.01 Å. Nevertheless, it is this puckered configuration that helps maintain the in-plane anisotropy and may simultaneously provide a superior mechanical flexibility to the 2ML BP-Bi(110) film. The stability of the 2ML film is then evaluated by formation energy, which is defined as

COMPUTATIONAL DETAILS

First-principles density functional theory (DFT) calculations were implemented by the plane wave basis Vienna Ab Initio Simulation Package (VASP).51,52 We employed the projectoraugmented wave method53 for describing the electron-ion potential. Generalized gradient approximation (GGA) in the Perdew−Burke−Ernzerhof54,55 form was adopted to approximate the electron−electron interaction. The kinetic energy cutoff for the plane wave basis was set to 450 eV, and all of the lattice constants and atom coordinates were optimized until the convergence of the force on each atom was less than 0.001 eV/ Å. The reciprocal space was meshed with 11 × 13 × 1 for geometry optimization and self-consistent electronic structure calculations using the Monkhorst−Pack method. A unit cell with periodic boundary condition was employed, and a vacuum space of 20 Å was applied to avoid interactions between periodic structures in the z direction. The hybrid HSE06 functional56 was used to confirm the band structure of the 2ML BP-Bi(110) film. The method of DFT-D257 and dipole corrections were taken into account throughout the calculation of the four-monolayer (4ML) BP-Bi(110) film. Besides, the SOC was included in self-consistent electronic structure calculations. The edge states of the BP-Bi(110) film were calculated using the Wannier90 package.58

Ef = E[Bi(110)] − nBiE Bi

where E[Bi(110)] represents the total energy of the 2ML BPBi(110) film. EBi is the chemical potential of the Bi atom obtained from bulk bismuth, and nBi is the number of Bi atoms in a unit cell. The calculated formation energy is −2.20 eV per unit cell. Further, we perform ab initio molecular dynamics (MD) simulations using a 5 × 5 × 1 supercell at 300 K for 6 ps, with a time step of 2 fs. The fluctuation of energy and snapshot of the structure are presented in Figure S1. In light of these results, we can conclude that the 2ML BP-Bi(110) film is both thermally and dynamically stable. Then, the electronic properties of the 2ML BP-Bi(110) film are investigated. The orbital-resolved band structure without SOC is depicted in Figure 2a, in which two bands dominated by Bi-pz orbitals cross at the Fermi level, forming a Dirac cone between the Y and Γ points. From the calculated local charge density around the Fermi level, as shown in Figure 2b, one can 21516


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Table 1. Calculated Lattice Constants, a and b; Puckered Height, h; Bond Lengths, l1 and l2; Interlayer Spacing, d; Bond Angles, α and β; Band Gap at the Dirac Cone, ED; and Global Band Gap Eg of 2M and 4ML BP-Bi(110) Films, Respectively structure

a (Å)

b (Å)

h (Å)

l1 (Å)

l2 (Å)

2ML 4ML

4.74 4.93

4.43 4.43

3.01 3.05

3.07 3.04

3.02 3.08

d (Å)

α (deg)

B (deg)

ED (meV)

Eg (meV)

3.33

92.48 94.70

93.27 95.18

98.3 70.0

88.9 0

Figure 2. (a) Orbital-resolved band structure of the 2ML BP-Bi(110) film in the absence of SOC. (b) The local charge density of the four regions marked in the band structure. (c) The calculated band structure with SOC. (d) The enlarged view of energy bands in the vicinity of the Fermi level. (e) Evolution of Wannier charge centers along ky. Arbitrary reference line (red dash line) paralleled to ky cross the evolution lines with odd times, indicating Z2 = 1. (f) The semi-infinite edge states of the 2ML BP-Bi(110) films. (g) Edge states with spin projection.

The existing band inversion and band gap opening induced by SOC strongly point toward the existence of nontrivial topological properties. To confirm this topological nature, we calculate Z2 topological invariant using the method proposed by Soluyanov and Vanderbilt,59,60 which tracks the evolution of Wannier center of charges (WCCs) for an effective 1-D system with fixed ky in the subspace of occupied bands. The Wannier functions (WFs) with regard to lattice vector R can be written as

see that regions 2 and 3 have similar charge densities, which mainly accumulate at the center of interlayer bonds, suggesting a typical bonding state of pz orbitals, whereas regions 1 and 4 show antibonding properties. Therefore, we can conclude that the bonding and antibonding states of Bi-pz orbitals are already inverted in the absence of SOC, which is in agreement with previous results.44 After turning on SOC, a sizable band gap of 98.3 meV opens up at the Dirac cone (ED), as illustrated in Figure 2c,d. Here, the valence band maximum (VBM) is located in the vicinity of the X point, leading to an indirect global band gap (Eg) of 88.9 meV, see Figure 2d. Such a band gap is larger than the thermal energy at room temperature, allowing for viable applications in spintronics. Considering that the GGA exchange potential usually underestimates the band gap, the more reliable hybrid HSE06 functional is adopted to ensure the accuracy of the band gap calculation, as shown in Figure S2. We note that the band gap opening is preserved at the Dirac cone and turns out to be 88.6 meV, with a slight decrease. However, an unexpected metallic property is arisen due to the upshift of energy band at the X point, which may be eliminated by specific manipulation, such as strain engineering.

|R , n⟩ =

1 2π

π

∫−π dk e−ik(R−x)|unk⟩

A WCC xn̅ is defined as the mean value ⟨0n|X̂ |0n⟩, where X̂ is the position operator and |0n⟩ is the state corresponding to a WF in the cell with R = 0. Then, we have xn̅ =

i 2π

π

∫−π dk⟨unk|∂k|unk⟩ 1

Assuming that ∑α xα̅ S = 2π ∫ AS, with S = I or II, where α is a BZ band index of the occupied states and I and II are the Kramer 21517


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Figure 3. Variation of band gaps (ED and Eg) as a function of in-plane x-axial (a), y-axial (b) and biaxial (c) strain, respectively. (d−e) The orbitalresolved band structure of the 2ML BP-Bi(110) film at the biaxial strain of 18% and the corresponding edge states.

partners, whereas A is the Berry connection. So, the Z2 topological invariant can be expressed as Z2 =

valence and conduction bands, as shown in Figure 2f. By projecting the LDOSs with spin contribution, see Figure 2g, we find that the counter-propagating edge states have opposite spin, indicating that the spin momenta are locked. Noticeably, such edge states are distinctly different from the dissipationless transport in Dirac spin-gapless semiconductors,62 which simultaneously show a nontrivial insulating state and breaking of TRS for the edge state due to the internal magnetization. Besides, the Fermi level crosses the edge states three times between the −π/a and 0 momentum points, which further confirms a nontrivial topology in the 2ML film. Remarkably, these edge states cross linearly at the 0 momentum point, with a Fermi velocity of ∼5.4 × 105 m/s, comparable to the value of 5.5 × 105 m/s in the HgTe/CdTe quantum well9 and 6.34 × 105 m/s in the tetragonal Bi film.32 It should be pointed out that the Dirac cone is buried in the bulk conduction band, so the favorable transport property is unavailable in the experiment. According to previous results,35,63 this drawback may be resolved by edge functionalization or specific-element doping, with the Dirac cone exposed to the insulating bulk state. Considering that strain engineering is an effective avenue to manipulate the electronic properties of 2-D materials, which can be easily realized in experiments, we explore the in-plane strain effect on the topological properties of a 2ML BP-Bi(110)

∑ [xα̅ I(TRIM1) − xα̅ II(TRIM1)] α

−

∑ [xα̅ I(TRIM 2) − xα̅ II(TRIM 2)] α

where the TRIM denotes the time-reversal-invariant momenta. The Z2 topological invariant can be evaluated by counting the even or odd number of crossings of any arbitrary horizontal reference line with evolution, among which the even and odd numbers, respectively, represent the topologically trivial and nontrivial phases. According to this classification, we can explicitly verify the nontrivial topology with Z2 = 1 in the 2ML BP-Bi(110) film because any arbitrary reference line invariably crosses the evolution curves an odd number times, as illustrated in Figure 2e. The most prominent characteristic of QSH insulators is the presence of helical edge states protected by TRS. So, we further calculate the edge states of the semi-infinite 2ML BP-Bi(110) nanoribbon by the iterative Green’s function method61 based on maximally localized Wannier functions. In light of the local density of states (LDOSs) at the edges for 2ML BP-Bi(110) film, there indeed exist gapless edge states, which connect 21518


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Figure 4. (a) Variation of band gaps (ED and Eg) as a function of Δh. (b−e) The band structures of 2ML BP-Bi(110) under different puckered heights. (f) Variation of band gaps (ED and Eg) as a function of electric field.

film to gain insight into the robustness of the QSH state. Because the 2ML film possesses structural anisotropy, both uniaxial strain and biaxial strain are taken into account. Herein, the uniaxial strain contains two components: (i) x-axial strain and (ii) y-axial strain, which are defined as εx = (ax − a0x)/a0x and εy = (ay − a0y)/a0y, where ax (ay) and a0x (a0y) are the lattice constants along the x (y) direction under strain and equilibrium conditions. Figure 3a presents the variation of band gaps (ED and Eg) as a function of x-axial strain. As the tensile strain increases, the ED increases monotonically and reaches a maximum of 195.5 meV at 15%, whereas it decreases significantly under pressure. Meanwhile, Eg shows a parabolic trend, with a maximal value of 136.1 meV occurring at 10%. Most importantly, we find that the nontrivial topological phase is preserved over a wide range from −5 to 15%. The nature of the indirect band gap is maintained throughout the regulation. For the case of y-axial strain, as depicted in Figure 3b, it is gratifying to note that the QSH state of the 2ML film also shows a favorable robustness over a wide strain range. The ED decreases roughly with increasing tensile strain. However, the Eg increases initially, reaching a maximal value of 94.5 meV at 1%, and then drops rapidly with further extension, simultaneously transforming into a direct gap, due to the shift in the VBM. Unfortunately, the y-axial compression can easily annihilate the band gap, leading to the emergence of selfdoping and a metallic property. It is obvious that the tolerance of the band topology in the 2ML BP-Bi(110) film along the y direction is inferior to that along the x direction, which further demonstrates the anisotropy of the 2ML film, consistent with that reported in BP system.64 Next, we investigate the response of topological and electronic properties of 2ML film under biaxial strain, as depicted in Figure 3c. The band topology can be sustained until the tensile strain reaches 11%, but it is destroyed facilely with compression. Within this range of strain, the evolution of Eg and ED is analogous to the case of y-axial strain, indicating that the variation of the lattice constant along the y direction plays a dominant role in operating the nontrivial topology. Then we explore an even larger stain of 12−16%; the topological phase would be annihilated, accompanied by the disappearance of band inversion and the Dirac cone, as shown in Figure S3. When the tensile strain is higher than 17%, fantastically, an unexpected topological phase with different inversion mecha-

nisms is observed. Taking 18% as an example, we present its band structure in Figure 3d, in which the band inversion originating from the px,y and pz orbitals can be observed at the Γ point. Such band inversion has been demonstrated as a topological mechanism for the tetragonal Bi bilayer.32 Thus, to verify the nontrivial topology in 2ML films with an 18% tensile strain, we directly calculate the LDOS of edges for this structure, as shown in Figure 3e, in which the valence and conduction bands are connected by edge states. Different from the equilibrium state of the 2ML film, the Fermi level crosses the edge states only one time and the Dirac point disappears as well, but the bulk gap here reaches up to 198.8 meV, which is two times as large as that in the ground state (88.9 meV), implying feasible operability at room temperature. It is noted that such a large tensile strain is impractical by using epitaxial grow techniques. So, it is more important to perceive a new topological phase from an academic perspective rather than applications in devices. Next, we focus on the tolerance of nontrivial topology with the effect of out-of-plane strain, which is employed by tuning the puckered height. The variation of band gap (ED and Eg) in response to puckered height is presented in Figure 4a. When decreasing the puckered height, it can be seen that Eg and ED increase initially at Δh = −0.1 Å, with a direct band gap feature (Figure 4a). Under this condition, the interplane bonds strength increases correspondingly, which lowers the energy of bonding orbitals but raises the antibonding state; thus, the intensity of band inversion becomes obviously weak (Figure 4b). At Δh = −0.3 Å, however, the bonding and antibonding states move back to low and high energy regions, respectively, resulting in the disappearance of band inversion and emergence of a trivial phase (Figure 4c). On the contrary, for a positive Δh, the band gap decreases monotonously and the film finally develops metallic characteristic. The interplane bond lengths become longer under the out-of-plane stretched strain, which leads to a smaller superposition of pz orbitals. Here, we must point out that charge transfer occurs from in-plane to interplane bonds, which triggers the self-doping phenomenon (Figure 4d,e), although the band inversion near the Γ point still exists. Obviously, the nontrivial band topology is sensitive to the change in the puckered height induced by out-of-plane strain. 21519


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ACS Applied Materials & Interfaces However, it is still challenging to control in-plane and out-ofplane strain in experiments, especially the latter. Here, to provide a feasible scheme for strain engineering on a 2ML BPBi(110) film, we propose several assumptions based on van der Waals heterostructures. For in-plane strain, first, one can transfer this film onto an elastic substrate and then assess the deformation of the substrate to realize the regulation of strain, as shown in Figure S4a. Further, biaxial strain can also be introduced by an alternative approach, in which this film is deposited on a piezoelectric substrate, such as [Pb(Mg1/3Nb2/3)O3]0.7-[PbTiO3]0.3 (PMN-PT), and a bias voltage between the top and bottom electrodes is applied. The corresponding schematic diagram is depicted in Figure S4b. A similar method has been used for tuning the band gap of the MoS2 sheet through compressive strain.65 In the case of out-ofplane strain, this can be achieved by sandwiching the film with two piezoelectric materials, as illustrated in Figure S4c. Then, the puckered height of film would be adjusted under an associated strain stage induced by the deformation of both piezoelectric materials in the vertical direction. So, we expect that these suggestions will be helpful for the experimental design and tunability of material properties in the future. Using a perpendicular electric field is a facile approach to modulate the electronic properties of a 2-D film and thus it is important to investigate this effect in a 2ML BP-Bi(110) film. In Figure 4f, the evolution of band gaps (ED and Eg) as a function of electric field is displayed. One can see that ED and Eg decrease monotonously with increasing electric field intensity, and no bulk gap closing can be observed until 0.9 V/Å, suggesting that the 2ML film is robust against the electric field. In the process, the band degeneracy is lifted due to the inversion symmetry breaking, especially the portion contributed by antibonding state of the pz orbital. Moreover, we also find that the band splitting is proportional to the electric field intensity and reaches a maximum of 41 meV at 0.9 V/Å. Even then, the band gaps are much larger than the thermal motion energy (26 meV) at room temperature. As mentioned above, even if the band inversion is retained, the in-plane compressive strain and out-of-plane strain can readily trigger the self-doping phenomenon and metallic nature. In other words, singly applying in-plane and out-of-plane strain engineering has great limitation on tailoring the nontrivial properties of 2ML BP-Bi(110) film. Thus, eliminating the influence of self-doping plays a pivotal role in solving this problem. Inspired by this idea, we conceived a route for engineering the band structure of a 2ML film by dual regulation of in-plane and out-of-plane strain, which may provide definite help for experiments, as shown in Figure 5. For the combination of Δh and x-axial strain (Figure 5a), it can be seen that the drawback of self-doping has not been resolved completely, especially for Δh large than 0.2 Å, whereas the bulk gap can be tuned efficiently, as compared to that the case of single strain applied along the x direction. Interestingly, if we suitably combine Δh and y-axial strain as well as Δh and biaxial strain, see Figure 5b,c, nontrivial topological properties with a favorable bulk gap can be obtained in most situations. In light of these results, to fabricate an excellent 2ML BP-Bi(110) film, a small puckered height and giant in-plane tensile strain should not coexist at the same time. In a word, the band topology of a 2ML film with considerable bulk gap can be achieved by this kind of dual regulation mechanism. Finally, we emphasized on the 4ML BP-Bi(110) film, which has two stacked 2ML films. The optimized lattice constants of

Figure 5. Diagram of transition between different phases for a 2ML BP-Bi(110) film obtained from the global band gap as a function of xaxial strain and Δh (a), y-axial strain and Δh (b), biaxial strain and Δh (c). The red dashed line separates the trivial and nontrivial topological phases. Plus and minus of the global band gap represents the gap of TI and NI, respectively.

the 4ML film are a = 4.93 Å and b = 4.43 Å, as listed in Table 1, with a slight extension along the x direction compared to that in 2ML films. To verify the reliability of this lattice constant, we also checked the energy of a 4ML film which is adopted with the lattice constant of a 2ML film, and the result shows that it is higher than the above structure by 0.04eV per unit cell, suggesting that the above 4ML film is more likely to be fabricated in experiments. The interlayer spacing between two 2ML films is found to be 3.33 Å, and each 2ML BP-Bi(110) film maintains its original puckered structure, as shown in Figure 1d. We further present the orbital-resolved band structure of the 4ML film in Figure 6. Regardless of SOC, a semimetallic character can be observed, with two bands crossing linearly at the Fermi level along the Y−Γ line, as depicted in Figure 6a. These bands are likewise derived from the Bi-pz orbitals, accompanied by the Dirac cone, presenting a better Fermi velocity than that of the 2ML film at the Dirac cone. From the local charge density of four regions around the Fermi level in Figure 6b, we find that the inverted bonding and antibonding states are analogous to those in the case of the 2ML film. When SOC is turned on, a band gap of 70.0 meV arises at the Dirac cone, but the system exhibits a metallic 21520


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Figure 6. (a) Orbital-resolved band structure of a 4ML BP-Bi(110) film without SOC. (b) The local charge density of four regions marked in the band structure. (c) The calculated band structure with SOC. (d) The semi-infinite edge states of the 4ML BP-Bi(110) film.

Figure 7. Variations of band gaps (ED and Eg) as a function of in-plane x-axial (a), y-axial, (b) and biaxial (c) strains, respectively. (d) Variation of ED as a function of electric field and Δd.

locate in the bulk gap at 1%, implying the transformation of the QSH insulator. This nontrivial topological phase can be maintained up to 9%, accompanied by the alternate occurrence of indirect and direct band gaps, and the Eg obtains a maximum of 82.9 meV. Similar to the result for the 2ML film under inplane strain, the variation of band gaps (ED and Eg) for the 4ML film as an effect of biaxial strain is greatly determined by the change in the lattice constant in the y direction; however, it has a smaller tunable range of 1−7% to preserve the TI feature, as shown in Figure 7c. These findings demonstrate that the 4ML BP-Bi(110) film has the potential to realize a nontrivial topology with in-plane strain engineering. In addition to utilizing strain engineering, we have also applied an external electric field and changed the interlayer spacing (Δd) to explore the TI transition, see Figure 7d. Regretfully, these two measures can only seriously amplify the charge transfer between two 2ML films and thus consolidate the metallicity. To be brief, the 4ML BP-Bi(110) film can transform into nontrivial 2-D TI through appropriate strain engineering, which can be easily achieved by specific experimental approaches, simultaneously providing potential applications in nanoelectronic devices.

feature, with Fermi level passing through conduction bands, as illustrated in Figure 6c. This consequence is further confirmed by the edge states of the 4ML film, see Figure 6d, in which the Fermi level indeed traverses the bulk state. According to Bader analysis, the presence of metallicity is mainly attributed to the accumulation of electrons (0.2e) between two 2ML BP-Bi(110) films. Notably, the electronic properties of the 4ML film are similar to that in the case of a 2ML film with stretched strain along the z direction; thus, it is expected to realize the transition from metal to a QSH insulator for a 4ML film by inplane strain engineering. Figure 7a presents the response of electronic properties to inplane strain along the x direction in a 4ML film. It shows that the transition from metal to 2-D TI occurs at the critical point of −7%, and the bulk gap of film can reach 62.8 meV at −9%. However, the 4ML film would turn into metal once again if the compressive strain exceeds −10%, resulting from the drastic geometric change. On the contrary, tensile strain can only exacerbate the metallic nature of the system, whereas strain applied along the y direction has an opposite effect, wherein the compressive strain has no contribution to the transition, see Figure 7b. In the case of tensile strain, the Fermi level would 21521


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CONCLUSIONS In summary, using ab initio calculations, we systematically investigated the controllable electronic and topological properties of BP-Bi(110) films against structural deformation and electric field. Intriguingly, irrespective of the isolate or combined strain engineering, the QSH state in the 2ML BPBi(110) film shows excellent robustness within the scope of a certain strain, and the bulk gap of film can be effectively tuned. Interestingly, the topological phase induced by two different inversion mechanisms appears successively throughout the process of biaxial strain regulation. The 2ML film can sustain an electronic field of up to 0.9 V/Å without destroying its QSH state, accompanied by the bulk gap decreasing monotonically. Besides, under strain engineering, the 4ML film can transform into a considerable QSH insulator. Our findings are of importance not only for further experimental studies, but also for practical applications in spintronic devices based on 2-D BPBi(110) films.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.7b02818. Fluctuation of energy and snapshots of the 2ML BPBi(110) film from MD simulation (Figure S1); band structures of the 2ML BP-Bi(110) film based on the HSE06 functional (Figure S2); band structures of the 2ML BP-Bi(110) film under biaxial strain from 12 to16% (Figure S3); scheme diagrams to apply in-plane strain in experiments (Figure S4) (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (C.-w.Z.). *E-mail: [email protected] (S.-s.Y.). ORCID

Sheng-shi Li: 0000-0002-0417-3174 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the key program of NSFC (No. 11434006), the NBRP of China (Nos. 2013CB922303 and 2015CB921502), the 111 project (No. B13029), and the general program of NSFC (No. 11274143).

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Tunability of the Quantum Spin Hall Effect in Bi(110 ... - ACS Publications

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