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Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX-XXX

Effect of Amidogen Functionalization on Quantum Spin Hall Effect in Bi/Sb(111) Films Sheng-shi Li,†,‡ Wei-xiao Ji,† Shu-jun Hu,‡ Chang-wen Zhang,*,† and Shi-shen Yan*,‡ †

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

‡

S Supporting Information *

ABSTRACT: Knowledge about chemical functionalization is of fundamental importance to design novel two-dimensional topological insulators. Despite theoretical predictions of quantum spin Hall effect (QSH) insulator via chemical functionalization, it is quite challenging to obtain a high-quality sample, in which the toxicity is also an important factor that cannot be ignored. Herein, using firstprinciples calculations, we predict an intrinsic QSH effect in amidogen-functionalized Bi/Sb(111) films (SbNH2 and BiNH2), characterized by nontrivial Z2 invariant and helical edge states. The bulk gaps derived from px,y orbitals reaches up to 0.39 and 0.83 eV for SbNH2 and BiNH2 films, respectively. The topological properties are robust against strain engineering, electric field, and rotation angle of amidogen, accompanied with sizable bulk gaps. Besides, the topological phases are preserved with different arrangements of amidogen. The H-terminated SiC(111) is verified as a good candidate substrate for supporting the films without destroying their QSH effect. These results have substantial implications for theoretical and experimental studies of functionalized Bi/Sb films, which also provide a promising platform for realizing practical application in dissipationless transport devices at room temperature. KEYWORDS: spintronics, quantum spin Hall effect, topological insulators, two-dimensional materials, first-principles calculations

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Starting from graphene,1 many 2D materials are predicted as TIs, including silicene,9,10 stanene,11 plumbene,12 phoshorene,13 and arsenene,14,15 whereas some of them are extrinsic and require the assistance of external factors due to the weak spin−orbit coupling (SOC). Thus, extensive efforts are devoted to the materials composed of the elements in the bottom right corner of the periodic table of elements, such as Sb and Bi, which can provide stronger SOC effect. For instance, the Bi(111) films16−18 have been theoretically verified to be intrinsic 2D TI when the thickness is below four bilayers, and the nontrivial bulk gap decreases with respect to the number of layered thickness. Meanwhile, the nontrivial topological phase can be readily realized in Sb(111) bilayer via appropriate strain engineering.19 In addition to the structural motif with hexagonal atomic rings, the QSH effect is also available for the tetragonal Bi bilayer20 and bismuthylene,21 which is derived from band inversion between Bi-p orbits. Very recently, the topological phase has been validated in Bi(110) film by detecting the gapless edge states at 77 K in experiment.22 Technologically, chemical functionalization of single atom or radical is an effective avenue to tailor the electronic and

INTRODUCTION Topological insulator (TI), which is theoretically predicted in 20051,2 and experimentally demonstrated in HgTe/CdTe quantum well in 2006,3 has attracted extensive research enthusiasm in material science and condensed matter physics. It allows control of spin configuration and spin current to be realized due to the presence of gapless edge (surface) states with protection of time-reversal symmetry (TRS) inside the bulk insulating gap. In other words, the propagation direction of electrons at the edge (surface) in TIs is relevant to their spin orientation, and such metallic states are robust against nonmagnetic perturbations, providing dissipationless transport channels. In light of these hallmarks, TIs are of promising potential for applications in electronic/spintronic4 and quantum computing devices.3,5 Two-dimensional (2D) TIs, namely, quantum spin Hall (QSH) insulators, host an advantage over three-dimensional (3D) TIs, as the electrons can only flow along two directions and thus the backscattering is completely prohibited.6 Experimentally, the HgTe/CdTe3,5 and InAs/GaSb7,8 quantum wells are amply confirmed as 2D TIs. However, the extremely small bulk gaps and incompatibility with conventional semiconductor devices seriously restrict their practical application at room temperature. In a word, it is a permanent goal to search for 2D TIs with sufficiently large bulk gap and experimental feasibility. © XXXX American Chemical Society

Received: August 31, 2017 Accepted: November 6, 2017

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DOI: 10.1021/acsami.7b13179 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

Figure 1. Schematic of the structure of XNH2 films from top view (a) and side view (b). (c) Variation of energy as a function of lattice constant.

hydrogenated SiC (111) is demonstrated as a suitable substrate for supporting these films, simultaneously preserving their topological behavior. These results greatly enrich the family of 2D TIs based on Bi/Sb(111) films and provide a promising candidate to design ultralow-dissipation electronic devices in future.

topological properties of 2D materials. Moreover, the stability of material can also be improved simultaneously due to the elimination of surface activity. To date, the most commonly used functionalization are hydrogenation and halogenation, which have been verified to credibly introduce topological nature in Sb/Bi(111) films.23−27 However, a recent experimental result shows that lattice disorder and increasing defects are inevitable under hydrogen and halogen plasma.28 Additionally, the hydrogenated film usually suffers from a probability to be oxidized when exposed to ambient condition.29,30 In view of these drawbacks, the preparation of hydrogenated and halogenated Sb/Bi(111) films with high quality may face a great challenge. On the other hand, radical functionalization, such as ethynyl (−C2H),31 methyl (−CH3),24,32 and cyano (−CN)26,33 group, is proposed to be an alternative route to achieve QSH effect with large bulk gap and favorable stability. Nevertheless, most operations are limited to the realm of theoretical prediction. Beyond that, the toxicity of radical deserves to be paid special attention to during the experimental process, i.e., −CN.26,33 Thus, there is an urgent need to search QSH insulators with experimental feasibility and nontoxicity. Amidogen (−NH2), a basic radical in organic chemistry, has shown an increased potential in surface functionalization on nanostructures34−38 and can effectively modify the electronic properties of materials. However, the effect of amidogen functionalization on QSH effect of 2D materials is unknown so far, especially for Sb/Bi(111) films. A question is naturally arisen whether the passivation of amidogen on Sb/Bi(111) films is viable and gives rise to distinct electronic and topological properties. In the present work, on the basis of first-principles calculations, we predict the presence of intrinsic QSH effect in amidogen-functionalized Bi/Sb(111) films (SbNH2 and BiNH2), which can be confirmed by nontrivial Z2 invariant and helical edge states. Different from previous functionalized cases,23−27,33 a semiconducting property is obtained in the absence of SOC, due to the lower symmetry induced by amidogens. The SOC gaps derived from px,y orbitals are 0.39 and 0.83 eV for SbNH2 and BiNH2 films, respectively, sufficiently large for practical application. Their nontrivial topology shows a favorable robustness against strain engineering, electric field, and rotation angle of amidogens, with tunable band gap. In addition, we note that the topological phases are independent of the arrangement of amidogens, i.e., both sides or single side, except the alteration of bulk gap. The

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COMPUTATIONAL DETAILS The first-principles calculations were implemented by the Vienna ab initio simulation package (VASP).39,40 The projector-augmented wave (PAW) method41 was employed for describing the electron-ion potential. Generalized gradient approximation (GGA) in Perdew−Burke−Ernzerhof form42,43 was adapted to approximate the electron−electron interaction. The cutoff energy of plane wave basis was set at 450 eV, and all of the lattice constants and atom coordinates were optimized until the convergence of force on each atom less than 0.001 eV/Å. The k-meshes of 11 × 11 × 1 and 13 × 13 × 1 generated by the Γ-center Monkhorst−Pack method were set for geometry optimization and self-consistent calculation, respectively. A vacuum space of 25 Å was applied to avoid interactions between periodic structures in the z direction. The method of DFT-D244 and dipole corrections were taken into account throughout the calculation of heterostructures. Besides, the SOC was included in calculations for the band structure. Hybrid HSE06 functional45 was used to confirm the band structures of amidogen-functionalized Sb/Bi(111) films. A QSH insulator can be characterized by a topological invariant Z2 = 1, whereas the trivial band topology is represented by Z2 = 0. To affirm the topological nature of amidogen-functionalized Bi/Sb(111) films with inversion symmetry, the Z2 invariant was established by using the scheme proposed by Fu and Kane.46,47 The equation is expressed as follows N

4

( −1)Z 2 =

∏ δ(K i) = δ(Γ)δ(M)3 , i=1

δ(K i) =

∏ ξ2im m=1

where δ is the product of parity eigenvalues at four timereversal invariant momenta points (TRIMs) in Brillouin zone (BZ), ξ = ±1 denotes parity eigenvalues, and N is the number of the occupied bands. For the passivated configurations without inversion symmetry, we employed the approach proposed by Soluyanov and Vanderbilt48,49 to calculate the Z2 invariant. This approach B


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ACS Applied Materials & Interfaces Table 1. Structural and Electronic Properties for XNH2 and S-XNH2 Filmsa configuration

a (Å)

dX−X (Å)

dX−N (Å)

h (Å)

Eg (eV)

EKSOC (eV)

EgSOC (eV)

Ef (eV/unit cell)

BiNH2 SbNH2 S-BiNH2 S-SbNH2

5.48 5.24 5.66 5.48

3.17 3.04 3.27 3.15

2.23 2.10 2.21 2.09

0.02 0.01 0.00 0.00

0.14 0.16 0.03 0.06

1.21 0.39 1.01 0.27

0.83 0.39 0.46 0.27

−9.22 −9.51 −9.32 −9.46

a

Calculated lattice constant (a), bond length (dX−X and dX−N), buckled height (h), formation energy (Ef), band gap without SOC (Eg), band gap opening at K point (EKSOC), and global band gap (EgSOC) with SOC for XNH2 and S-XNH2 configurations.

To evaluate the stability of XNH2 films, we first calculate their formation energy per unit cell, which is defined as

tracks the evolution of Wannier charge centers (WCCs) for an effective one-dimensional system with fixed ky in the subspace of occupied bands. The Wannier functions (WFs) in regard to lattice vector R can be written as |R , n⟩ =

1 2π

Ef = E XNH2 − nX E X − nNE N − nHE H

where EXNH2 is the total energy of amidogen-functionalized X(111) films, whereas EX, EN, and EH are the chemical potentials of X, N, and H atoms obtained from bulk X, nitrogen molecule, hydrogen molecule, respectively; nX, nN, and nH are the numbers of X, N, and H atoms in an unit cell, respectively. The calculated formation energies are found to be −9.51 and −9.22 eV per unit cell for SbNH2 and BiNH2, respectively, which are significantly larger than methyl- and cyano-functionalized X(111) films..24,33 These indicate that the XNH2 films are relatively stable structures. Moreover, we perform ab initio molecular dynamics (MD) simulations at room temperature (300 K) using a 6 × 6 × 1 supercell with a time step of 1 fs to explore the structural perturbation of XNH2 films. The results of SbNH2 film are presented in Figure 2. One can see that the

π

∫−π dke−ik(R−x)|unk⟩

The WF depends on a gauge choice for the Bloch states |unk⟩. A WCC xn̅ is defined as the mean value of ⟨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 can obtain 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, I and II are the Kramer partners, and A is the Berry connection. So, the Z2 topological invariant can be expressed as Z2 =

∑ [xα̅ I(TRIM1) − xα̅ II(TRIM1)] α

−

∑ [xα̅ I(TRIM 2) − xα̅ II(TRIM 2)] α

The identification of Z2 invariant can be obtained by counting the numbers of crossing between any arbitrary horizontal reference line and evolution of the WCCs, where the odd and even numbers represent nontrivial and trivial topological phases, respectively.

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RESULTS AND DISCUSSION Pristine 2D Bi/Sb(111) films possess a buckled configuration due to the relatively weak π−π bonding between Bi/Sb atoms. When functionalized with amidogen, these films prefer the quasi-plane structure, as shown in Figure 1a,b, in which the rhombohedral unit cell is represented by the red dotted line. Herein, we find that the system presents a spatial inversion symmetry with amidogen regularly decorated on both sides of the film. For convenience, the functionalized films are uniformly denoted as XNH2 (X = Sb, Bi). The obtained lattice constants of SbNH2 and BiNH2 films are 5.23 and 5.48 Å, respectively, which are established by the energy minimization procedure, as depicted in Figure 1c. Compared with pristine X(111) films, lattices of XNH2 films are obviously enlarged, leading to dramatical decrease of buckled height (h) and slight increase of X−X bond lengths (dX−X), as listed in Table 1. Meanwhile, the calculated X−N bond lengths (dX−N) for SbNH2 and BiNH2 turn out to be 2.10 and 2.23 Å, respectively. It should be pointed out that, different from other functionalized cases,23−25,33 the amidogen was decorated on X(111) films with an angle of 96.22° rather than perpendicular to the 2D plane, which may trigger distinct electronic properties.

Figure 2. (a) Variation of energy with increasing time obtained from MD simulation at 300 K for SbNH2 film. (b, c) Top and side views of the snapshot of SbNH2 film at 1000 and 2000 fs, respectively.

fluctuation of energy (Figure 2a) tends to be a constant with increasing heating time. As can be seen from the snapshot of geometric structure at 1000 and 2000 fs (Figure 2b,c), the honeycomb skeleton along with slight distortion can be observed, but no bond breaking arises. A similar result can also be extracted from BiNH2, as shown in Figure S1. It is noteworthy that the amidogens are freely rotating, indicating C


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Figure 3. Orbital-resolved band structures, accompanied with partial charge density at VBM and CBM, and 3D band structure of BiNH2 film without (a, b) and with (c, d) SOC.

Figure 4. Parities of occupied bands at TRIMs for BiNH2 (a) and SbNH2 (b) films. Total and spin-projected edge states of semi-infinite lattice for BiNH2 (c, d) and SbNH2 (e, f) films.

separating each other at the Fermi level, forming a band gap (Eg) of 0.14 eV (left panel of Figure 3a), which is significantly different from the semimetallic nature in other functionalized cases.23−25,33 By projecting energy bands with atomic orbitals, the states near the Fermi level are mainly derived from Bi-px,y orbitals, whereas the pz orbital is removed from the Fermi level due to the saturation, namely, orbital-filtering effect.31,32,50,51 To further confirm the existence of band gap, a 3D energy dispersion near the Fermi level is plotted in Figure 3b, in which a sizable band gap opening can be observed at the K point. For

that the inversion symmetry is not inevitable. As regards the rotation angle of amidogens, we discuss its effect in subsequent sections. In a word, the XNH2 films are intrinsically stable at room temperature, which is important for their practical applications. In the following, we turn to the electronic properties of XNH2 films. The typical band structures of the BiNH2 film are presented in Figure 3. Without considering SOC, a semiconducting property can be observed, with valence band maximum (VBM) and conduction band minimum (CBM) D


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Figure 5. Band gap opening at K and Γ points and global gap as a function of SOC strength for BiNH2 (a) and SbNH2 (b) films.

Figure 6. Values of Eg, EKSOC, and EgSOC as a function of in-plane strain for BiNH2 (a) and SbNH2 (b) films.

SbNH2 film, a similar band structure with a smaller band gap of 0.16 eV is obtained, as shown in Figure S2a,b. To visualize the electronic properties, we further plot the charge density distribution corresponding to VBM and CBM (see right panels of Figure 3a and Figure S2a). Notably, σ-type bonding feature is located along zigzag and armchair directions for VBM and CBM, respectively, which has also been reported in previous results.52−54 Such resonance distribution of charge density belongs to typical Kekulé or Dewar structure. When taking SOC into account, as depicted in Figure 3c, the band gap of BiNH2 film at the K point (EKSOC) increases to 1.21 eV, whereas a global indirect band gap (EgSOC) of 0.83 eV is obtained, with VBM and CBM locating at K and Γ points, respectively. The 3D plot of band structure in Figure 3d exactly reveals the behavior of indirect band gap. It notes that the electronic states in the vicinity of Fermi level are still determined by px,y orbitals. In the case of SbNH2 film, the direct band gap is sustained and enhances to 0.39 eV, as illustrated in Figure S2c,d. Here, from the right panels of Figures 3c and S2c, we find that the charge density of VBM and CBM are separately localized at different X atoms in a unit cell. Considering that the GGA functional generally underestimates the band gap, the hybrid HSE06 functional is adopted to check the accuracy of band gap calculation (see Figure S3). Extremely large EgSOC’s of 1.00 and 0.51 eV are established for BiNH2 and SbNH2 films, respectively, which are conducive to experimental observability and potential application in spintronic devices. To verify the nontrivial topological phase of XNH2 films, the Z2 invariant is calculated using the method proposed by Fu and Kane.46,47 The parity eigenvalues of the Bloch wave functions for occupied bands at four TRIMs are presented in Figure 4a,b. It shows that the parity eigenvalues at Γ and M points are −1

and +1, respectively, implying that XNH2 films host nontrivial topological nature with Z2 = 1. Therefore, amidogen functionalization is an efficient approach to achieve QSH effect with extremely large bulk gap in X(111) films. The hallmark of 2D TI is the presence of helical gapless edge states. Here, on the basis of maximally localized Wannier functions, we calculate their edge states of a semi-infinite lattice constructed by an iterative Green’s function method.55,56 In Figure 4c−f, we find that the local density of states (LDOSs) at the edges traverse the bulk gap and connect the valence and conduction bands. More importantly, by projecting the contribution of spin, it shows that the counter-propagating edge states are fully spin-polarized. In comparison, a prominent difference is captured, in which the Dirac cone of SbNH2 is lower than the VBM. Thus, it is difficult to observe the favorable transport property in experiment. Inspired by a previous result, this drawback may be overcome by edge functionalization or specific element doping, driving the Dirac cone expose to the insulating bulk gap. In contrast, the intrinsic Dirac state located in larger bulk gap makes the BiNH2 film more advantageous for practical applications. Having established the QSH effect in XNH2 films, it is necessary to understand the underlying topological mechanism because the semiconducting property is obtained before and after considering SOC effect. Here, the evolutions of EgSOC, EKSOC, and EΓSOC (band gap opening at the Γ point) for XNH2 films as a function of SOC strength are investigated. With increasing SOC strength (see Figure 5a), one can see that the EKSOC of BiNH2 film is enhanced monotonously, whereas EΓSOC shows a contrary trend. The emergence of indirect band gap can be observed in the range of 0.8−1.6, in which the EgSOC almost remains a constant. Remarkably, when the relative SOC E


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Figure 7. Values of Eg, EKSOC, and EgSOC as a function of external electric field for BiNH2 (a) and SbNH2 (b) films.

Figure 8. Variation of global band gap and energy difference with different rotation angles of amidogens for BiNH2 (a) and SbNH2 (b) films.

then increases rapidly with further compression, which obtains a maximal value of 0.93 eV at −10%. On the contrary, the EgSOC is enhanced slowly and finally reaches a constant (∼0.90 eV) under tensile strain. A similar change trend of EKSOC (EgSOC) is also observed for SbNH2 film, which undergoes a parabolic trend, as shown in Figure 6b. The EKSOC drops sharply with further compression and reduce to 0.37 eV and continually decreases to 0.38 eV under expansion. This phenomenon can be well explained by the increasing buckled height, as illustrated in Figure S4. Under this circumstance, the transition from sp2 to sp3 hybridization occurs, namely, the SOC strength related to in-plane px,y orbitals is weakened. Thus, the band gap at the K point decreases under stain engineering. More interestingly, the topological properties of XNH2 films remain in the strain range of ±10%, accompanied by tunable band gaps, which offers a route to manipulate their band topology. It should be pointed out that although the strain decreases the band gap, the nontrivial bulk gap is still sufficiently large for application in spintronics. Next, we explore the effect of perpendicular electric field on the electronic and topological properties of XNH2 films. The response of band gap to electric field intensity is given in Figure 7. The apparent change induced by electric field is the removal of band degeneracy, due to the inversion symmetry breaking. The splitting value (ΔS) is proportional to the electric field intensity (see inset of Figure 7). In light of this phenomenon, the band gaps are found to decrease monotonously with increasing electric field, along with VBM and CBM shifting toward Fermi level. Even so, the band gap is larger than the thermal motion energy (26 meV) at room temperature, implying that the QSH effect in XNH2 films is robust against

strength exceeds 1.7, the direct global band gap would arise again, but locates at the Γ point. For SbNH2 film, as depicted in Figure 5b, the overall trend of EKSOC and EΓSOC is analogous to that in the BiNH2 film, but the critical point of transition for band gap occurs at 1.8 due to the rather weak SOC strength in Sb atom. In general, despite the global indirect band gap, the EKSOC is proportional to SOC strength. Thus, we can conclude that the XNH2 films belong to the Kane−Mele-type QSH insulator,1 rather than the Bernevig−Zhang-type topological insulator, in which the band gap would close and reopen at a certain SOC strength. Strain engineering has been demonstrated as a common and efficient avenue to tailor electronic properties of 2D materials. Here, the applied biaxial strain is simulated by changing the lattice constant as ε = (a − a0)/a0, where a (a0) is lattice constant under the strain (equilibrium) condition, and then fully optimizes the atom positions. The variation of band gap as a function of biaxial strain is plotted in Figure 6. For BiNH2 film (Figure 6a), regardless of SOC effect, the band gap shows a continually increasing trend under compressive strain, whereas the tensile strain supports an opposite effect. The bonding and antibonding states at the K point are dominated by the Bi−Bi (Sb−Sb) bonds. When the in-plane lattice is compressed, the reduced bond lengths lead to the bonding and antibonding states further separated energetically, resulting in an increase of band gap. Reversely, the band gap would decrease with the expansion of bonding length. When SOC is taken into account, the EKSOC presents a parabolic trend, in which the ground state holds the maximum value. However, the change trend of EgSOC is complicated due to the irregular change of CBM at the Γ point. With increasing compression, the EgSOC decreases initially and reaches the minimum of 0.81 eV at −5% and F


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Figure 9. Schematic of the structure of S-XNH2 films from top view (a) and side view (b). Orbital-resolved band structures of S-BiNH2 film without (c) and with (d) SOC.

Figure 10. (a) Evolution of Wannier charge centers along ky for S-BiNH2 film. Arbitrary reference line (red dash line) paralleled to ky crosses the evolution lines with odd times, indicating Z2 = 1. (b, c) Total and spin-projected edge states of semi-infinite lattice.

external electric field, which also provides an alternative route to manipulate their nontrivial band gaps. Additionally, the amidogen may have different angles on the surface of XNH2 films due to its irregular configuration. To give an insight into the effect of rotation angles, we investigate the stabilities and the electronic and topological properties of XNH2 films with different functionalized angles. First, the situation of amidogen in Figure 1a is defined as 0°; then, the rotating cases can be classified into two categories according to rotation mode, i.e., symmetric rotation and free rotation. Here, the former is realized by rotating the angle symmetrically from 0 to 315° with a rotation step of 45°, and we choose a representation for the latter by operating two amidogens in a unit cell with 45 and 135°, respectively. These configurations with different rotation angles are stable after full structural optimization. To evaluate their relative stability, the energy difference (ΔE) is employed, which is defined as ΔE = Er(XNH2) − E0(XNH2), where Er(XNH2) and E0(XNH2) are total energies of rotating and pristine XNH2 films. The variation of ΔE with regard to rotation angles is shown in Figure 8. Although the pristine structure is the most stable, other configurations may also be synthesized under different experimental conditions. Interestingly, the band gaps of all of these structures are still larger than 26 meV, especially the maximum value reaching up to 0.40 and 0.83 eV for SbNH2 and BiNH2 films, respectively. These guarantee the observations of QSH effect in experiment.

Motivated by the above-discussed issue, we wonder that whether the amidogen functionalization on single side of X(111) films would render a nontrivial band topology. Figure 9a gives the geometric structure of amidogen-functionalized X(111) films on single side, which is defined as S-XNH2 films. Compared with XNH2, the lattice of S-XNH2 films is further enlarged, due to the intensive arrangement between amidogen, accompanied with stretching X−X bond length, as listed in Table 1. On this occasion, a planar configuration is formed for S-XNH2 films, and the amidogens present a specific arrangement pattern. From the aspect of structural stability, we find that the formation energies of S-XNH2 films are almost identical to the cases of XNH2 films, suggesting a high thermodynamic stability. The orbital-resolved band structures of S-XNH2 films are presented in Figures 9b,c and S5. In the absence of SOC, S-XNH2 films likewise exhibit semiconducting properties with a small gap locating at K point. When the SOC effect is included, the band degeneracy is lifted as a consequence of the lack of inversion symmetry, and the global indirect and direct band gaps of 0.46 and 0.27 eV are generated for S-BiNH2 and S-SbNH2 films, respectively. Analogous to XNH2 films, the states near the Fermi level are mainly derived from the px,y orbitals of Bi/Sb atoms. Such electronic properties of S-XNH2 films strongly suggest the existence of the topological nature. To verify the above supposition, the Z2 invariant is identified by counting the numbers of crossing between any arbitrary G


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Figure 11. (a) Schematic diagram of BiNH2/SiC(111) heterostructure. (b, c) Calculated band structure of BiNH2/SiC(111) without (b) and with (c) SOC. (d−f) The corresponding results for S-BiNH2/SiC(111) heterostructure.

Realistically, the complicated interaction between substrate and film usually affects the electronic properties and intrinsic QSH effect in 2D TIs.57−60 To eliminate the influence of substrate as much as possible, we attempt to construct a van der Waals (vdW) heterostructure composed of 1 × 1 amidogenfunctionalized Bi(111) film (BiNH2 and S-BiNH2) and √3 × √3 H-terminated SiC(111) substrate, denoted as BiNH2/ SiC(111) and S-BiNH2/SiC(111), respectively, as shown in Figure 11, in which the lattice mismatch is less than 6.2%. Recently, the Bi(111) film has been synthesized on Bi2Se3 substrate with a lattice mismatch of 9.0% between them.61 This indicates that our proposed heterostructure may be feasible in experiments. After full structural optimization, we find that the BiNH2 and S-BiNH2 films can be supported by the substrate commendably, without any lattice distortion. Moreover, the interlayer distances are found to be 4.14 and 3.24 Å for BiNH2/ SiC(111) and S-BiNH2/SiC(111), respectively, far exceeding the chemical bonding range. To further understand the interaction between substrate and films, the adsorption energy is employed, which is expressed as Ead = Etotal − (Efilm + Esub), where E total, Efilm, and Esub represent the energies of heterostructures, free-standing films, and substrate. The calculated results for BiNH2/SiC(111) and S-BiNH2/SiC(111) are −112.45 and −126.94 meV/Å2, respectively, which indicate that they have equal probabilities to be fabricated in experiments. Besides, similar heterostructures are constructed for SbNH2 and S-SbNH2 films (SbNH2/SiC(111) and S-

horizontal reference line and evolution of the WCCs, as shown in Figures 10a and S6a, where an odd number crossing can be observed, exactly confirming that S-XNH2 films are 2D TIs. On the other hand, the LDOSs of semi-infinite lattice for S-XNH2 films are explored, as depicted in Figures 10b,c and S6b,c. We note that the dispersion of the edge states starts from conduction bands and then is adsorbed into valence bands, which spans the bulk gap and forms a pair of conducting channels for spin current transport. The presence of helical edge states inside the bulk gap further evidences that the SXNH2 films are indeed nontrivial QSH insulators. Having established that the fully functionalized X(111) films host QSH effect, we turn to the case of half-passivated films, denoted as H-XNH2, which might lead to the quantum anomalous Hall (QAH) effect through breaking TRS. Distinct from fully functionalized cases, the H-XNH2 films become a buckled structure (Figure S7a), whose lattice constants are 5.11 and 4.85 Å, respectively. Figure 7b−e gives the calculated electronic properties of H-XNH2 films. Before turning on SOC, the H-SbNH2 film is nonmagnetic, but H-BiNH2 exhibits a spin-polarized behavior with a magnetic moment of 0.17 μB per unit cell, which is an essential factor to achieve QAH effect. However, H-XNH2 films show metallic character when including SOC; thus, it is impossible to realize the QAH effect in half-functionalized X(111) films. From the perspective of practical application for predicted 2D TIs, it is essential to deposit the film on a suitable substrate. H


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Sb(111) films by identifying Z2 invariant and the presence of helical edge states. Different from other functionalized cases, the XNH2 films are endowed with a semiconducting property when excluding SOC. Giant nontrivial gap ranging from 0.27 to 0.83 eV can be observed, mainly derived from px,y orbitals of Bi/Sb atoms. The topological phase in Bi/SbNH2 films shows a favorable robustness against strain engineering, perpendicular electric field, and rotation angle of amidogens, accompanied with effectively modulated bulk gap. Moreover, the topological nature is persisted with different arrangements of amidogen. It is also demonstrated that the H-terminated SiC(111) is an appropriate substrate that can support these films and preserve their QSH effect simultaneously. These findings not only introduce new vitality into 2D TIs family based on group-V films, but also provide a platform for the application in spintronics.

SbNH2/SiC(111)) with a better lattice match (mismatch less than 3%). The films preserve their pristine geometric properties, and the interlayer distances of the heterostructures reduce to 1.59 and 2.44 Å. Their adsorption energies turn out to be −114.95 and −122.77 meV/Å2. In view of these results, the constructed configurations belong to typical vdW heterostructures. Then, the electronic properties of BiNH2/SiC(111) and SBiNH2/SiC(111) heterostructures are studied, as illustrated in Figure 11, in which the contributions of films and substrate are marked separately. For the former, the role of substrate is confined to the alteration of band gap due to the proximity effect. Instead, without considering SOC, the deposition on substrate makes S-BiNH2 film transform into an indirect band gap semiconductor (Figure 11e). As the SOC effect is taken into account, the band splitting is enhanced and suppresses the band gap (Figure 11f). Moreover, the prominent effect of substrate for SbNH2 and S-SbNH2 is the regulation of band gaps, as depicted in Figure S8. It is worth mentioning that the electronic states near the Fermi level are still dominated by px,y orbitals of Sb/Bi atoms, revealing that the nontrivial topological phase is not disturbed by the substrate. So, we can conclude that SiC(111) is an ideal candidate substrate for supporting the intrinsic topological properties in amidogen-functionalized Bi/ Sb(111) films. In addition to SiC(111), many other semiconductors, such as transition-metal dichalcogenides, 62 BN, 32 InSb, 63 and Si(111),64 have also been proposed as substrate to support 2D TI films. Here, we select MoS2 monolayer as a potential substrate to construct heterostructures because the lattice mismatch is less than 4.6%, as shown in Figures S9a and S10a. It is important to note that the interlayer distances and adsorption energies are 2.53−3.21 Å and −88.31 to −114.80 meV/Å2, respectively, which indicates that the vdW interaction plays an important role. From the calculated band structures in Figures S9 and S10, one can see that the states at the Fermi level are jointly dominated by the films and MoS 2 . Unexpectedly, a phenomenon of self-doping occurs due to the charge transfer from film to substrate. The BiNH2/MoS2 heterostructure still maintains its band topology, which is ascribed to the strong effect of SOC. Additionally, we also select the BN substrate to grow SbNH2 (2.6%) and S-SbNH2 (0.1%) films. As can be seen in Figure S11, the S-SbNH2/BN suffers from self-doping, exhibiting a metallic property, whereas the nontrivial topology in SbNH2/BN preserves. In a word, the predicted QSH insulators could be realized on appropriate substrate for potential device applications. Finally, apart from the intrinsic topological phase, the nontoxicity of amidogen radical and experimental feasibility are other advantages of XNH2 films. The Bi(111) film has been fabricated via molecular-beam epitaxy.65−68 Then, amidogen functionalization may be achieved by exposing the film to a N2 + H2 environment, which has been carried out on other nanodiamonds.37 Additionally, drawing on previous measure of amidogen passivation on carbon nanotube,69,70 the XNH2 films may be achieved through N2/NH3 plasma treatment. It is remarkable that these proposed preparation procedures are all nontoxic, accompanied with high-quantity functionalized films, which would greatly promote the experimental process.

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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.7b13179. Fluctuation of energy and snapshots of BiNH2 film from MD simulation (Figure S1); band structures of SbNH2 film (Figure S2); band structures of BiNH2 and SbNH2 films with hybrid HSE06 functional (Figure S3); buckled height as a function of biaxial strain (Figure S4); band structures of S-SbNH2 film (Figure S5); evolution of WCC and edge states for S-SbNH2 film (Figure S6); structural and electronic properties of H-XNH2 films (Figure S7); band structures of SbNH2 and S-SbNH2 films on SiC(111) substrate (Figure S8); structural and electronic properties of XNH2 films on MoS2 substrate (Figure S9); structural and electronic properties of SXNH2 films on MoS2 substrate (Figure S10); and structural and electronic properties of SbNH2 and SSbNH2 films on BN layers (Figure S11) (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), 111 project (No. B13029), and the general program of NSFC (No. 11274143).

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REFERENCES

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CONCLUSIONS In summary, on the basis of first-principles calculations, we predict the intrinsic QSH effect in amidogen-functionalized Bi/ I


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