Abstract
Twodimensional (2D) groupIIIV honeycomb films have attracted significant interest for their potential application in fields of quantum computing and nanoelectronics. Searching for 2D IIIV films with high structural stability and largegap are crucial for the realizations of dissipationless transport edge states using quantum spin Hall (QSH) effect. Based on firstprinciples calculations, we predict that the methylfunctionalized InBi monolayer (InBiCH_{3}) has no dynamic instability and hosts QSH state with a band gap as large as 0.29 eV, exhibiting an interesting electronic behavior viable for roomtemperature applications. The topological characteristic is confirmed by sp_{xy} band inversion, topological invariant Z_{2} number and the timereversal symmetry protected helical edge states. Noticeably, the QSH states are tunable and robust against the mechanical strain, electric field and different levels of methyl coverages. We also find that InBiCH_{3} supported on hBN substrate maintains a nontrivial QSH state, which harbors the edge states lying within the band gap of substrate. These findings demonstrate that the methylfunctionalized IIIV films may be a good QSH platform for device design and fabrication in spintronics.
Introduction
Twodimensional (2D) topological insulators (TIs), known as quantum spin Hall (QSH) insulators, have attracted significant researches interest in condensed matter physics and materials science ^{1,2,3}. The unique characteristic of 2D TI is generating 1D helical edge states inside the bulkgap, where the states moving in opposite direction have opposite spin. Therefore, the backscattering is prohibited as long as the scattering potential does not break timereversal symmetry (TRS) and such helical edge states provide a new mechanism to realize nondissipative electronic transportation, which promises potential application in lowpower and multifunctional device^{1,2}. This opens a new avenue in the quest for searching and designing TIs in 2D systems. From this point of view, a 2D TI with a large gap, chemically stable under ambient condition exposure to air and easy to prepare experimentally, is highly desired^{4,5}. The prototypical concept of QSH insulator is first proposed by Kane and Mele in graphene^{6,7}, in which the spinorbital coupling (SOC) opens a band gap at the Dirac point. However, due to the rather weak SOC, the associated gap is extremely small (~10^{–3} meV)^{8}, which makes the QSH effect can only be observed at an unrealistically low temperature. Fortunately, this unobservable bulk band gap has predicted to be enhanced by constructing van der Waals heterostructures with graphene and other 2D materials which possess strong SOC effect, such as Bi_{2}Se_{3}^{9}, WS_{2}^{10} and chalcogenides BiTeX (X = Cl, Br and I)^{11}. Quantized conductance through QSH edge states have been experimentally demonstrated in HgTe/CdTe^{12,13} and InAs/GaSb^{14,15} quantum wells, demonstrating an interesting in further experimental studies and possible applications.
Currently, searching for new QSH insulators with controllable quantum phase transitions and tunable electronic and spin properties is crucial for promoting TI technology. After the discovery of QSH phase in graphene, silicene, germancene and stanene are authenticated as QSH insulator sequentially^{16}, in which the band gap in stanene reaches 0.1eV due to its stronger SOC^{16,17}. Then the research focus extends to GroupV bilayer films and the results prove that Bi (111)^{18} bilayer is a QSH insulator intrinsically. Recently, the investigation emphasis is transferred to the 2D inversionasymmetric materials which contain two different elements, such as Group IIIV binary compounds^{19,20,21}. According to prediction, suitable bulk band gap and isolated Dirac cone in these 2D IIIV compounds make them suitable for roomtemperature applications. A computational study^{22} has suggested the possible synthesis and potential applications for 2D IIIV compounds. Moreover, due to the inversionasymmetry in IIIV films, they may host nontivial topological phenomena, such as crystallinesurfacedependent topological electronic states^{23,24}, natural topological pn junctions^{25} and topological magnetoelectric effects^{26}. Nevertheless, the surface activity is a major problem for these materials, whose topology may be destroyed by substrate. Besides, some 2D transitionmetal dichalcogenides^{27} and halide^{28} are predicted to be a new class of QSH insulator with a large band gaps.
Recent studies have highlighted that the orbital filtering effect (OFE) plays an important role on tuning the bulk band gap, which has received intense attentions in designing of QSH insulators^{16,17,29,30,31,32}. The 2D films are advantageous in this aspect since their bonding properties are easy to be modified in the processes of synthesis to enhance SOC by surface adsorption. For instance, the band gap of stanene will be enhanced to 0.3 eV with the effect of halogenation^{17} and the SOC is confined in the p_{xy} orbitals rather than p_{z} in pristine one. The Xdecorated plumbene monolayers (PbX; X = H, F, Cl, Br, I) is predicted as a 2D QSH insulator with giant bulk gaps from 1.03 eV to a record value of 1.34 eV^{33}. Recently, it is reported that the functionalized dumbbell stanene also obtains largegap QSH state^{34}. The 2D BiX/SbX (X = H, F, Cl and Br) films are demonstrated as TIs with extraordinarily large band gap from 0.32 eV to 1.08 eV^{29}. Also, the Bi and Sb films have been demonstrated to contain a large band gap using Si substrate as a tool to achieve OFE^{30,31}. Recently, OFE is also applicable in materials with inversionasymmetric sublattices. The Group IV noncentrosymmetric honeycomb lattices functionalized with halogen atoms are theoretically confirmed to be topological insulators with appropriate condition^{35}. Meanwhile, for the functionalized IIIBi films, they can preferably realize nontrivial topological states, producing remarkable large Rashba spin splitting effect^{21,32}. By the way, through the combination of Si (111) substrate and hydrogenation, it can still implement OFE in IIIV compounds films^{36}. These QSH insulators are essential for realizing many exotic phenomena and for fabricating new quantum devices that operates at room temperature. Unfortunately, though their band gap has been enhanced greatly, further experimental works^{37} find that the fluorination and hydrogenation exhibit quick kinetics, with rapid increasing of defects and lattice disorder even under short plasma exposures, which will disturb their potential applications completely. Therefore, the realization of these QSH insulators with high quality is rather difficult^{38,39,40}.
Recently, the small molecule functionalization has been the focus to enhance the geometric stability and nontrivial band gap of new 2D films. For instance, the ethynyl (C_{2}H) has been reported to be an efficient way to stabilize stanene by decoration on its surface and its band gap can be enhanced to 0.3 eV^{41}. Methyl (CH_{3}), another organic molecule, has also been suggested as a promising tool to stabilize 2D systems, such as methylfunctionalized germanane (GeCH_{3})^{42} and BiCH_{3}^{43}, to realize large gap QSH insulators. Experimentally, GeCH_{3} film has been synthesized in recent work^{44}. In contrast to hydrogenated germanane, the GeCH_{3} film has considerably enhanced thermal stability at hightemperature^{44}. This raises an interesting question: can the methyl be applied to stabilize group IIIV films and whether their band gap can be enhanced significantly in QSH phase?
In this work, we address the aforementioned question by demonstrating the effect of methylfunctionalization as an effective way to stabilize InBi monolayer (InBiCH_{3}) as a representative for group IIIV films. Indeed, the methyl removes the imaginary frequency modes from the phonon spectrum of InBi, indicating no dynamic instability. In this case, the band gap of InBiCH_{3} can be enhanced to 0.29 eV, which is larger than that of pristine InBi monolayer. The physical origin of QSH effect is confirmed by identifying the sp_{xy} band inversion, topological invariant Z_{2} = 1 and helical edge states in bulk band gap. Noticeably, the QSH effects are robust and tunable against the mechanical strain, electric field and different level of methyl coverages. In addition, the InBiCH_{3} on hBN sheet is observed to support a nontrivial large gap QSH, which harbors the edge states lying within the band gap of hBN sheet. Therefore, our work reveals a unique advantage of atomically thin IIIV materials in realizing 2D topological phase.
Calculation Details
Firstprinciples calculations based on density functional theory (DFT) were carried out using the plane wave basis Vienna ab initio simulation package^{45,46}. The electronion potential was described by the projectoraugmented wave (PAW) method^{47} and the electron exchangecorrelation functional was approximated by generalized gradient approximation (GGA) in PerdewBurkeErnzerhof (PBE) form^{48}. The energy cutoff of the plane waves was set to 500 eV with the energy precision of 10^{−5} eV. The vacuum space was applied at least 20 Å to eliminate the interactions between neighboring slabs in zdirection. We employed a kpoint set generated by the 11 × 11 × 1 MonkhorstPack mesh^{49} for geometry optimizations and 17 × 17 × 1 for selfconsistent calculations. The atomic coordinates were fully optimized until the force on each atom was less than 0.01 eV/Å. The SOC is included in selfconsistent electronic structure calculations. The phonon spectra were calculated using a supercell approach within the PHONON code^{50}.
Results and Discussion
Before discussing the electronic properties of the methylfunctionalized InBi, we examine the crystal structure, dynamic stability and electronic properties of the pristine InBi monolayer. Figure 1(a) presents the geometric structure of InBi, composed of a triangular lattice with In and Bi atoms located in two different sublattices. Our calculations indicate that, in analogy to buckled silicene^{51}, InBi exhibits a hexagonal structure with a buckling parameter Δ = 0.873 Å, lattice constant a = 4.78 Å and bond length d = 2.89 Å, which consist with those reported in previous literature^{20,36}, but are smaller than the cases in two films of InBi^{52} except Δ. The resultant band structure indicates that it is a QSH insulator, with a band gap of 0.16 eV. Such an upper limit, however, can be significantly broken through, as we will show in the following part. In addition, the phonon spectrum calculations in Fig. 1(c) indicate that it has obviously imaginary frequency modes, exhibiting a dynamically unstable structure.
To stabilize InBi monolayer, we saturate the uncoordinated In and Bi atoms with methyl alternating on both sides of InBi sheet, as shown in Fig. 1(b). In comparison with InBi monolayer, the lattice constant of InBiCH_{3} is stretched to a = 4.89 Å upon methylfunctionalization, along with the Ga−Bi bond length increasing by 0.08 Å. Noticing that this lattice constant is larger than hydrogenated case^{36}, which will enhance the localization of atom orbitals, the methylfunctionalized InBi film may process a more favorable character than the hydrogenated one. Meanwhile, the In−CH_{3} and Bi−CH_{3} bonds are 2.23 and 2.30 Å, respectively. Importantly, the stability of 2D InBiCH_{3} is confirmed by phonon spectrum that clearly removes the imaginary frequencies from pristine InBi monolayer, as displayed in Fig. 1(d). Also, we calculate the formation energy of InBiCH_{3} defined as:
where E(InBiCH_{3}) and E(InBi) are total energies of InBiCH_{3} and InBi, respectively, while E(CH_{3}) is chemical potential of methyl. It is found to be E_{f} = −3.23 eV, greatly lager than the cases of GaBiCl_{2}^{53} and GeCH_{3} (−1.75 eV). These indicate that the methyl strongly binds to InBi monolayer by chemical bonds, showing a higher thermodynamic stability relative to their elemental reservoirs. Considering that the GeCH_{3} has been successfully synthesized^{44}, InBiCH_{3} is also expected to be feasible experimentally.
Figure 2 displays the calculated band structures in InBiCH_{3} monolayer. In the absence of SOC, it is a semiconductor with a direct band gap of 0.21 eV at the Г point, as shown in Fig. 2(a,b). When SOC is switched on, there still has a direct band gap (E_{Г}) of 0.31 eV at the Г point, which is twice larger than that of pristine one. However, the valence band minimum (VBM) moves slightly away from the Г point, leading to an indirect band gap (E_{g}) of 0.29 eV [Fig. 2(c,d)], which is significantly larger than the InBi film with hydrogenation(0.19 eV)^{36}, verifying the assumption proposed above. The SOCinduced band structure deformation near the Fermi level is a strong indication of the existence of topologically nontrivial phase. To further reveal the effect of chemical decoration of methyl, we project the bands onto different atomic orbitals. The energetically degenerated VBM without SOC are mainly derived from p_{xy} orbitals, whereas the conduction band minimum (CBM) is contributed by s orbital [Fig. 2(a)]. It is known that the s orbital locates typically above p orbitals in conventional IIIV compounds. Consequently, the InBiCH_{3} exhibits a normal band order. However, the effect of SOC makes s and p_{xy} components at the Γ point exchanged, resulting in an inverted band order, as shown in Fig. 2(c). Here, there is a nontrivial bulk band gap of 0.29 eV at the Fermi level, considerably exceeding the presumed upper limits settled by the system without decoration. Here, we highlight that the QSH states of InBiCH_{3} are markedly different from hydrogen or methylfunctionalized stanene^{17} and germanene^{42}, which are trivial TIs at the equilibrium state. In addition, due to the inversionsymmetry breaking in InBiCH_{3}, we also find that the resulting band structure is different from stanene film^{16} and shows intriguing Rashbatype dispersions, as shown in Fig. 2(c,d). This spin splitting is also similar to what occurs for the hydrogenated InBi monolayer^{20}.
The most important performance for TIs is the existence of helical edge states with spin polarization protected by TRS, which can be calculated by the Wannier 90 package^{50}. Based on maximally localized Wannier functions (MLWFs), the edge Green’s function^{54} of the semiinfinite lattice is constructed using the recursive method and the local density of state (LDOS) of the edges is presented in Fig. 3(a). We can see that all the edge bands connect completely the conduction and valence bands and span the 2D bulk band gap, yielding a 1D gapless edge states. Further, by identifying the spinup (↑) and spindown (↓) contributions in the edge spectral function [Fig. 3(b)], the counterpropagating edge states can exhibit opposite spinpolarization, in accordance with the spinmomentum locking of 1D helical electrons. Furthermore, the Dirac point located at the band gap are calculated to have a high Fermi velocity of ~2.0 × 10^{6} m/s, comparable to that of 5.3 × 10^{5} m/s in HgTe/CdTe quantum well^{12,13}. All these results consistently demonstrate that the InBiCH_{3} is an ideal 2D TI.
The topological states can be further confirmed by calculating topological invariant Z_{2}. Due to the inversionsymmetry breaking in InBiCH_{3}, the method proposed by Fu and Kane^{55} cannot be used and thus, an alternative one independent of the presence of inversionsymmetry is needed. Here, we introduce the evolution of Wannier Center of Charges (WCCs)^{56} to calculate the Z_{2} invariant, which can be expressed as:
which indicates the change of timereversal polarization (P_{θ}) between the 0 and T/2. Then the WFs related with lattice vector R can be written as:
Here, a WCC can be defined as the mean value of , where the is the position operator and is the state corresponding to a WF in the cell with R = 0. Then we can obtain
Assuming that with S = I or II, where summation in α represents the occupied states and A is the Berry connection. So we have the format of Z_{2} invariant:
The Z_{2} invariant can be obtained by counting the even or odd number of crossings of any arbitrary horizontal reference line.
Figure 3(c) displays the evolution lines of WCCs calculated for InBiCH_{3}. One can see that the WCCs evolution curves cross any arbitrary reference lines odd times, which indicates Z_{2} = 1, verifying the existence of topologically nontrivial phase in InBiCH_{3}.
Strain engineering is an efficient way of modulating the electronic and topological properties in 2D materials^{57,58}. We employ inplane strains to InBiCH_{3} by changing the lattices as ε = (a − a_{0})/a_{0}, where a (a_{0}) is lattice constant under the strain (equilibrium) condition. Figure 4(a) presents the variation of band gap (E_{g}, E_{Г}) as a function of the biaxial strain. One can see that the nontrivial QSH phase survives in InBiCH_{3} over a wide range of strains. Under tensile strain, the E_{Γ} enlarges monotonically and reaches a maximum of 0.79 eV at 20%. While in the compressive case, the E_{g} and E_{Г} are almost consistent with each other and the sp_{xy} inversion maintains beyond critical point −7%. If the compressive strain keeps increasing, the trivial band order occurs, forming a normal insulator (NI). The characteristics of band inversion with respect to the strain are illustrated in the insert of Fig. 4(a). Here, we must point out that the crystal deformation occurs clearly with relatively large strains, suggesting a robustness of QSH effect against crystal deformation.
To elucidate the origin of band topology, we analyze the orbital evolution of InBiCH_{3} and the results are schematically presented in Fig. 4. Since the methyl hybridizes strongly with p_{z} orbital of In and Bi atoms overlapping in the same energy range, it effectively removes p_{z} bands away from the Fermi level, leaving only the s and p_{x,y} orbitals at the Fermi level. As shown in Fig. 4(c,d), the chemical bonding between In and Bi atoms make the s and p_{x,y} orbital split into the bonding and antibonding states, i.e., s^{±}> and p^{±}_{x,y}>, which the superscripts + and − represent the parities of corresponding states, respectively. In the absence of SOC, the bands near the Fermi level are mainly contributed by the s^{−}> and p_{x,y}^{+}>, with the s^{−}> locating above p_{x,y}^{+}>, possessing a normal band order in the sequence of sp. After taking SOC into account, the p_{x,y}^{+}> will further split into p_{ ± 3/2}^{+}> and p_{ ± 1/2}^{+}>, while the p_{ ± 3/2}^{+}> is pushed up and p_{ ± 1/2}^{+}> is shifted down in energy. The hopping between those atomic orbitals plays a vital role in tuning the splitting strength of p_{ ± 3/2}^{+}> and p_{ ± 1/2}^{+}>. In the case of ε < −7%, the compressive strain leads to a shorter bond length, which increases the splitting degree of bonding and antibonding states, generating a large energy difference between p_{x,y}^{+}> and s^{−}>. Thus, the p_{ ± 3/2}^{+}> cannot inverse with s^{−}>, indicating a trivial band order like conventional IIIV compounds, as shown in Fig. 4(c). While for ε > −7%, a smaller energy separation introduced will be arisen and the SOC effect can easily promote the p_{ ± 3/2}^{+}> higher than s^{−}> [Fig. 4(d)], leading to an extraordinary band inversion order in the sequence of psp, namely inversion of parities, indicating the existence of QSH phase. Moreover, to further confirm the nontrivial topological properties, we calculate the edge states when the strain is 105%. The result is presented in Figure S1(a,b) and a pair of helical edge states can be observed obviously, indicating that it still maintains the QSH states except the change of bulk band gap compared with the equilibrium state. It is worth mentioning that this topological states originate from the sp inversion mechanism, which is common in such IIIV compounds rather than pd or dd band inversion in transitionmetal compounds^{27,28}. But it is still different from the case of InBi film with fluoridation^{32}, in which the p_{x,y}^{+}> and s^{−}> orbitals have inversed in the progress of chemical bonding and the bulk band gap is determined by the splitting of p_{x,y}^{+}> under the SOC effect, the bulk band gap in InBiCH_{3} film is the combined effect of functionalization and SOC, thus yields a smaller bulk band gap.
In addition to strain engineering, the effects of a perpendicular electric field (Efiled) on band topology are investigated for InBiCH_{3}. We find that both E_{g} and E_{Г} possess a nearlinear dependency with respect to Efield, as illustrated in Fig. 4(b). The increases of the positive Efield leads to a larger band gap, while the negative Efield will make it decrease monotonically. More importantly, different from 1T’MoS2^{27} whose topological state will be destroyed by electric field, the InBiCH_{3} maintains its nontrivial TI nature all the way, indicating a robustness against Efield in the range of −1–1V/Å. Meanwhile, as a representative, the edge state of 0.5V/Å is shown in Figure S1(c,d), which is analogous to the case of strain [Figure S1(a,b)]. The nontrivial bulk band gaps are still very large (0.24−0.35 eV), allowing for viable applications at room temperature.
As discussed above, the methyl functionalization does not alter the band topology of InBi monolayer. Thus, we further examine the robustness of nontrivial TI phase by considering different levels of methyl coverages in InBiCH_{3}. A 2 × 2 supercell is selected to simulate coverages of 0.25, 0.50 and 0.75 monolayer by removing/adding up to methyl molecules. Followed the previous work^{59}, the methyl molecules are positioned on opposite sides of InBi sheet, yielding a greater stability. Figure 5 presents the relaxed structures and corresponding band structures for 0.25−0.75 monolayer coverage, respectively. Interestingly, all the methyl molecules are strongly hybridized with p_{z} orbital of In and Bi atoms, thus the atomic states near the Fermi level is still mainly determined by the s and p_{xy} orbitals. Meanwhile, the sp band inversion can be observed, thus the band topology of these films is highly robust against chemical bonding effects of the environment, making these films particularly flexible to substrate choices for device applications. Besides, we also calculate the phonon spectrums of these different covered monolayers, as shown in Figure S2. According to the results, these structures still possess little imaginary frequency. So the best insurance method is functionalized the InBi film with methyl completely. However, even if it emerges with unsaturated position, it can still own the QSH state, which is a good guarantee. To further verify its robustness against the coverage, taking 0.25 monolayer as a representative, we straightforward construct a ribbon with zigzag edges. The width of this ribbon is 73.53 Å, which is large enough to ignore the effect between two sides. Meanwhile, to eliminate the interaction induced by periodicity, a sufficient vacuum slab is adopted and the edges are passivated by hydrogen atoms. Figure S3(a) presents the corresponding band structure. Different from the results of semiinfinite lattice, two pairs of helical edge states span the bulk energy gap connecting the valence and conduction bands. Due to the asymmetry for edges in zigzag ribbon, a pair of edge bands is determined by the In termination and the other is derived from the Bi termination, also they form two Dirac cones simultaneously at the M point. Noticeably, each pair of edge state crosses the Fermi level with odd number along the direction form M to Γ point which can adequately prove its nontrivial topological properties.
From the view of devices applications, selecting a suitable substrate for InBiCH_{3} is a very important issue. Considering that one film of InBi with hydrogenation deposited on Si(111) will annihilate its nontrivial topological states^{52}, we hope to achieve it by constructing a van der Waals heterostructure for its growth. However, the hBN has been reported to be an ideal substrate for 2D materials^{60,61}, due to its large band gap with a high dielectric constant. Thus, we construct an InBiCH_{3}@2 × 2hBN heterobilayer (HBL), as shown in Fig. 6(a), in which the lattice mismatch is only 0.41% for both layers. After a full relaxation, the distance between adjacent layers is 3.11 Å from the bottom methyl to substrate, with a binding energy of −71 meV, indicating the InBiCH_{3} interacts weakly with hBN substrate via van der Waals interaction^{62}. Figure 6(b) presents the band structure of InBiCH_{3}@2 × 2hBN HBL with SOC. In these weakly coupled system, there is essentially no charge transfer between the adjacent layers and the HBL remains semiconducting property. By projecting the band structure, we find that the contributions of hBN substrate locate far away from the Fermi level, the states around the Fermi level being dominantly determined by InBiCH_{3} with an inverted band order. In addition, based on aforesaid method about validation for edge states, we also investigate the band structure of InBiCH_{3}@2 × 2hBN ribbon. The edge states and odd number of crossing further verify the existence of nontrivial topological property and it is robust against substrate, as illustrated in Figure S3(b). If we compare the bands of InBiCH_{3} with and without hBN substrate, little difference can be observed, which is analogous to the case of tetragonal Bi film on NaCl substrate^{63}. As a result, the InBiCH_{3}@2 × 2hBN HBL is a robust QSH phase with a gap of 0.27 eV.
Conclusions
In summary, on the basis of firstprinciples calculations, we have investigated the geometric and electronic properties of InBiCH_{3}. The results indicate that InBiCH_{3} has no dynamic instability and is a QSH insulator with a band gap lager than 0.29 eV, suitable for roomtemperature application. The topological characteristic can be confirmed by sp_{xy} band inversion, topological invariant Z_{2} = 1 and the timereversal symmetry protected helical edge states. We also find that the band gap of InBiCH_{3} can be effectively tuned by external strain and electric field. The TI phase is robust against strain (−7–20%) and Efield (−1–1V/Å). Also, the InBiCH_{3} can preserve nontrivial topology under different levels of methyl coverages. In addition, the InBiCH_{3} on hBN sheet is observed to support a nontrivial largegap QSH, which harbors a Dirac cone lying within the band gap. These findings demonstrate that the methylfunctionalized IIIV films may be a good QSH platform for device design and fabrication.
Additional Information
How to cite this article: Li, S. et al. Robust RoomTemperature Quantum Spin Hall Effect in Methylfunctionalized InBi honeycomb film. Sci. Rep. 6, 23242; doi: 10.1038/srep23242 (2016).
References
Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X.L. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (1057).
Yan, B. & Zhang, S. C. Topological materials. Rep. Prog. Phys. 75, 096501 (2012).
Moore, J. E. The birth of topological insulators. Nature 464, 194–198 (2010).
Rasche, B. et al. Stacked topological insulator built from bismuthbased graphene sheet analogues. Nat. Mater. 12, 422–425 (2013).
Kane, C. L. & Mele, E. J. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett. 95, 226801 (2005).
Kane, C. L. & Mele, E. J. Z2Topological Order and the Quantum Spin Hall Effect. Phys. Rev. Lett. 95, 146802 (2005).
Yao, Y., Ye, F., Qi, X.L., Zhang, S.C. & Fang, Z. Spinorbit gap of graphene: Firstprinciples calculations. Phys. Rev. B 75, 041401 (2007).
Kou, L. et al. Graphenebased topological insulator with an intrinsic bulk band gap above room temperature. Nano Lett. 13, 6251–6255 (2013).
Kaloni, T. P., Kou, L., Frauenheim, T. & Schwingenschlögl, U. Quantum spin Hall states in graphene interacting with WS2 or WSe2. Appl. Phys. Lett. 105, 233112 (2014).
Liangzhi Kou, S.C. W., Felser, C., Frauenheim, T., Chen, C. & Yan, B. Robust 2D Topological Insulators in van der Waals Heterostructures. ACS Nano 8, 10448 (2014).
Lima, E. N. & Schmidt, T. M. Topological phase driven by confinement effects in Bi bilayers. Phys. Rev. B 91, 075432 (2015).
Dziawa, P. et al. Topological crystalline insulator states in Pb(1x)Sn(x)Se. Nat Mater 11, 1023–1027 (2012).
Du, L., Knez, I., Sullivan, G. & Du, R.R. Robust Helical Edge Transport in GatedInAs/GaSbBilayers. Phys. Rev. Lett. 114, 096802 (2015).
Liu, C., Hughes, T. L., Qi, X.L., Wang, K. & Zhang, S.C. Quantum Spin Hall Effect in Inverted TypeII Semiconductors. Phys. Rev. Lett. 100, 236601 (2008).
Liu, C.C., Jiang, H. & Yao, Y. Lowenergy effective Hamiltonian involving spinorbit coupling in silicene and twodimensional germanium and tin. Phys. Rev. B 84, 195430 (2011).
Xu, Y. et al. LargeGap Quantum Spin Hall Insulators in Tin Films. Phys. Rev. Lett. 111, 136804 (2013).
Koroteev, Y. M., Bihlmayer, G., Chulkov, E. V. & Blügel, S. Firstprinciples investigation of structural and electronic properties of ultrathin Bi films. Phys. Rev. B 77, 045428 (2008).
Li, X. et al. Prediction of largegap quantum spin hall insulator and RashbaDresselhaus effect in twodimensional gTlA (A = N, P, As and Sb) monolayer films. Nano Res. 8, 2954–2962 (2015).
Chuang, F. C. et al. Prediction of largegap twodimensional topological insulators consisting of bilayers of group III elements with Bi. Nano Lett. 14, 2505–2508 (2014).
Zhao, M., Chen, X., Li, L. & Zhang, X. Driving a GaAs film to a largegap topological insulator by tensile strain. Sci. Rep. 5, 8441 (2015).
Zhuang, H. L., Singh, A. K. & Hennig, R. G. Computational discovery of singlelayer IIIV materials. Phys. Rev. B 87, 165415 (2013).
Bahramy, M. S., Yang, B. J., Arita, R. & Nagaosa, N. Emergence of noncentrosymmetric topological insulating phase in BiTeI under pressure. Nat. Commun. 3, 679 (2012).
Murakami, S. Quantum spin Hall effect and enhanced magnetic response by spinorbit coupling. Phys. Rev. Lett. 97, 236805 (2006).
Wang, J., Chen, X., Zhu, B.F. & Zhang, S.C. Topologicalpnjunction. Phys. Rev. B 85, 235131 (2012).
Kuroda, K. et al. Experimental realization of a threedimensional topological insulator phase in ternary chalcogenide TlBiSe(2). Phys. Rev. Lett. 105, 146801 (2010).
Xiaofeng Qian, J. L. & Liang Fu, Ju Li. Quantum spin Hall effect in twodimensional transition metal dichalcogenides. Science 346, 1344 (2014).
Zhou, L. et al. New Family of Quantum Spin Hall Insulators in Twodimensional TransitionMetal Halide with Large Nontrivial Band Gaps. Nano Lett. 15, 7867–7872 (2015).
Song, Z. et al. Quantum spin Hall insulators and quantum valley Hall insulators of BiX/SbX (X = H, F, Cl and Br) monolayers with a record bulk band gap. NPG Asia Materials 6, e147 (2014).
Zhou, M. et al. Epitaxial growth of largegap quantum spin Hall insulator on semiconductor surface. Proc. Natl. Acad. Sci. USA 111, 14378–14381 (2014).
Zhou, M. et al. Formation of quantum spin Hall state on Si surface and energy gap scaling with strength of spin orbit coupling. Sci. Rep. 4, 7102 (2014).
Ma, Y. et al. Twodimensional inversionasymmetric topological insulators in functionalized IIIBi bilayers. Phys. Rev. B 91, 235306 (2015).
Zhao, H. et al. Unexpected GiantGap Quantum Spin Hall Insulator in Chemically Decorated Plumbene Monolayer. Sci. Rep. 6, 20152 (2016).
Wang, Y. P. et al. Largegap quantum spin Hall state in functionalized dumbbell stanene. Appl. Phys. Lett. 17, 083036 (2016).
Ma, Y., Kou, L., Du, A. & Heine, T. Group 14 elementbased noncentrosymmetric quantum spin Hall insulators with large bulk gap. Nano Res. 8, 3412–3420 (2015).
Crisostomo, C. P. et al. Robust Large Gap TwoDimensional Topological Insulators in Hydrogenated IIIV Buckled Honeycombs. Nano Lett. 15(10), 6568–6574 (2015).
Wu, J. et al. Controlled chlorine plasma reaction for noninvasive graphene doping. J. Am. Chem. Soc. 133, 19668–19671 (2011).
Becerril, A. H. et al. Evaluation of SolutionProcessed Reduced Graphene Oxide Films as Transparent Conductors. ACS Nano 2, 463−470 (2008).
Dahn, J. R., Way, B. M., Fuller, E. & Tse, J. S. Structure of siloxene and layered polysilane (Si6H6). Phys. Rev. B 48, 17872–17877 (1993).
Yamanaka, S., Matsuura, H. & Ishikawa, M. New deintercalation reaction of calcium from calcium disilicide. Synthesis of layered polysilane. Mater. Res. Bull 31, 307−316 (1996).
Zhang, R.W. et al. Ethynylfunctionalized stanene film: a promising candidate as largegap quantum spin Hall insulator. New J. Phys. 17, 083036 (2015).
Ma, Y., Dai, Y., Wei, W., Huang, B. & Whangbo, M. H. Straininduced quantum spin Hall effect in methylsubstituted germanane GeCH3. Sci. Rep. 4, 7297 (2014).
Ma, Y., Dai, Y., Kou, L., Frauenheim, T. & Heine, T. Robust twodimensional topological insulators in methylfunctionalized bismuth, antimony and lead bilayer films. Nano Lett. 15, 1083–1089 (2015).
Jiang, S. et al. Improving the stability and optical properties of germanane via onestep covalent methyltermination. Nat Commun. 5, 3389 (2014).
Kresse, G. & Furthmüller, J. Efficiency of abinitio total energy calculations for metals and semiconductors using a planewave basis set. Mater. Sci. 6, 15−50 (1996).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set. Phys. Rev. B. 54, 11169−11186 (1996).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave methods. Phys. Rev. B 59, 1758−1775 (1999).
Perdew, P. J., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865−3868 (1996).
Monkhorst, H. J. & Pack, J. D. Special points for Brillouinzone integrations. Phys. Rev. B 13, 5188–5192 (1976).
Mostofi, A. A. et al. wannier90: A tool for obtaining maximallylocalised Wannier functions. Comput. Phys. Commun. 178, 685–699 (2008).
Zhang, C.w. & Yan, S.s. FirstPrinciples Study of Ferromagnetism in TwoDimensional Silicene with Hydrogenation. J. Phys. Chem. C 116, 4163–4166 (2012).
Yao, L. Z. et al. Predicted Growth of TwoDimensional Topological Insulator Thin Films of IIIV Compounds on Si(111) Substrate. Sci. Rep. 5, 15463 (2015).
Li, L., Zhang, X., Chen, X. & Zhao, M. Giant topological nontrivial band gaps in chloridized gallium bismuthide. Nano Lett. 15, 1296–1301 (2015).
Sancho, P. L. M., Sancho, M. L. J. & Rubio, J. Quick iterative scheme for the calculation of transfer matrices: application to Mo (100). J. Phys. F: Met. Phys. 14, 1205 (1984).
Fu, L. & Kane, C. L. Josephson current and noise at a superconductor/quantumspinHallinsulator/superconductor junction. Phys. Rev. B 79, 161408 (2009).
Yu, R., Qi, X. L., Bernevig, A., Fang, Z. & Dai, X. Equivalent expression of Z2 topological invariant for band insulators using the nonAbelian Berry connection. Phys. Rev. B 84, 075119 (2011).
Hsieh, T. H. et al. Topological crystalline insulators in the SnTe material class. Nat. Commun. 3, 982 (2012).
Liu, J., Qian, X. & Fu, L. Crystal field effect induced topological crystalline insulators in monolayer IVVI semiconductors. Nano Lett. 15, 2657–2661 (2015).
Chuang, F.C., Huang, Z.Q., Lin W.H., Albao, A. M. & Su, W.S. Structural and electronic properties of hydrogen adsorptions on BC3 sheet and graphene: a comparative study. Nanotechnology 22, 135703 (2011).
Britnell, L. et al. FieldEffect Tunneling Transistor Based on Vertical Graphene Heterostructures. Science. 335, 947–950 (2012).
Ju, L. et al. Photoinduced doping in heterostructures of graphene and boron nitride. Nat. Nanotechnol. 9, 348–352 (2014).
Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).
Liangzhi, K. et al. Tetragonal bismuth bilayer: a stable and robust quantum spin hall insulator. 2D Mater. 2, 045010 (2015).
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos 11434006, 11274143, 61172028 and 11304121), Natural Science Foundation of Shandong Province (Grant Nos ZR2013AL004, ZR2013AL002), Technological Development Program in Shandong Province Education Department (Grant No. J14LJ03), Research Fund for the Doctoral Program of University of Jinan (Grant Nos XBS1433, XBS1402, XBS1452).
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S.L. and C.Z. conceived the study and wrote the manuscript. P.L and P.W. performed the firstprinciples calculations. W.J. calculated the phonon spectrum. S.H., B.Z. and C.C. prepared figures. All authors read and approved the final manuscript.
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Li, Ss., Ji, Wx., Zhang, Cw. et al. Robust RoomTemperature Quantum Spin Hall Effect in Methylfunctionalized InBi honeycomb film. Sci Rep 6, 23242 (2016). https://doi.org/10.1038/srep23242
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