Abstract
Group IIIV films are of great importance for their potential application in spintronics and quantum computing. Search for twodimensional IIIV films with a nontrivial largegap are quite crucial for the realization of dissipationless transport edge channels using quantum spin Hall (QSH) effects. Here we use firstprinciples calculations to predict a class of largegap QSH insulators in functionalized TlSb monolayers (TlSbX_{2}; (X = H, F, Cl, Br, I)), with sizable bulk gaps as large as 0.22 ~ 0.40 eV. The QSH state is identified by Z_{2} topological invariant together with helical edge states induced by spinorbit coupling (SOC). Noticeably, the inverted band gap in the nontrivial states can be effectively tuned by the electric field and strain. Additionally, these films on BN substrate also maintain a nontrivial QSH state, which harbors a Dirac cone lying within the band gap. These findings may shed new light in future design and fabrication of QSH insulators based on twodimensional honeycomb lattices in spintronics.
Introduction
One of the grand challenges in condensed matter physics and material science is to develop roomtemperature electron conduction without dissipation. Twodimensional (2D) topological insulators (TIs), namely quantum spin Hall (QSH) insulators, are new states of quantum matter with an insulating bulk and metallic edge states^{1,2,3,4,5}. Their helical edge states are spinlocked due to the protection of timereversal symmetry (TRS), namely the propagation direction of surface electrons is robustly linked to their spin orientation^{6}, leading to dissipationless transport edge channels. However, the working temperature of QSH insulators in experiments like HgTe/CdTe^{7,8} and InAs/GaSb films^{9,10} are very low (below 10 K), limited by their small energy gap. The search of QSH insulators with largegap is urgently required.
Chemical functionalization of 2D materials is an effective way to realize QSH state with desirable largegaps. The most reported cases include hydrogenated or halogenated stanene^{11,12,13} and plumbene^{14} films. These films are QSH insulators with gaps as large as 0.2 ~ 1.34 eV, sufficient for practical applications at room temperature. Group V films, including As^{15}, Bi^{16} and Sb^{17}, are largegap QSH insulators, when functionalized with hydrogen or halogens. Recently, the organic molecule ethynylfunctionalized stanene^{18,19} films have been reported to be good QSH insulators in the previous works. Progress also undergoes simultaneously in experiments, Bi (111) film has been successfully grown on Bi_{2}Te_{3} or Bi_{2}Se_{3} substrates^{20,21,22,23}. The common feature of these materials is that they all own 2D honeycomblike crystal structures, indicating that 2D hexagonal lattice could be an excellent cradle to breed QSH insulators with SOC. These largegap QSH insulators are essential for realizing many exotic phenomena and for fabricating new quantum devices that can operate at room temperature.
Group IIIV materials are of importance applicable to semiconductor devices in semiconductor industry. Especially, the π bonding between p_{z} orbitals on groupIII and V atoms can generally open a bulk gap with SOC, similar to graphene^{1}. Different from the inversionsymmetry (IS) in graphene, the geometry of group IIIV films is not IS (inversionasymmetry) due to IS breaking. The previous works have shown that the not IS materials host many nontrivial phenomena such as the crystalline surfacedependent topological electronic states^{24,25}, pyroelectricity^{26}, topological pn junctions^{27}, as well as topological superconductivity^{28,29}, et al. However, one important characteristic of IIIV films is that its unsaturated p_{z} orbital is chemically active, due to the weak ππ interaction as caused by the bond length between IIIV atoms (~3 Å). This feature, together with the outofplane orientation of p_{z} orbital, facilitates strong orbital interaction with external environments and thus its electronic properties are easily affected by adsorbates and substrates, unfavorable for practical applications in spintroncis.
As a representative, here we provide a systematical study on structural and topological properties of 2D TlSb monolayers functionalized with hydrogen and halogens, namely TlSbX_{2} (X = H, F, Cl, Br, I). We find that the surface functionalization on TlSb, i.e., saturating the p_{z} orbital composed of TISb with hydrogen or halogens, can stabilize the 2D TlSb, according to the calculated phonon spectrum of TlSbX_{2} films. All the systems are found to be QSH insulators, with the bulk gap in the range of 0.22 ~ 0.40 eV, tunable by external strain and electric field. A single pair of topologically protected helical edge states is established for these systems with the Dirac point locating in the bulk gap and the odd numbers of crossings between edge states and Fermi level prove the nontrivial nature of these TlSbX_{2} films. These findings may provide a new platform to design largegap QSH insulator based on group IIIV films, which is important for device application in spintronics.
Results and Discussion
The geometric structure of TlSbX_{2} (X = H, F, Cl, Br, I) are displayed in Fig. 1(a), in which the Tl or Sb atoms are saturated with X atoms on both sides of the plane in an alternating manner along the hexagonal axis and thus breaks IS of TlSbX_{2}. Table 1 lists the calculated equilibrium lattice constants, buckling heights, as well as TlSb, TlX and SbX bond lengths after structural optimization. In comparison to pristine TlSb, the TISb bonds in TlSbX_{2} slightly expand, while the buckling changes differently due to the weakly hybridization between π and σ orbitals, stabilizing these structures. The stability of functionalized TlSbX_{2} is studied through the formation energy defined as
where E_{TlSbX2}, E_{TISb} and E_{X} are the total energy of doubleside functionalized TlSbX_{2}, pristine TlSb and molecule X_{2}, respectively. N_{X} is the number of X atoms. The calculated formation energies for TlSbH_{2}, TlSbF_{2}, TlSbCl_{2}, TlSbBr_{2} and TlSbI_{2}, are −1.862, −2.997, −1.613, −1.567 and −1.420 eV, respectively, suggesting that hydrogen or halogens are chemically bonded to TlSb, indicating a higher thermodynamic stability relative to their elemental reservoirs. The dynamic stability of TlSbH_{2}, as an example, is further confirmed by the phonon dispersion curves in Fig. 1(b), in which all branches have positive frequencies and no imaginary phonon modes, confirming the stability of TlSbH_{2}.
Figure 2(a,d) display the calculated band structure for TlSbH_{2} and TlSbF_{2} as representative examples, in which the red and blue lines correspond to band structures without and with SOC. In the absence of SOC, they are both gapless semimetal with the valence band maximum (VBM) and conduction band minimum (CBM) degenerate at the Fermi level. When takes SOC into account, the band structures of TlSbH_{2} and TlSbF_{2} produce a semimetaltosemiconductor transition, with sizeable bulkgaps of 0.22 eV and 0.40 eV, respectively. As observed in previously reported 2D TIs like ZeTe_{5}^{30}, HfTe_{5}^{31} and GaSe^{32}, graphenelike materials^{33,34,35}, the SOCinduced bandgap opening at the Fermi level is a strong indication of the existence of topologically nontrivial phases.
An important character of the QSH insulator is helical edge states which is key to spintronic applications due to the ability to conduct dissipationless currents. Thus, we calculate the topological edge states by the Wannier90 package^{36}. We construct the maximally localized Wannier functions (MLWFs) and fit a tightbinding Hamiltonian with these functions. The calculated edge Green’s function^{37} of semiinfinite TlSbX_{2} (X = H, F) is shown in Fig. 3(a,d). One can see that all the edge bands connect completely the conduction and valence bands and span 2D bulk band gap, yielding a 1D gapless edge states. Besides, the counterpropagating edge states exhibit opposite spinpolarization, in accordance with the spinmomentum locking of 1D helical electrons. In addition, the Dirac point located at the band gap are calculated to have a high velocity of ~2.0 × 10^{5 }m/s, comparable to that of 5.5 × 10^{5 }m/s in HgTe/CdTe quantum well^{7,8}. All these consistently indicate that TlSbX_{2} (X = H, F) are ideal 2D TIs. The topological states can be further confirmed by calculating topological invariant Z_{2} after the band inversion. Due to IS breaking in TlSbX_{2}, the method proposed by Fu and Kane^{38} cannot be used to calculate the Z_{2} invariant. Thus, a method independent of the presence of IS is needed. As reported by Yu et al.^{39}, we employ a recently proposed equivalent method for the Z_{2} topological invariant based on the U(2N) nonAbelian Berry connection. This approach allows the identification of the topological nature of a general band insulator without any of the gaugefixing problems that plague the concrete, previous implementation of invariants. Here, we introduce the evolution of Wannier Center of Charges (WCCs)^{39} to calculate the Z_{2} invariant, which can be expressed as:
which indicates the change of timereversal polarization () between the 0 and T/2. The evolution of the WCC along ky corresponds to the phase factor, θ, of the eigenvalues of the position operator,, projected into the occupied subspace. Then the WFs related with lattice vector R can be written as:
Here, a WCC can be defined as the mean value of , where theis 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. In Fig. 3(c,f), we display the evolution lines of Wannier function centers (WFC) for TlSbH_{2} and TlSbF_{2}, respectively. It can be seen that the WFC evolution curves cross any arbitrary reference lines odd times, thus yielding Z_{2} = 1.
Now, we turn to the physics of QSH effect in TlSbX_{2}. Since the decorated atoms hybridizes strongly with the dangling bonds of p_{z} orbital in TISb, it effectively removes the p_{z} bands away from the Fermi level, leaving only the s and p_{x,y} orbitals, as displayed in Fig. 2(b,c,e,f). However, through projecting the bands onto different atomic orbitals, we find that there are two scenarios for the effect of SOC on the bands around the Fermi level, in which the s and p_{x,y} band inversion are different from each other. For TlSbH_{2}, at the Γ point, the two p_{x,y} orbitals from TI and Sb atoms are energy degenerate, while the bands away from the Γ point are well separated due to orbital splitting. The Fermi level is located between one s and two p_{x,y} orbitals, rendering the s above p_{x,y} orbitals in energy, thus forming a normal band order, similar to the cases in conventional IIIV semiconductors. While for TlSbF_{2}, the band structures are changed drastically, as shown in Fig. 2(d–f). In sharp contrast to TlSbH_{2}, the band order at the Γ point is inverted, i.e., the s is shifted below two p_{x,y} orbitals. These two different band orders may be attributed to the chemical bonding and orbital splitting between TI and Sb atoms. To further understand the physics of band inversion, we display in Fig. 4 the schematic of orbital inversion at the Γ point around the Fermi level in TlSbH_{2} and TlSbF_{2} films. On can see that, the chemical bonding and crystal field splitting between TI and Sb 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. As displayed in Fig. 4(a), the s^{+} orbital for hydrogenated one is significantly higher somewhere above p^{−}_{x,y} orbital of Tl and Sb atoms under the effect of crystal field. The inclusion of SOC makes the degeneracy of p^{−}_{x,y} orbital split into p^{−}_{x + iy,↑}& p^{−}_{x−iy,↓} and p^{−}_{x−iy,↑}& p^{−}_{x + iy,↓}, leading s^{+} locate in between them. On the other hand, for TlSbF_{2} in Fig. 4(b), the larger lattice constant results in a weaker sp hybridization and accordingly a smaller energy separation between the bonding and antibonding states. Thus, the s^{−} orbital is downshifted while the p^{+}_{x,y} is upshifted, i.e., the s^{−} will be occupied, while the degenerate P^{+}_{x,y} is half occupied, resulting in semimetallic character (Fig. 2(d)).Though the inclusion of SOC make also the degeneracy of p^{+}_{x,y} orbital split into p^{+}_{x + iy,↑}& p^{+}_{x−iy,↓} and p_{ + x−iy,↑}& p^{+}_{x + iy,↓}, but its sp band order are not changed. As a result, the mechanism of QSH effect can be roughly classified into two categories: i.e., typeI: SOCinduced psp TI (TlSbH_{2}) and typeII: Chemical bonding induced pps TI (TlSbF_{2}). Obviously, it is the s orbital insertion into p^{+}_{x + iy,↑}& p^{+}_{x−iy,↓} and p^{+}_{x−iy,↑}& p^{+}_{x + iy,↓} that the topological bulkgap (0.22 eV) of TlSbH_{2} is smaller twice than that (0.40 eV) of TlSbF_{2} film.
Here, we wish to point out that fluorination in TlSb is not the only way to achieve largegap QSH state, the same results can be obtained by decorating the surface with otherwise halogens, such as Cl, Br and I. We thus performed calculations for TlSbX_{2} (X = Cl, Br, I) films to check their topological properties, as illustrated in Fig. S1. Table 1 summarizes their lattice constants, SbX and TlX bond lengths and nontrivial QSH bulkgaps at their equilibrium states. The results demonstrate that the electronic structures of all these TlSbX_{2} films are similar to TlSbF_{2} and exhibit nontrivial topological states (Fig. S2). Interestingly, as can be seen in Fig. 4(c) and Fig. S1, the global gaps in QSH state are obtained to be 0.34, 0.32 and 0.29 eV for TlSbCl_{2}, TlSbBr_{2} and TlSbI_{2}, respectively, which are sufficient for practical applications at room temperature. However, when comparing the band gaps with each other, we can find some fascinating phenomena that the global band gaps of these systems monotonically decrease in the contrary order of TlSbF_{2} > TlSbCl_{2} > TlSbBr_{2} > TlSbI_{2}. It is known that, from F to I, the SOC becomes stronger in the order of F < Cl < Br < I, thus the SOCinduced bulkgap should be increased correspondingly. This interesting contradiction can be attributed to the variation of band components of Tl and Sb atoms near the Fermi level, as the band splitting driven by SOC can directly determine QSH gap. As shown in Fig. 4(c), the ratio (R_{1}) from the Sbp_{x,y} to Xp_{x,y} orbitals at Γ point can be established by R_{1} = Sbp_{x,y}/Xp_{x,y}, which decreases in the order of TlSbF_{2} > TlSbCl_{2} > TlSbBr_{2} > TlSbI_{2}. Similar results are obtained for the ratio R_{2} = TIp_{x,y}/Xp_{x,y} in Fig. 4(d). Considering that the Tl and Sb atoms exhibits stronger SOC strength than halogens, it is expected that the larger the ratio is, the larger the contribution to the states near the Fermi level and thus the larger the SOC strength.
Strain engineering is a powerful approach to modulate electronic properties and topological natures in 2D materials and thus it is interesting to study these effects in TlSbX_{2} films. We employ an external strain on these monolayers maintaining the crystal symmetry by changing its lattices as ε = (a–a_{0})/a_{0}, where a (a_{0}) is the strained (equilibrium) lattice constants. As shown in Fig. 5(a,b), the magnitude of nontrivial bulkgaps of TlSbH_{2} and TlSbF_{2} can be modified significantly by strain, implying the interatomic coupling can modulate the topological natures of these systems. For TlSbH_{2}, with increasing the strain, the CBM is continuously to shift downward to the Fermi level, while the VBM increases reversibly, leading the band gap to decrease significantly (Fig. 5(a)). When the critical value reaches up to −3.8%, a semimetallic state with zero density of states at the Fermi level occurs. If increases the strain beyond −3.8%, a trivial topological phase appears. While for TlSbX_{2} (see also Fig. 5(b) and Fig. S3), both the direct and indirect band gaps decreases steadily with respect to tensile strain. Especially, these QSH states are robust with the strain in the range of −8 ~ 16%. Such robust topology against lattice deformation makes TlSbX_{2} easier for experimental realization and characterization on different substrate.
On the other hand, from the perspective of potential device applications, the ability to control topological electronic properties via the vertical electric field (Efield) is highly desirable. Thus, we study the change of band gaps of TlSbH_{2} and TlSbF_{2} under different vertical Efield, as shown in Fig. 5(c,d). One can see that the band gaps increase monotonically with increasing Efield strength for both cases. For TlSbF_{2} (Fig. 5(d)), under −0.8 V Å^{−1} ≤ Efield ≤0.8 V Å^{−1}, the trend of band gaps increase monotonically from 0.34 eV to 0.41 eV, with E_{Γ} larger than E_{g} significantly. While for TlSbH_{2}, when Efield ≤−5.5 V Å^{−1}, it is a normal metal. But for large Efield (>−0.4 V Å^{−1}), it becomes a QSH insulator, along with E_{Γ} being almost equal to E_{g}. Noticeably, if Efield is in the range of ±8%, the nontrivial bulkgaps of other TlSbX_{2} (X = Cl, Br, I) are still very large (~0.2−0.5 eV) (Fig. S3), allowing for viable applications at room temperature. The predicted QSH insulators tuned by vertical Efield may provide a platform for realizing topological fieldeffect transistor (TFET).
The substrate materials are inevitable in device application, thus a freestanding film must eventually be deposited or grown on a substrate. As a 2D largegap insulator with a high dielectric constant, the BN sheet has been successfully used as the substrate to grow graphene or assemble 2D stacked nanodevices^{40,41}. Thus, we use it as a substrate to support TlSbX_{2} films. Figure 6(a,b) show the geometrical structures of TlSbH_{2} and TlSbF_{2} on (2 × 2) BN sheet, where the lattice mismatch is only about 1.68% and 2.80%, respectively. After full relaxation with van der Waals (vdW) forces^{42}, they almost retain the original structure with a distance between the adjacent layers of 3.35 Å. The calculated binding energy is about −69, −87, −98, −108 and −114 meV for TlSbH_{2}, TlSbF_{2}, TlSbCl_{2}, TlSbBr_{2} and TlSbI_{2 }per unit cell, respectively, showing that they are typical van der Waals heterostructures. The calculated band structure with SOC is shown in Fig. 6(c,d). In these weakly coupled systems, TlSbH_{2} on the BN sheet remains semiconducting, there is essentially no charge transfer between the adjacent layers and the states around the Fermi level are dominantly contributed by TlSbH_{2}. If we compare the bands of TlSbH_{2} with and without BN substrate, little difference is observed. Similar results are also found for all halogenated TlSbX_{2} films on BN substrate (see also Fig. S4), except that TlSbF_{2} on the BN sheet exhibits a metallic state. Evidently, all TlSbX_{2} films on BN substrate are robust QSH insulators.
Conclusions
To conclude, on the basis of firstprinciples calculations, we predict a class of new QSH insulator of TlSbX_{2} (X = H, F, Cl, Br, I) films, with a sizable bulk gap (0.22 ~ 0.40 eV), allowing for viable applications in spintronic devices. Two mechanisms, typeI: SOCinduced psp type TI (TlSbH_{2}) and typeII: the chemical bonding induced pps type TI (Halogenated ones) are obtained, significantly different from one in TISb monolayer. The topological characteristic of TlSbX_{2} films are confirmed by the Z_{2} topological order and topologically protected edge states. Furthermore, the band gap and topological phase transition could be tuned by the external strain and vertical Efield. When TlSbX_{2} deposited on BN substrate, both the band gaps and lowenergy electronic structures are only slightly affected by the interlayer coupling from the substrate. These predicted QSH insulators and their vdW heterostructures may provide a platform for realizing lowdissipation quantum electronics and spintronics devices.
Computational method and details
To study the structural and electronic properties of TlSbX_{2} (X = H, F, Cl, Br, I) films, our calculations were performed using the planewave basis Vienna ab initio simulation package known as VASP code^{43,44}. We used the generalized gradient approximation (GGA) for the exchange and correlation potential, as proposed by PerdewBurkErnzerhof (PBE)^{45}, the projector augmented wave potential (PAW)^{46} to treat the ionelectron interactions. The energy cutoff of the plane waves was set to 500 eV with the energy precision of 10^{−6 }eV. The Brillouin zone was sampled by using a 21 × 21 × 1 Gammacentered MonkhorstPack grid. The vacuum space was set to 20 Å to minimize artificial interactions between neighboring slabs. SOC was included by a second vibrational procedure on a fully selfconsistent basis. The phonon spectra were calculated using a supercell approach within the PHONON code^{47}.
Additional Information
How to cite this article: Zhang, R. et al. Functionalized Thallium Antimony Films as Excellent Candidates for LargeGap Quantum Spin Hall Insulator. Sci. Rep. 6, 21351; doi: 10.1038/srep21351 (2016).
References
Hasan, M. Z. & Kane, C. L. Colloquium: Topological Insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X. L. & Zhang, S. C. Topological Insulators and Superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Yan, B. & Zhang, S. C. Topological Materials. Rep. Prog. Phys. 75, 096501 (2012).
Moore, J. E. Majorana’s Wires. Nat. Nanotechnol. 8, 194–198 (2013).
Rasche, B. et al. Stacked Topological Insulator Built from Bismuthbased Graphene Sheet Analogues. Nat. Mater. 12, 422–425 (2013).
Zhang, H. J. et al. Topological Insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with A Single Dirac Cone on the Surface. Nat. Phys. 5, 438–442 (2009).
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 Pb1−xSnxSe. Nat. mater. 11, 1023–1027 (2012).
Du, L., Knez, I., Sullivan, G. & Du, R. R. Robust helical edge transport in gated InAs/GaSb bilayers. Phys. Rev. Lett. 114, 096802 (2015).
Liu, C. X., 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., Hua, J. & Yao, Y. G. Lowenergy Effective Hamiltonian Involving Spinorbit Coupling in Silicene and Twodimensional Germanium and Tin. Phys. Rev. B 84, 195430 (2011).
Yang, F. et al. Spatial and Energy Distribution of Topological Edge States in Single Bi (111) Bilayer. Phys. Rev. Lett. 109, 016801 (2012).
Tang, P. Z. et al. Stable twodimensional dumbbell stanene: A quantum spin Hall insulator. Phys. Rev. B 90, 121408 (2014).
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. Tunable quantum spin Hall effect via strain in twodimensional arsenene monolayer. J. Phys. D: Appl. Phys. 49, 055305 (2016).
Jin, K. H. & Jhi, S. H. Quantum Anomalous Hall and Quantum SpinHall Phases in Flattened Bi and Sb Bilayers. Sci. Rep. 5, 8426 (2015).
Song, Z. G. 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 Mater. 6, e147 (2014).
Zhang, R. W. et al. Ethynylfunctionalized stanene film: a promising candidate as largegap quantum spin Hall insulator. New J. Phys. 17, 083036 (2015).
Zhang, R. W. et al. Room Temperature Quantum Spin Hall Insulator in Ethynyl Derivative Functionalized Stanene Films, Sci. Rep. 6, 18879 (2016).
Yang, F. et al. Spatial and energy distribution of topological edge states in single Bi (111) bilayer. Phys. Rev. Lett. 109, 016801 (2012).
Hirahara, T. et al. Atomic and electronic structure of ultrathin Bi (111) films grown on Bi2Te3 (111) substrates: evidence for a strain induced topological phase transition. Phys. Rev. Lett. 109, 227401 (2012).
Fukui, N. et al. Surface relaxation of topological insulators: Influence on the electronic structure. Phys. Rev. B 85, 115426 (2012).
Wang, Z. F. et al. Creation of helical Dirac fermions by interfacing two gapped systems of ordinary fermions. Nat. Commun. 4, 1384 (2013).
Murakami, S. Quantum Spin Hall Effect and Enhanced Magnetic Response by SpinOrbit Coupling. Phys. Rev. Lett. 97, 236805 (2006).
Bahramy, M. S., Yang, B. J., Arita, R. & Nagaosa, N. Emergence of noncentrosymmetric topological insulating phase in BiTeI under pressure. Nat. Comm. 3, 679 (2012).
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermiarc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).
Wang, J., Chen, X., Zhu, B. F. & Zhang, S. C. Topological pn junction. Phys. Rev. B 85, 235131 (2012).
Bauer, E. et al. Heavy Fermion Superconductivity and Magnetic Order in Noncentrosymmetric CePt3S. Phys. Rev. Lett. 92, 027003 (2004).
Frigeri, P. A., Agterberg, D. F., Koga, A. & Sigrist, M. Superconductivity without Inversion Symmetry: MnSi versus CePt3Si. Phys. Rev. Lett. 92, 097001 (2004).
Liu, Q. et al. Switching a Normal Insulator into a Topological Insulator via Electric Field with Application to Phosphorene. Nano Lett. 15, 1222–1228 (2015).
Weng, H., Dai, X. & Fang, Z. Transitionmetal pentatelluride ZrTe5 and HfTe5: A paradigm for largegap quantum spin Hall insulators. Phys. Rev. X 4, 011002 (2014).
Zhu, Z., Cheng, Y. & Schwingenschlögl, U. Topological phase transition in layered GaS and GaSe. Phys. Rev. Lett. 108, 266805 (2012).
Kane, C. L. & Mele, E. J. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett. 95, 226801 (2005).
Liu, C. C., Feng, W. X. & Yao, Y. G. Quantum spin Hall effect in silicene and twodimensional germanium. Phys. Rev. Lett. 107, 076802 (2011).
Xu, Y. et al. Largegap Quantum Spin Hall Insulators in Tin films. Phys. Rev. Lett. 111, 136804 (2013).
Mostofi, A. A. et al. Wannier90: A tool for obtaining maximallylocalised Wannier functions. Comput. Phys. Commun. 178, 685 (2008).
Sancho, M. P. L., Sancho, J. M. L. & 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).
Kim, K. K. et al. Synthesis of monolayer hexagonal boron nitride on Cu foil using chemical vapor deposition. Nano Lett. 12, 161–166 (2011).
Yang, W. et al. Epitaxial growth of singledomain graphene on hexagonal boron nitride. Nat. Mater. 12, 792–797 (2013).
Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set. Phys. Rev. B 54, 11169 (1996).
Kresse, G. & Furthmüller, J. Efficiency of abinitio total energy calculations for metals and semiconductors using a planewave basis set. Comput. Mater. Sci. 6, 15–50 (1996).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865 (1996).
Blöchl, P. E. Projector augmentedwave method. Phys. Rev. B 50, 17953 (1994).
Zimmermann, H., Keller, R. C., Meisen, P. & SeelmannEggebert, M. Growth of Sn Thin Films on CdTe (111). Surf. Sci. 904, 377–379 (1997).
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 11274143, 11434006, 61172028 and 11304121) and Research Fund for the Doctoral Program of University of Jinan (Grant no. XBS1433).
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R.Z. and C.Z. conceived the study and wrote the manuscript. R.Z. and W.J. performed the firstprinciples calculations. S.L and S.Y calculated the phonon spectrum. P.L. prepared figures 1–3, P.W. prepared figures 4–6. All authors read and approved the final manuscript.
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Zhang, Rw., Zhang, Cw., Ji, Wx. et al. Functionalized Thallium Antimony Films as Excellent Candidates for LargeGap Quantum Spin Hall Insulator. Sci Rep 6, 21351 (2016). https://doi.org/10.1038/srep21351
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