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NPG Asia Materials (2014) 6, e147; doi:http://dx.doi.org/10.1038/am.2014.113

Web End =www.nature.com/am

Zhigang Song1,5, Cheng-Cheng Liu2,5, Jinbo Yang1,3, Jingzhi Han1, Meng Ye1, Botao Fu2, Yingchang Yang1, Qian Niu3,4, Jing Lu1,3 and Yugui Yao2

We demonstrate that the honeycomb structures of BiX monolayers remain stable even at 600 K. Owing to these features, the giant-gap TIs BiX/SbX monolayers are an ideal platform to realize many exotic phenomena and fabricate new quantum devices operating at RT. Furthermore, biased BiX/SbX monolayers become a quantum valley Hall insulator, exhibiting valley-selective circular dichroism.

NPG Asia Materials (2014) 6, e147; doi:http://dx.doi.org/10.1038/am.2014.113

Web End =10.1038/am.2014.113; published online 12 December 2014

INTRODUCTION

Quantum spin Hall (QSH) insulators, also known as two-dimensional (2D) topological insulators (TIs), have generated great interest in condensed matter physics and materials science because of their scientic importance as a novel quantum state and potential applications ranging from spintronics to topological quantum computation.13 QSH insulators are characterized by an insulating bulk and fully spin-polarized gapless helical edge states without backscattering at the sample boundaries, which are protected by time-reversal symmetry. The prototypical concept of the QSH effect was rst proposed by Kane and Mele4,5 in graphene, in which the spin-orbit coupling (SOC) opens a band gap at the Dirac point.However, the rather weak second-order effective SOC makes the QSH effect in graphene only appear at an unrealistically low temperature.6

To date, only the HgTe/CdTe quantum well has been veried to be a well-established QSH insulator experimentally.7,8 Experimental evidence has also been presented recently for helical edge modes in inverted InAs/GaSb quantum wells.9 The critical drawback of such a reported QSH state is their small bulk gaps, which are too small to make the predicted QSH effect observable under easily accessible experimental conditions. Thus, to observe the QSH effect at room

5These authors contributed equally to this work.

Received 11 February 2014; revised 25 September 2014; accepted 27 October 2014

ORIGINAL ARTICLE

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

temperature (RT) in TIs, a large bulk band gap is essential; the edge current can be stabilized against the interference of the thermally activated carriers in the bulk because the carrier concentration in the bulk decreases exponentially with the band gap. Extensive effort has been devoted to the search for new 2D TIs with a large bulk band gap.1014 Some layered materials such as silicene, germanene15 and stanene16 have been proposed, and the bulk band gap of 2D TI has been elevated to a remarkable 0.3 eV in a chemically modied tin lm,SnX (X = F, Cl, Br and I).13 Recently, ultrathin Bi lms have drawn much attention as promising candidates for QSH insulators, and the 2D topological properties of the ultra-thin Bi(111) lms have been reported.17 To the best of our knowledge, no bulk band gap has exceeded 0.7 eV in either 2D or 3D TIs.18

Because Bi and Sb are well known for their strong SOC that can drive and stabilize the topological non-trivial electronic states, it is wise to search for large-band-gap QSH insulators based on Bi/Sb-related materials. Here, we predicted that the free-standing 2D honeycombBi/Sb halide and Bi/Sb hydride (we call these structures bismuthu-mane and stibiumane, respectively, by analogy with graphane, silicane and stanane) systems are stable huge-band-gap QSH insulators based on rst-principles (FP) calculations of the structure optimization,

1State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing, China; 2School of Physics, Beijing Institute of Technology, Beijing, China;

3Collaborative Innovation Center of Quantum Matter, Beijing, China and 4International Center for Quantum Materials, Peking University, Beijing, China

Correspondence: Professor J Yang or Professor J Lu, School of Physics, Peking University, State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, China or Professor Y Yao, School of Physics, Beijing Institute of Technology, Beijing, China.

E-mail: mailto:[email protected]

Web End [email protected] or mailto:[email protected]

Web End [email protected]

Quantum spin and valley Hall insulators of BiX/SbX Z Song et al

Figure 1 (a) Lattice geometry for BiX/SbX monolayer (X = H, F, Cl and Br) from the top view (upper) and side view (lower), respectively. In a unit cell, BiX/SbX is related to Bi'X'/Sb'X' by an inversion operation. (b) The rst Brillouin zone of BiX/SbX monolayers and the points of high symmetry. (c) Corresponding phonon spectrum for BiH monolayer.

Table 1 The lattice constant a, Bi-Bi and Sb-Sb bond length b, Bi-X and Sb-X bond length d, buckling height h shown in Figure 1a (h is dened as the distance from the center of the upper to that of the lower Bi/Sb atoms), global band gap (the superscripts d and i represent the direct gap and indirect gap, respectively)

Monolayers a () b () d () h () (eV) vF(105 m/s) SO Z2

BiH 5.53 3.19 1.82 0.08 1.03i 8.9 0.56 1 BiF 5.38 3.14 2.12 0.46 1.08i 7.2 0.55 1 BiCl 5.49 3.17 2.54 0.24 0.95i 6.9 0.56 1 BiBr 5.52 3.18 2.69 0.16 0.74i 8.0 0.65 1 SbH 5.29 3.05 1.73 0.08 0.41d 8.6 0.21 1 SbF 5.12 2.96 1.99 0.30 0.32d 7.9 0.16 1 SbCl 5.17 2.98 2.42 0.14 0.36d 7.7 0.18 1 SbBr 5.25 3.03 2.57 0.09 0.40d 8.6 0.20 1

Fermi velocity vF and magnitude of the intrinsic effective SOC SO for Bi and Sb hydride/halide monolayers obtained from the rst-principles calculations. Note that SO = Eg/2, with the local gap Eg opened by SOC at the Dirac point.

phonon modes and nite temperature molecular dynamics (MD) as well as their electronic structures. The topological characteristic of these TIs is conrmed by the FP-calculated nontrivial Z2 index. The low-energy effective Hamiltonian (LEEH) is given to capture the low-energy long-wavelength properties of these systems. Signicantly, among these new TIs, we observed a bulk band gap of approximately1.0 eV related to the px and py orbitals of the Bi atoms in BiX (X = H, F and Cl) monolayers. To the best of our knowledge, these are the largest-band-gap TIs. Their gaps opened by SOC in the QSH phase can be effectively tuned by the X atom. All of the above features make these compounds promising for applications at RT. Moreover, when the inversion symmetry of the honeycomb lattice for BiX/SbX monolayers is broken, the BiX/SbX monolayers become a quantum valley Hall insulator, and chiral optical selectivity of the valleys is obtained.

METHODSFor these materials, we rst performed a geometry optimization including SOC interaction using the VASP package within the framework of the projector augmented wave pseudopotential method using a plane-wave basis set. The

Brillouin-zone integrations were performed on a 9 9 1 -centered k mesh. Vacuum regions with thicknesses larger than 14 were placed to avoid interaction between the monolayers and their periodic images. Both the atomic positions and lattice constant were relaxed until the maximal force on each relaxed atom was smaller than 0.001 eV1. The cutoff energy for wave-function expansion was set as 1.3* Emax of the X atoms. The stability of the optimized structure for the BiH monolayer was conrmed by a vibrational analysis using the phonopy package19 with a supercell of 5 5 unit cells. Fully relativistic band calculations were performed with the linearized augmented plane wave method implemented in the WIEN2K package, and the results are in good agreement with those generated by the VASP package. SOC was included as a second vibrational step using scalar-relativistic eigenfunctions as the basis after the initial calculation was converged to self-consistency. The relativistic p1/2 corrections were also considered for the 6p orbital of Bi to improve the accuracy. A 20 20 3 k-point grid was utilized in the rst

Brillouin zone sampling, and the cutoff parameter RmtKmax was 4 for Bi(Sb)H monolayers and 6 for BiX/SbX (X = F, Cl and Br) monolayers. The Fermi energy was calculated, where each eigenvalue was temperature-broadened using a Fermi function with a broadening parameter of 0.002 Ry. The exchange-correlation functional was treated using the Perdew-Burke-Ernzerhof generalized gradient approximation throughout this study.

RESULTSFigure 1a plots the typical optimized geometries for BiX monolayers, which have a threefold rotational symmetry similar to that in graphene. The inversion symmetry holds for all the tested compounds. The equilibrium lattice constants, nearest neighbor Bi-X distances and buckling heights obtained through the structural optimization are listed in Table 1. A quasi-planar geometry is observed to be more stable for the BiH monolayer (bismuthumane), whereas a low-buckled conguration is more stable for the BiF, BiCl and BiBr monolayers. This nding is related to the bonding between Bi and the X atoms. Because F, Cl and Br are more electronegative than H, the bond between Bi and F atoms is stronger than that between Bi and H atoms, leading to a low buckling in BiX (X = F, Cl and Br) monolayers. The lattice constants of BiX monolayers follows the sequence of a(F)o a(Cl)oa(Br), in accordance with the electronegativity. The bond distances of the Bi-X lms slightly increases with the sequence of d(Br)4d(Cl)4d(F) determined by their covalent bond radii. The kinetic stability of these 2D TIs is further conrmed by the calculations of the phonon spectrum without SOC. Taking BiH

NPG Asia Materials

Quantum spin and valley Hall insulators of BiX/SbX Z Song et al

monolayer for example (Figure 1c), there is no imaginary frequency along all momenta, which indicates that this structure is kinetically stable, corresponding to an energy minimum in the potential energy surface.

The thermodynamic stability of the BiX/SbX monolayers was then veried by calculating the per-atom Gibbs free energy of formation (G),

dG E nBimBi nXmX; 1

where E represents the cohesive energy per atom of the BiX/SbX monolayers, nBi and nX are the mole fractions of Bi and X atoms, respectively, for a given structure, and Bi and X are the per-atom chemical potentials of Bi and X, respectively, at a given state. We selected Bi and X as the binding energies per atom of bulk Bi and the

X2 molecule, respectively. The formation energy data of all the checked BiX/SbX monolayers are presented in Table 2. The calculated G value for the BiH monolayer was 0.30 eV. Bismuthine is a chemical compound with the formula BiH3 and is stable below 60 C.20,21 G of bismuthine is 0.53 eV. G of the BiH monolayer is smaller than that of bismuthine; therefore, it is possible to synthesize a BiH monolayer.

Remarkably, bismuth/antimony-halide monolayers have negative G, indicating a higher thermodynamic stability relative to their elemental reservoirs.

We performed ab initio MD simulations using a supercell of 3 3 unit cells at various temperatures (see Figure 2 and Supplementary Figure S1) with a time step of 1.5 fs to verify the thermal stability of the BiX monolayers. After running 1500 steps at 300 and 600 K, no bond was broken, suggesting that the structures of the BiX (X = H, F, Cl and Br) monolayers were thermally stable even at 600 K. We also performed an ab initio MD simulation for a larger 4 4 supercell for the BiH monolayer and observed that the structure of the BiH monolayer was stable after 2.25 ps at 600 K (see Supplementary Figure S2). In fact, it was observed that the Bi-X bond energy was much higher than that of the Bi-Bi bonds because of the large bond distance between Bi-Bi atoms. The snapshots of the MD simulations at higher temperature reveal that the Bi-Bi bonds are broken whereas Bi-X bonds remain at 700 K. The SbX monolayers are also stable at 300400 K (see Supplementary Figure S1). The thermal stability of these structures enables these lms to be used at or even above RT, which is very important for practical applications.

The typical band structures of the predicted systems BiH, BiF and SbF are shown in Figure 3. The band structures of other monolayers are shown in Supplementary Figure S3. The valence and conduction bands near the Fermi level are mostly composed of the px and py orbitals from the Bi atoms according to the partial band projections.

Notably, the two energy bands are observed to cross linearly at the K (and K = K) point, suggesting the existence of Dirac-cone-like

features in the band structure of these 2D honeycomb systems without SOC. These materials can thus be considered as a gapless semiconductor, or alternatively, as a semi-metal with zero density of states at the Fermi level. Because the honeycomb structure consists of two hexagonal Bi sublattices, the electrons in these predicted materials can formally be described by a Dirac-like Hamiltonian operator containing a two-component pseudospin operator.

When SOC is switched on, the degeneracy at the Dirac points is lifted, and the valence bands are downshifted whereas the conduction bands are upshifted, yielding a huge band gap opened by SOC for all BiX monolayers. The local gap at the Dirac point K (K) is a result of the rst-order relativistic effect related to Bi elements. Thus, the gap is robust. In contrast, the conduction bands are downshifted, whereas the valence bands are upshifted at the point, which produces a global indirect band gap. The X atoms mainly hybridize with the Bi atom near the point in the conduction and valence bands. The band gap can be effectively tuned by the X atoms. The global gaps of BiX (X = H, F, Cl and Br) monolayers range from 0.74 to 1.08 eV because of the strong SOC of the Bi atoms, especially for BiH and BiF monolayers with bulk gaps larger than 1.0 eV. For SbX (X = H, F, Cl and Br) monolayers, the valence bands are downshifted, whereas the conduction bands are upshifted at the K point, producing a global direct band gap. The values of the gaps range from 0.3 to 0.4 eV, which are comparable with the values of the theoretically predicted chemically modied tin lms.13

The band topology of BiX/SbX (X = F, Cl and Br) monolayers can be characterized by the Z2 invariant.22 Z2 = 1 characterizes a nontrivial band topology (corresponding to a QSH insulator), whereas Z2 = 0 represents a trivial band topology. The Z2 invariants can be directly obtained from the FP lattice computation method.23 Taking a BiH monolayer as an example, the n-eld conguration is shown in 3from FP calculations. Note that different gauge choices result in different n-eld congurations; however, the sum of the n-eld over half of the Brillouin zone is gauge invariant module 2, namely Z2 topological invariant.24 The honeycomb BiH monolayer has nontrivial band topology with the topological invariant Z2 = 1, and at the Dirac point K, the gap opened by SOC is sizable. We also calculate the Z2 topological invariant for the other systems and nd that all the invariants are topologically non-trivial. Therefore, the QSH effect can be steadily achieved in the 2D honeycomb Bi(Sb) hydride/halide with huge SOC gap.

To the best of our knowledge, a bulk band gap of greater than1.0 eV in BiH and BiF monolayers is the largest bulk band gap of all the reported TIs. The band gaps of these compounds are approximately three times the values of the recent results of theoretically predicted chemical modied tin lms (a bulk gap of0.3 eV)13 and the superstar 3D TI Bi2Se3 (a bulk gap of 0.35 eV).25 Furthermore, the predicted large bulk gap makes BiX/SbX monolayers capable of enduring considerable crystal defects and thermal uctuation, which are benecial to applications in high-temperature spin-tronics devices. Bi is among the main group elements that have the strongest SOC, a fundamental mechanism to induce the Z2 topology.

Therefore, the predicted TIs consisting of Bi exhibit huge gaps opened by SOC.

The bulk band gap is one of the most important parameters for TIs and is analogous to the superconducting transition temperature (Tc)

for a superconductor. Insulation of the bulk is critical to observe the surface metallic state of a TI because the surface metallic state would be masked if the bulk state becomes metallic. A large bulk band gap is critical to maintain bulk insulating. If the bulk band gap is too small, the defect and disorder, which are difcult to avoid in material growth,

Table 2 Comparisons between Gibbs free energies of BiX/SbX monolayers and those of BiX3/ SbX3 molecules

Monolayer G (eV) Molecule G (eV)

BiH 0.299 BiH3 0.53 BiF 1.23 BiF3 1.976

BiCl 0.509 BiCl3 0.792 BiBr 0.412 BiBr3 0.899

SbH 0.219 SbH3 0.264 SbF 1.288 SbF3 2.204

SbCl 0.478 SbCl3 0.858 SbBr 0.374 SbBr3 0.579

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Quantum spin and valley Hall insulators of BiX/SbX

Z Song et al

Figure 2 Snapshots from the MD simulation of the structure for BiH monolayer at 300 K (a) and 600 K (b) after 2.25 ps. Pink balls: Bi atoms; green balls: H atoms; the dashed line indicates a supercell with a 3 3 unit cell.

p pBx itzpBy, with z representing the valley degree of freedom, K and K, which indicates that the basis functions are different around the K and K points. The SOC term generally reads HSO x0 L

would most likely shift the Fermi level to the conduction or valence band, making the bulk conductive. In addition, if the bulk band gap is too small, carriers (electrons and holes) can be more easily produced at a nite temperature. The generations of the TIs can be categorized chiey in terms of their bulk band gap values:1,26 The rst-generation

Tls include Bi-Sb alloy with a bulk gap smaller than 0.1 eV, and the second-generation TIs include Bi2Se3, Sb2Te3 and Bi2Se3. The previously reported TIs SnX (X = F, Cl, Br and I) can also be categorized into this generation. Our reported TI BiX (X = H, F, Cl and Br) monolayers have a bulk band gap of approximately 1.0 eV and can be regarded as third-generation TIs. Therefore, although the idea to realize a new TI by functionalization of a 2D material in this study is similar to that in our previous work, our results predict a new generation of TIs and represent an important breakthrough in the study of TIs.

Large lattice distortion greatly affects the energy band and band gap of a BiH monolayer. On the basis of MD calculations, we predicted that the phase transition temperature of the BiH monolayer is between 600 and 700 K. At 600 K, the lattice distortion is very large, and the inversion symmetry is destroyed (see Figure 2). However, the band gap remains larger than 0.22 eV after 2.25 ps. The bands are split by SOC in the absence of inversion symmetry, and the splitting is mainly a Rashba type. We calculated the Z2 number of the structure of the

MD simulation at 600 K after 2.25 ps and observed that the BiH monolayer remains a TI. Hence, the topology of the BiH monolayer is very robust against a lattice distortion.

We also studied the effects of inversion symmetry breaking induced by an electric eld on the band gap and topology of a BiH monolayer. The band gap was observed to decrease with increasing electric eld (see Supplementary Figure S4) and closes at E = 0.67 V/; however, the nontrivial topology remains. It is noteworthy that under a certain range of electric elds (0.610.67 V/), BiX monolayers may generate perfect free electron gas and serve as a spin eld effect transistor (see details in the Supplementary Information).

The nontrivial topology of SnX monolayers in the previous work originates from s- and p-band inversion at the point similar to that in a HgTe quantum well and in Bi2Se3.8,25 However, the nontrivial topology in BiX/SbX monolayers results from the massive Dirac cone, and there is no band inversion. In fact, the origin of the nontrivial topology in BiX/SbX monolayers is similar to that in graphene and silicene; however, the type of SOC in BiX/SbX monolayers is brand new. We constructed a minimal model Hamiltonian based on FP calculations and general symmetry considerations. The symmetry of these systems possesses a D3d point group, and the groups of the wave vector at the Dirac points K and K are both D3, which splits the

p orbitals at the Dirac points into two groups: A2 (pz) and E (px, py). On the basis of the FP calculations, around the Dirac points and Fermi level, the low-energy band structure mainly consists of px and py orbitals from Bi/Sb atoms in the band components. The px and py orbitals form a 2D irreducible representation of the wave vector of D3 at the Dirac points, which is relevant for the low-energy physics. There are massive Dirac cones at the K(K) point and at bands (the second band below the Fermi level)27 in BiX/SbX monolayers. Massive Dirac cones and at bands mainly consisting of the px and py orbitals distinguish BiX/SbX monolayers from graphene/silicene and lead to new phenomena, such as the orbital analog of the quantum anomalous Hall effect28 and Wigner crystallization.27

Considering that there are two distinct sites, A and B, in the unit cell (Figure 1a), the symmetry-adopted basis functions can be written as F1

j i 12

p pAx itzpAy, F2

j i

, where

S = Sx iSy and L = Lx iLy denote the creation (annihilation) operator for the spin and angular momentum, respectively. 0 is the magnitude of effective intrinsic SOC. A straightforward calculation leads to the on-site SOC in the spinful low-energy Hilbert subspace

Fm1

E; Fk1

!? S

! x0 LS L S2 LzSz

n o, HSO = SzSOzz, with lSO 12x0. The low-energy Hilbert subspace consisting of px and py orbitals differs signicantly from that consisting of a pz orbital similar to in graphene and silicene. Moreover, the SOC term is on-site rather than the next nearest neighbor as in the Kane-Mele model.4,5,15,16 This nding

indicates that the SOC mechanism in BiX/SbX monolayers is completely different from that in graphene or silicene.

To the rst order of k, the symmetry-allowed four-band LEEH involving SOC can be written as

H _vFkxsx tkysy SzlSOtzsz; 2 where the Pauli matrix denotes F1

j i and F2

j i orbital degrees of

freedom, and z represents the valley degree of freedom K and K. The

energy spectrum of the total LEEH is E

E; Fm2

E; Fk2

k 7

_2v2Fk2 l2SO

q with a gap Eg = 2SO at the Dirac points. The above LEEH is invariable under the space reversal and the time reversal operation. In fact, the low-energy basis functions are mixed with small components of other orbitals (see Figure 3), whereas the low-energy physics can be grasped by the low-energy effective model. The only two parameters vF and SO in the above effective Hamiltonian can be obtained from FP calculations, whose values are listed in Table 1. The band structures around the K point for BiH, BiF and SbF monolayers calculated using the DFT and LEEH methods are compared in Figure 4. It is apparent that in the vicinity of the Dirac K point, there is good agreement between the calculated results of these two methods.

There is a valley degree of freedom in BiX/SbX monolayers, and the SOC opens a large gap at the corners of the Brillouin zone. If the inversion symmetry is broken in BiX/SbX monolayers, for example by a vertical electric eld, the valley-contrast Berry curvature appears, and the monolayers become a quantum valley Hall insulator. In contrast, SnX monolayers are not a quantum valley Hall insulator at all (the band gap appears at the point).13 The valley-contrast Berry curvature and spin in BiX/SbX monolayers will yield novel transport properties, such as the valley Hall effect,29 valley spin Hall effect30 and valley orbital moment Hall effect. In addition, valley-contrast circular dichroism will appear. Generally, the degree of valley polarization (k) and circular dichroism can be described by the degree of circular

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Quantum spin and valley Hall insulators of BiX/SbX Z Song et al

Figure 3 Band structures of the BiX monolayers without (gray) and with (red) the SOC and Z2 topological invariant: (a) BiH, (b) BiF and (c) SbF monolayers. The Fermi level is set to zero. The bands near the Fermi level consist of the px and py orbitals. The size of the symbols is proportional to the population of the px and py orbitals. (d) n-eld conguration for BiH monolayer. The calculated torus in the Brillouin zone is spanned by G1 and G2. Note that the two reciprocal lattice vectors form an angle of 120. The white and black circles represent n = 1 and 1, respectively, while the blank represents 0. The Z2 invariant is 1, obtained by summing the n-eld over half of the torus mod 2.

Figure 4 A comparison of the band structures near the K point for (a) BiH, (b) BiF and (c) SbF monolayers calculated using DFT and LEEH methods. The solid gray and solid red lines denote the data calculated using DFT theory without SOC and with SOC, respectively. The dashed blue and dashed green lines represent the data calculated using the LEEH method with SOC and without SOC, respectively. The Fermi level is set to zero.

2 sz; 3

where 1 is the additional band gap induced by inversion symmetry breaking. In the low-energy limit, the valley magnetic moments of

BiX/SbX systems can be expressed as m t

e_v2F

z2sztzlSOD1, where sz is the

real spin. In contrast, in the MoS2 monolayer, the valley moments are31 m tz ev

polarization (k) in the Brillouin zone. (k) is dened as Zk jpkj

j i are the periodic parts of

the conduction and valence band of the Bloch function, respectively. The calculated (k) in the irreducible Brillouin zone of the BiH monolayer under a vertical eld is shown in Figure 5, and a perfect optical selection rule at two valleys is apparent. Namely, the valley K absorbs left-handed photons, whereas the valley K absorbs right-handed photons. Thus, a circular polarized light can be used to create imbalanced electron occupation between the two valleys in BiX/SbX monolayers. However, in graphene and silicene, valleytronics is difcult to achieve because of the quite small SOC.

Moreover, in BiX/SbX monolayers, there is a new and strong coupling between spin and valley pseudo-spin because of the large band gap opened by SOC, which is different from that in the MoS2 system. The valley pseudo-spin can be controlled using the electric eld due to the strong spin-orbital coupling in the BiX/SbX mono-layers. According to the low-power model, there is an intrinsic valley degree of freedom, and the valley orbital moment couples to the spin. The low-energy effective model with broken inversion symmetry in BiX/SbX monolayers is

H _vFkxsx tkysy SzlSOtzsz

2_D1. The valley magnetic moments of BiX/SbX mono-layers are related to not only the valley pseudo-spin but also the real spin. 1 is a variable that can be adjusted by the electric eld.

DISCUSSIONChemical functionalization of 2D materials is a powerful tool to create new materials with desirable features, such as graphane or uorinated graphene. In the current study, we have investigated the properties of a bismuth monolayer with planar or low-buckled structure and observed that its structure is unstable without the X atom. The high-buckled Bi monolayer, that is, bilayer bismuth lm with a lattice constant of 4.52 , is more stable than the bismuth planar monolayer with a lattice constant of approximately 5.4 .11 High-buckled bismuth monolayers compounded with X elements may increase their crystal lattice constants by approximately 1.0 , resulting in a quasi-

2 jp kj2

jpkj2jpkj2, where P

= Px iPy and p is the matrix element between the conduction and valence bands and is given by

Pa uvk 1_Hk

uck

D E. uck

j iand uvk

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Quantum spin and valley Hall insulators of BiX/SbX Z Song et al

1.000

0.7500

0.5000

0.2500

0.000

-0.2500

-0.5000

-0.7500

-1.000

Figure 5 Degree of circular polarization (k) in irreducible Brillouin zone of BiH monolayer under a vertical electric eld.

planar or low-buckled monolayer conguration. BiX monolayers exhibit completely different band structures from bismuth monolayers characterized by a doubled bulk band gap. In fact, we observed that the chemical functionalization of As, P and N monolayers can also result in 2D TIs with bulk band gaps of 0.18, 0.03 and 0.01 eV, respectively. Therefore, functionalization is an effective approach to obtain 2D TIs. On the experimental side, it has been known that stable halides of Bi and Sb such as BiX/SbX (X = F, Cl, Br and I)32,33 have

been synthesized, although hydrides of Bi and Sb are unstable at RT.20,21

Four different preparation methods were proposed here: (i) The method to synthesize graphane34 may be applied to prepare BiH monolayers. High-buckled monolayer bismuth can be prepared by peeling off the bulk bismuth.17 A bismuth monolayer should rst be annealed in an argon atmosphere to remove any possible contamination and then exposed to cold hydrogen plasma.34 (ii) Before hydrogenation, monolayer bismuth samples are heated in vacuum to remove physisorbed polymers and other contaminants that might block the hydrogenation of the graphene surface. Monolayer bismuth can be exposed to hydrogen gas under suitable conditions. Hydrogenation can be performed in a vacuum system equipped with a hot tungsten lament that can split the H2 gas into hydrogen atoms.35,36(iii) Monolayer bismuth samples are deposited on Si wafers. Then, a layer of hydrogen silsesquioxane is coated on the bismuth samples, and the samples are irradiated with electrons at various doses.37

Hydrogen atoms are generated in situ by breaking the Si-H bonds of hydrogen silsesquioxane during the e-beam lithography process. Finally, a BiH monolayer is formed. (iv) According to the exfoliation mechanism of monolayer BN using molten hydroxides,38 the bulk

bismuth might be exposed to a cold hydrogen plasma to grow the BiH monolayer. When Bi atoms on the surface of bulk bismuth are combined with hydrogen atoms, the Bi-Bi bonding becomes longer, and the bismuth layer with hydrogen can be separated from the bulk. After a certain time, a BiH monolayer might form. Upon acceptance of our paper, we notice that Zhou et al.39 just published a paper proposing to grow large-gap QSH insulator on semiconductor surface.

The MD simulation indicates that BiX monolayers will deform to some degree if the partial concentration of oxygen gas is high at RT; however, their honeycomb structure can remain (see details in the Supplementary Information (II)). BiX monolayers should be protected under vacuum or using an inert gas environment or an anti-oxidization layer such as 2D graphene, BN or MoS2. The application of strain can further modify the band gaps of the BiX/SbX monolayers.

For example, a strain of 5% can increase the band gap of a BiH monolayer by 0.06 eV (see Supplementary Figure S5).

In conclusion, we have identied a new family of huge-gap 2D TI phase BiX/SbX monolayers (X = H, F, Cl and Br) using FP calculations, especially BiH and BiF monolayers with known largest bulk band gaps (41.0 eV) that far exceed the gaps of the current experimentally realized 2D TI materials. The topological characteristic of these TIs are conrmed by the calculated nontrivial Z2 index and an explicit construction of the low-energy effective model in the system.

These giant-gaps are entirely due to the result of strong spin-orbit interaction being related to the px and py orbitals of the Bi/Sb atoms around the two valley K and K of the honeycomb lattice, which is sufciently large for practical application at RT. The newly discovered BiX monolayer structure survives even at a 600 K. These results represent a signicant advance in the study of TIs are expected to stimulate further work to synthesize, characterize and utilize these new 2D TIs for fundamental exploration and practical applications at RT. In addition, the biased BiX/SbX monolayers become a quantum valley Hall insulator, and valley-selective circular dichroism is available. We observe a strong coupling between the real spin and the valley pseudo-spin, which is induced by the large SOC and modied the valley magnetic moments.

CONFLICT OF INTERESTThe authors declare no conict of interest.

ACKNOWLEDGEMENTSThis work was supported by the MOST Project of China (Nos. 2010CB833104, 2014CB920903, 2011CBA00100 and 2013CB932604), the National Natural Science Foundation of China (Nos. 51371009, 51171001, 11174337, 11225418, 50971003 and 11274016), the National High Technology Research and Development Program of China (No. 2011AA03A403), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Nos. 20121101110046 and 20130001110002) and the Excellent Young Scholars Research Fund of the Beijing Institute of Technology (No. 2013YR1816).

Author contributions: Z.S., J.Y., J.L. and Y.Y. conceived the research. Z.S., B.F. and M.Y. performed the calculations. C.-L. and Z.S. performed the analysis. Z.S., C.-L., J.Y., J.L. and Y.Y. wrote the manuscript. J.H, Y.Y., Q.N., J.L and Y.Y. contributed to the discussions and editing of the manuscript.

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A large bulk band gap is critical for the application of quantum spin Hall (QSH) insulators or two-dimensional (2D) topological insulators (TIs) in spintronic devices operating at room temperature (RT). On the basis of first-principles calculations, we predicted a group of 2D TI BiX/SbX (X=H, F, Cl and Br) monolayers with extraordinarily large bulk gaps from 0.32 eV to a record value of 1.08 eV. These giant-gaps are entirely due to the result of the strong spin-orbit interaction related to the p_x and p_y orbitals of the Bi/Sb atoms around the two valleys K and K[variant prime] of the honeycomb lattice, which is significantly different from that consisting of the p_z orbital as in graphene/silicene. The topological characteristic of BiX/SbX monolayers is confirmed by the calculated nontrivial Z₂ index and an explicit construction of the low-energy effective Hamiltonian in these systems. We demonstrate that the honeycomb structures of BiX monolayers remain stable even at 600 K. Owing to these features, the giant-gap TIs BiX/SbX monolayers are an ideal platform to realize many exotic phenomena and fabricate new quantum devices operating at RT. Furthermore, biased BiX/SbX monolayers become a quantum valley Hall insulator, exhibiting valley-selective circular dichroism.

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Title

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

Author

Song, Zhigang; Liu, Cheng-cheng; Yang, Jinbo; Han, Jingzhi; Ye, Meng; Fu, Botao; Yang, Yingchang; Niu, Qian; Lu, Jing; Yao, Yugui

Pages

e147

Publication year

2014

Publication date

Dec 2014

Publisher

Nature Publishing Group

ISSN

18844049

e-ISSN

18844057

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1038/am.2014.113

ProQuest document ID

1646782979

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

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