Optical Identification of Topological Defect Types in MonolayerArsenene by First-Principles CalculationXiaoxu Liu,† Lizhe Liu,† Lun Yang,† Xinglong Wu,*,† and Paul K. Chu‡

†Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics and Collaborative Innovation Center of AdvancedMicrostructures, National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China‡Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong China

*S Supporting Information

ABSTRACT: Recent theoretical research has demonstratedthat a new two-dimensional material, the monolayer of grayarsenic (arsenene), can respond to the blue and ultravioletlight leading to possible optoelectronic applications. However,some topological defects often affect various properties ofarsenene. Here we theoretically investigate the arsenene withmonovacancy (MV), divacancy (DV), and Stone−Wales (SW)defects. Three kinds of MVs are identified and thereconstructed structures of DV and SW defects are confirmed.The dynamical stability, rearrangement, and migration forthese defects are investigated in detail. Optical spectralcalculations indicate that the MVs enhance optical transitionsin the forbidden bands of arsenene and two new characteristic peaks appear in the dielectric and absorption spectra. However,there is only one new peak in the spectrum induced by DV and SW defects. Calculations of band structures indicate that the MVinduces two defect bands in the forbidden bands of pristine arsenene, which are responsible for the two new peaks in thedielectric and absorption spectra. Our findings suggest that the optical dielectric and absorption spectra can help identify thetypes of topological defects in arsenene.

■ INTRODUCTION

Since the isolation of a monolayer of carbon atoms(graphene),1 research on two-dimensional (2D) materials hasaroused much interest. Although graphene has high electronmobility, the intrinsic zero bandgap restricts its application inoptoelectronics. In order to overcome this disadvantage, other2D materials with the proper bandgaps and unique propertiessuch as boron nitride (h-BN),2 silicene,3 germanene,4

phosphorene,5,6 and transition metal dichalcogenides(TMDs)7 have been studied theoretically and experimentally.During synthesis and processing of 2D materials, topologicaldefects appear inevitably and affect the materials properties andperformance, and so it is important to characterize thesedefects.It has been theoretically demonstrated that the monolayer of

gray arsenic (arsenene) can be transformed from indirect todirect bandgap semiconductor under biaxial strain.8−10 Theweak interaction between the gray arsenic layers makes themechanical exfoliation possible9 and arsenene exhibits interest-ing interactions with blue and ultraviolet light leading topossible optoelectronics applications. However, since defectsaffect the properties of arsenene, they must be betterunderstood. Transmission electron microscopy11 and scanningtunneling microscope12 are commonly used to examinetopological defects in the 2D materials, and Raman scatteringand photoluminescence13,14 are often employed to study

defects. In order to fathom the origin and evolution of defects,theoretical studies are critical. In this work, first-principlescalculation is performed to determine the optical properties andelectronic structure of arsenene with monovacancy (MV),divacancy (DV), and Stone−Wales (SW) defects.The density functional method is adopted to investigate the

effects of several kinds of defects on the optical properties ofarsenene. Since arsenene, graphene, and silicene have the samehexagonal geometry, we build the initial configurations withspecial defects according to the similar defective structures ingraphene and silicene demonstrated by experiments and theory.Six types of initial defect configurations are constructed andoptimized to form the final stable ones energetically. Theformation energy of each configuration is calculated so that wecan predict which type of defects most likely appears.Subsequently, the dielectric functions and absorption coef-ficients of the optimized configurations are derived. It is foundthat each type of defect produces characteristic peaks in thecurves of the imaginary part of the dielectric function but theabsorption coefficient curves are similar. Hence, the differentkinds of defects in arsenene can be identified from the opticalspectra. To determine the causes for these changes in theoptical properties, the band structures of the supercells of

Received: October 12, 2016Published: October 13, 2016

Article

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© 2016 American Chemical Society 24917 DOI: 10.1021/acs.jpcc.6b10303J. Phys. Chem. C 2016, 120, 24917−24924

arsenene with different types of defects are studied and ourresults reveal that the defects indeed alter the dielectric andabsorption spectra.

■ METHODS

The first-principles calculation is based on the densityfunctional theory (DFT) in the Vienna ab initio simulationpackage (VASP).15,16 The projector augmented wave method17

is adopted and the total energy of each supercell is calculated bygeneralized gradient approximation (GGA) in the framework ofthe Perdew−Burke−Eruzerhof (PBE)18 exchange-correlationfunctional. The electron−ion interaction is described by thenorm-conversing pseudopotential and the As 4s24p3 orbitals aretreated as valence bands. To expand the plane-wave, the cutoffenergies in the calculation are set to 325 eV and the van derWaals (vdW) interactions are considered using the DFT-D2method of Grimme.19 Since the semiconductor bandgap isunderestimated in local density approximation (LDA), thehybrid (HSE06)20 functional is implemented to overcome thislimitation. The vacuum region in the z direction between twoadjacent As slabs is 16 Å to avoid the interaction. Three kindsof hexagonal supercells 4 × 4 × 1, 5 × 5 × 1, and 6 × 6 × 1 areadopted and MV, DV, and SW are introduced. TheMonkhorst−Pack21 method is used to sample the Brillouinzone and the k-point meshes are set to be 5 × 5 × 1 in all thesupercells. The self-consistent field (SCF) tolerance is 1.0 ×10−5 eV/atom in the energy calculation, and all the atompositions and supercell lattices are relaxed. The optimizedgeometries are adopted to calculate the associated opticalproperties and electronic structures.

■ RESULTS AND DISCUSSION

We first construct a 4 × 4 × 1 supercell of the pristinemonolayer arsenene consisting of 32 atoms. The supercell is

optimized with and without vdW correction. Due to theoptimization, the length difference of the lattices along the xdirection is only 0.023 Å. When the vdW correction is notintroduced, the optimized geometric structure of the pristinemonolayer arsenene has a buckled height of h = 1.398 Å in thez direction and As−As bond length of 2.509 Å. The twoparameters are similar to those found previously.10,22 We thenremove one As atom and relax the supercell, and the finalconfiguration is shown in Figure 1a, named MV-1. Here weonly depict the optimized structures without vdW correction.The equivalent three atoms A, B, and C move toward thevacancy center by the same distance consequently deformingthe configuration slightly. The distance between any two of thethree atoms decreases from 3.608 to 3.297 Å. The side-view ofthe structure in Figure 1a indeed shows a small changecompared to the pristine geometry. The similar MV-1configurations also exist in graphene23 and silicene24,25 buthave a higher symmetry than any other types of MV structures.The reconstructed structure of the second MV, denoted MV-2,is shown in Figure 1b. The initial configuration of MV-2 isconstructed by referring to the self-healing MV in silicene.25 Inthe MV-2 structure, atom A moves toward the y direction whileatoms B and C move in the opposite direction. Thedisplacement of atom A is larger than that of atom B or C.The distance between atoms B and C decreases from 3.608 to3.490 Å, but it is still longer than that (3.297 Å) in the MV-1structure. The equivalent Si atom in the self-healing MVstructure25 of silicene bonds with its nearest four Si atoms andlengths of four Si−Si bonds are equal to each other. The Siatom in the center forms a saturated valence state by sp3

hybridization, and there are no dangling bonds. However, oneAs atom in arsenene tends to form valence bonds with the nearthree As atoms to achieve the saturated state. Finally, atom Ashown in Figure 1b is not located at the center of the vacancy.The third kind of MV structure (MV-3) is depicted in Figure 1c

Figure 1. Top and side views of six optimized defect configurations of arsenene in the 4 × 4 × 1 supercells: (a−c) Three kinds of MVs denoted byMV-1, MV-2, and MV-3, respectively. (d) Stone−Wales defect called SW. (e,f) Divacancy defects called DV-1 (5−8−5) and DV-2 (555−777).

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and the top view of this configuration resembles that of the MV(5−9 type) configuration in graphene and carbon nanotubescontaining one pentagon and one nonagon ring. As shown bythe side view of the MV-3 structure in Figure 1c, atom A movesa little in the y and z directions. However, the Si atom in thecorresponding MV configuration in silicene moves upwardfrom the silicene plane.25 Although the top views of the MV-3structures of arsenene and silicene are similar, the side views aredifferent from each other. The distance between atoms B and Cdecreases to 2.832 Å and is much shorter than those in the MV-1 and MV-2 structures. Because the shorter distance betweenatoms B and C eliminates the dangling bonds in MV-3, it isinferred that MV-3 is in the ground state and more stable thanMV-1 and MV-2. In order to investigate the SW defects inarsenene, we construct the initial structure by rotating the twoadjacent As atoms by 90° with regard to the midpoint of theirbond. The most notable feature of this optimized structure isthat in the top view, the bond orientation of atoms A and B andthe y axis forms a 23° angle instead of being parallel to eachother. The shape of the two five-membered rings and twoseven-membered rings in the final SW structure is moreirregular than those in the graphene26 and silicene.27 The sideview in Figure 1d clearly shows this characteristic of the SWstructure. The two kinds of DVs, named DV-1 and DV-2, areshown in Figures 1e and 1f, respectively. The relaxed DV-1structure shows a 5−8−5 pattern which is similar to that ingraphene.28 DV-1 can be derived from the coalescence of twoMVs or formed when the two nearest atoms are lost. Thereconstructed DV-2 (555−777) defect contains three penta-gons and three heptagons, which can stem from transformationof DV-1 by rotating a bond. The DV-2 defects also exist in thegraphene28 and silicene.29 In the same way, the defectiveconfigurations are constructed in the 5 × 5 × 1 and 6 × 6 × 1supercells and the reconstructed defective structures in thesupercells are similar. The differences mainly originate from theinteractions of adjacent defects and it is inferred that the defectstructure will converge when the volume of the supercell isincreased.The defect formation energy ΔEf of each configuration is

calculated to determine which kind of defects is more stableand the results are listed in Table I. The defect formation

energy is defined as ΔEf = Esupercell − NEAs, where Esupercell is thetotal energy of the supercell with defects, N is the number ofthe As atoms in the supercell, and EAs is the energy of the Asatom in pristine arsenene. The defect formation energy ΔEfincreases when the vdW correction is included. As the defectconcentration goes up, the enhanced interactions betweendefects relax the system to a lower energy state. For instance, in

the MV-0 defect structure, ΔEf of the 4 × 4 × 1 supercell is thesmallest and that of the 6 × 6 × 1 supercell is the largest in thecases with or without vdW correction. MV-3 is more stablethan the other two MVs and MV-1 is the most unstable. ΔEf ofSW is about 1.0 eV which is the smallest because only bondsare rotated and no atoms are lost in this defect structure.Compared with silicene29 and graphene,24,26,30 arsenene withthe same kind of defect has smaller ΔEf, indicating that it ismore likely to form defects in arsenene. The reported ΔEf ofphosphorene31 is close to ΔEf of arsenene based on ourcalculation.There are other important problems associated with the

thermal stability of the defects in arsenene. We study thestability of vacancies and SW defect in arsenene by the first-principles MD simulations in which the canonical ensemblesare selected. The simulation time and time step are set to be10.0 ps and 1.0 fs, respectively. It is found that MV-3, DV, andSW configurations are thermally stable and can keep themselvesat room temperature (300 K). The temperature fluctuation ofMV-3, SW, and DV configurations in the MD simulations at300 K are shown in Figures S1a−d (Supporting Information).The previously reported result also demonstrated that MV-3can keep itself at room temperature (300 K),32 which isconsistent with our conclusion. However, MV-1 and MV-2quickly transform into MV-3 at low temperature (30 K) in theinitial 2.0 ps and several hundred femtoseconds, respectively.This suggests that the MV-1 and MV-2 possible transform intoMV-3 when there is thermal perturbation and MV-2 is changedmore easily. At the low temperature, it is still possible toobserve the MV-1 and MV-2 defects.In addition, we are interested in the rearrangement and

migration of the defects in the monolayer arsenene. Figure 2a−c shows the energy barriers and structure transformation ofMV-3. It can be seen that TS, TS1, and TS2 denote the saddlepoints and IM respects the metastable hollow site. As shown inFigure 2a, the defect structure rotates by overcoming a ratherlow barrier (0.054 eV), which is lower than the barrier (0.1 eV)of graphene.33 Hence, the rotation of MV-3 is easy to occur bythe thermal perturbation. The second structure transformationof MV-3 is depicted in Figure 2b. The As atom climbs over the0.373 eV barrier and reaches the location of the lost As atom.The two kinds of structure transformations do not involve inthe migration of the MV-3 defect. There is another morecomplicated structure transformation in Figure 2c. It causes thecenter of MV-3 to move toward down-right. The brown atomdiffuses from the initial to final position with a distance of 3.7 Å.The diffusion coefficient D is obtained by the formula of D ≈ga2ν0 exp(−E/kBT),

25 where g is the geometrical factor and isset to 1, a is the distance of 3.7 Å, ν0 is the vibration frequencyof 1012 Hz, E is the energy barrier of 0.744 eV, kB is theBoltzmann constant, and T is set to 300 K. We finally obtainthe diffusion coefficient of 1.33 × 10−11 cm2/s, which is muchlower than that of MV in silicene,25,29 but higher than that ofMV in graphene.34

In Figure 3a, the activation barrier and path for SW defect areshown, and SW defect transforms from the pristine arsenene byrotating the As−As bond. The forward barrier is 1.136 eV,which is lower than those in graphene (10 eV)30 and silicene(2.64 eV).29 Compared to graphene and silicene, arsenenemore easily generates the SW defect. In addition, the reversebarrier is 0.056 eV, which is much smaller than those ingraphene (5.0 eV)30 and silicene (0.5 eV).29 It is inferred thatthe SW defect can be eliminated by rapid annealing and the

Table I. Defect Formation Energies Calculated with andwithout vdW Correctionsa

4 × 4 × 1 5 × 5 × 1 6 × 6 × 1

defecttype GGA

GGA+vdW GGA

GGA+vdW GGA

GGA+vdW

MV-l 2.058 2.220 2.168 2.331 2.221 2.384MV-2 2.052 2.220 2.104 2.298 2.123 2.321MV-3 2.029 2.211 2.072 2.260 2.088 2.277DV-1 1.943 2.304 1.994 2.363 2.030 2.406DV-2 1.824 2.267 1.998 2.443 2.094 2.518SW 1.068 1.264 1.079 1.269 1.093 1.285

aThe defect formation energy unit is eV.

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material transforms into the pristine arsenene. As shown inFigure 3b, the DV-1 (5−8−5) defect can also transform intothe DV-2 (555−777) defect by rotating the As−As bond. Theenergy of DV-1 is 0.061 eV lower than that of DV-2, which isopposite to the case in graphene30 and silicence.29 Though the

structure transformations in Figure 3a,b both involve in theAs−As bond rotations, the difference of the curves is obvious,which indicates that the shapes of the potential energy surfacesin these two cases are different. Because the shape of the curvein Figure 3b is almost symmetrical and both forward and

Figure 2. Energy barrier and structure transformation of MV-3. (a,b) The defect with no migration and (c) the defect with migration.

Figure 3. Energy barrier and transformation path from pristine to SW configuration (a) and from DV-1 (5−8−5) to DV-2 (555−777) (b).

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reverse energy barriers are approximately equal to 1.4 eV, theprobability of mutual transformation between DV-1 and DV-2is almost the same.To find an effective method to examine these defects, we

calculate the optical properties of the pristine and defectivearsenene described in the independent-particle picture. Theimaginary part ε2(ω) of the dielectric function ε(ω) can bedetermined by the following equation:35

∑ε ω πε

δ ω=Ω

|⟨Ψ | · |Ψ ⟩| − − ℏ

e

u r E E( )2

( )k c v

kc

kv

kc

kv

2

2

0 , ,

2

(1)

where the real part ε1(ω) is obtained by the Kramer−Kronigrelationship. The absorption coefficient α(ω) can be derivedf rom the d i e l e c t r i c func t i on by the equa t ion

α ω ω ε ω ε ω ε ω= + −( ) 2 [ ( ) ( ) ( )]12

22

11/2. To obtain

accurate optical spectra, the HSE06 hybrid functional isadopted. Figure 4a−g plots the imaginary parts ε2(ω) of thedielectric functions of the pristine and defective structures usingthe 4 × 4 × 1 supercells. The black and red curves correspondto the two polarization directions of the electric field of theincident light along the x and y axes of the supercells,respectively, and the incident light is perpendicular to thearsenene plane. As shown in Figure 4a, the two curves of ε2(ω)

coincide completely because of the geometric symmetry of thepristine arsenene. Despite the absence of an As atom in theMV-1 structure, the reconstructed supercell retains the highestsymmetry among the three MV defect structures. Therefore,the two curves in Figure 4b also coincide completely. As shownin Figure 4b−d, there are two main peaks induced by MV ineach curve. In Figure 4b, the top left and lower right peaks areat 0.40 and 1.54 eV, respectively, and the height ratio is about3.0. With regard to the MV-2 configuration in Figure 4c, thereis clear separation between the two lines because of thegeometric asymmetry along the x and y directions. The heightratio of the two main peaks on the x curve is larger (2.31) thanthat (1.39) in the y curve. Each main peak in the curves of MV-2 is smaller than that in the curves of MV-1. In the MV-3structure in Figure 4d, the height ratio of the two main peaks inthe x curve is less than 1.0, whereas the height ratio of the twomain peaks in the y curve is greater than 1.0. As shown inFigure 4e−g, there is only one main peak in each curve whenthe energy of incident photon is less than 3.0 eV. Figure S2a(Supporting Information) presents the curves of the pristineand SW configurations and the main peaks at different locationsare denoted by arrows E1 and E2. The shapes of the curves inthe pristine and SW configuration are different from each otherand the difference can be used to identify the existence of the

Figure 4. Imaginary part of the dielectric function of the pristine and defect 4 × 4 × 1 supercells: (a) Pristine, (b) MV-1, (c) MV-2, (d) MV-3, (e)SW, (f) DV-1, and (g) DV-2..

Figure 5. Absorption coefficients of the pristine and defect structures. The polarization direction of the electric field of the incident light is along thex axis (a) and y axis (b) of the 4 × 4 × 1 supercell, respectively.

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SW defects. Figure S2b (Supporting Information) shows thecurves of the pristine and DV-2 configurations and the mainpeaks of DV-2 is indicated by arrow E3. The difference of theshapes of these curves can also be utilized to identify the DV-2defect. In order to determine the reliability of the results fromthe independent-particle approximation, we adopt 3 × 3 × 1supercells to calculate the optical properties of the MV-1, SW,and DV configurations with and without local field effects. It isfound that the local field corrections reduce the intensities ofthe main peaks in the curves of the imaginary part of thedielectric function from the pristine arsenene, while theintensities of the peaks associated with the defects decreaseslightly. The most important is that all the peak positions donot change when the local field effects are included, and no newpeak is induced by the local field corrections. This means thatthe conclusions are reliable if the local field corrections are notincluded in the calculations. Because the calculations becomevery time-consuming, we no longer calculate all the largersupercells when the local field corrections are included. All theanalyses of the optical properties are based on the calculationresults in the independent-particle picture.The absorption coefficients of the various configurations

using 4 × 4 × 1 supercells are calculated and shown in Figure5a,b. For the polarization direction of the electric field of theincident light along the x axis, the corresponding curves areplotted in Figure 5a. Arrows 1 and 2 represent the two mainpeaks of the curve of the MV-1 structure, and the curve of theother MV structure also has two peaks in Figure 5a. The shapesof the curves of the SW and DV structures differ from that ofthe curve of the pristine structure. When the polarizationdirection of the electric field of the incident light is along the yaxis, a similar feature occurs as shown in Figure 5b. In general,we can also use the absorption spectra to determine the typesof the defects in arsenene and it is a better strategy if both ofthese two spectra are employed to identify the defects.Considering that the optical properties may change with defectconcentrations, the 5 × 5 × 1 supercells are constructed toderive the dielectric and absorption spectra. The results areshown in Figures S3 and S4 (Supporting Information). Thereare still two main peaks in each curve of the MV structure butthe intensity and position of each peak change slightly withdecreasing defect concentration. When the concentrations ofthe MV-2 and MV-3 defects decrease, the change of theimaginary part of the dielectric function is more obvious, and soinformation about the defect concentrations can be obtainedfrom the optical spectra. In general, the dielectric andabsorption spectral characteristics impart information aboutthe types of topological defects.Since the optical properties are dominated by the band

structure, the energy bands are derived to determine the originof the spectral changes. We calculate the band structure ofprimitive cell of monolayer arsenene and obtain the bandgap(2.22 eV) to compare with the previous research results.9,22 It isfound that they are consistent. The band structures of thepristine and MV-1 4 × 4 × 1 supercells are shown in Figure6a,b, which are plotted along the high symmetrical path Γ − M− K − Γ. The horizontal blue dash line represents the Fermilevel of which the energy is set to zero. The MV defectintroduces two defect bands (red lines) in the forbidden energyrange of the pristine structure. With regard to the pristinearsenene, the conduction band minimum (CBM) is located at apoint on the ΓM line and the valence band maximum (VBM)corresponds to the Γ point. When MV is introduced, the

valence band edge around the K point moves up and the VBMat Γ moves down slightly. Finally, the VBM of the MV-1structure corresponds to the Γ and K points. In contrast, theconduction band edge changes little. The Fermi level passesthrough the defect band below. Because the optical transitionbetween the parallel conduction and valence bands is high, thetransition denoted by the arrow in Figure 6b between the twored bands around K point is responsible for the left peak at 0.40eV in Figure 4b. The other two arrows around M and Γrepresent the transitions which induce the peak at 1.54 eV inFigure 4b. The band structures of the other defect structuresare shown in Figure S5 (Supporting Information,). There aretwo defect bands in the MV-2 and MV-3 structures, and thelower bands are intersected by the Fermi levels. However, thetwo defect states at Γ are no longer degenerate because of thelower symmetry than the MV-1 configuration. In the SW andDV structures, the Fermi levels do not pass through the defectbands, which are close to the conduction and valence bandedges. These band characteristics are responsible for the singlepeak in Figure 4e−g. In general, the topological defects inarsenene induce the defect states and significantly alter theoptical spectra. The charge distribution in the defect states isalso studied. The charge density isosurface belonging to the twodefective bands of MV-1 is depicted in Figure 6c by integratingthe whole path Γ − M − K − Γ in the Brillouin zone. Thecharge is mainly around the vacancy and therefore theseelectronic states are quite localized. The shape of the isosurfaceis symmetrical due to the geometrical symmetry of the MV-1structure. For the MV-2 and MV-3 structures, the shape of thecharge density isosurfaces (Supporting Information, Figure S6)is similar to that of the MV-1 structure. The local differences inthese isosurfaces originate from structural changes in MVs.

■ CONCLUSIONIn the buckled monolayer arsenene, the MV-3 configurationwith the minimal defect formation energy is the most stable andthe DV and SW defects show the reconstructed structures.First-principles MD simulations show that MV-1 and MV-2

Figure 6. Band structures of (a) pristine and (b) MV-1 4 × 4 × 1supercells. The arrows represent the optical transitions. (c) Chargedensity isosurfaces of the two red defect bands of the MV-1configuration..

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easily convert to MV-3 at low temperature, and MV-3, DV, andSW configurations are thermally stable at room temperature.Several energy barriers and paths are found by the transitionstate searches when the structure transformations take place.The diffusion coefficient of MV-3 is 1.33 × 10−11 cm2/s, whichis much lower than that of MV in silicene, but higher than thatof MV in graphene. Producing a SW defect requiresovercoming a barrier of 1.136 eV while eliminating a SWdefect is much easier. The probability of mutual transformationbetween DV-1 and DV-2 is almost the same. Calculations of theimaginary part of the dielectric function and absorptioncoefficient show that MV can enhance optical transitions inthe forbidden bands of pristine arsenene and two characteristicpeaks emerge from the spectrum of the MV structures but theDV and SW defects produce rather different features in theoptical spectra. These spectroscopic properties provideinformation about the topological defects in arsenene.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcc.6b10303.

Temperature fluctuation, imaginary part of the dielectricfunction, absorption coefficient, band structure, chargedensity isosurface (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: hkxlwu@nju.edu.cn. Fax: 86-25-83595535. Tel: 86-83686303.Author ContributionsThe manuscript was written through contributions of allauthors. All authors have given approval to the final version ofthe manuscript.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was jointly supported by National Basic ResearchPrograms of China under Grant Nos. 2014CB339800 and2013CB932901 and National Natural Science Foundation ofChina (Nos. 11374141 and 11404162). Partial support wasfrom City University of Hong Kong Applied Research Grants(ARG) No. 9667122. We also acknowledge the computationalresources provided by High Performance Computing Center ofNanjing University.

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Supporting Information

Optical Identification of Topological Defect Types in Monolayer

Arsenene by First-Principles Calculation

Xiaoxu Liu,† Lizhe Liu,

† Lun Yang,

† Xinglong Wu*

,† and Paul K. Chu

‖

† Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics and

Collaborative Innovation Center of Advanced Microstructures, National Laboratory

of Solid State Microstructures, Nanjing University, Nanjing 210093, China

‖Department of Physics and Materials Science, City University of Hong Kong, Tat

Chee Avenue, Kowloon, Hong Kong, China

s2

Figure S1. Temperature fluctuation of (a) MV-3, (b) SW, (c) DV-1 and (d) DV-2 in

the first-principles MD simulations at 300 K.

s3

Figure S2. (a) Imaginary parts of the dielectric functions of the pristine and SW

4×4×1 supercells. (b) Imaginary parts of the dielectric functions of the pristine and

DV-2 4×4×1 supercells.

s4

Figure S3. Imaginary parts of the dielectric functions of the defective 5×5×1

supercells with (a) MV-1, (b) MV-2, (c) MV-3, (d) SW, (e) DV-1, and (f) DV-2. (g)

Imaginary parts of the dielectric functions of the pristine and SW 5×5×1 supercells. (h)

Imaginary parts of the dielectric functions of the pristine and DV-2 5×5×1 supercells.

s5

Figure S4. Absorption coefficients of the pristine and defective 5×5×1 supercells. (a)

Polarization direction of the electric field of the incident light along the x axis of the

5×5×1 supercell and (b) polarization direction of the electric field of the incident light

along the y axis of the 5×5×1 supercell.

s6

Figure S5. Band structures of the 4×4×1 supercells with (a) MV-2, (b) MV-3, (c) SW,

(d) DV-1 and (e) DV-2 defects. The path is KΓ − Μ − − Γ in the Brillouin zone.

s7

Figure S6. Charge density isosurfaces of the two defect bands of (a) MV-2 and (b)

MV-3.