Two-Dimensional AuMX2 (M = Al, Ga, In; X = S, Se) Monolayers

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Functional Nanostructured Materials (including low-D carbon)

Two-Dimensional AuMX2 (M=Al, Ga, In; X=S, Se) Monolayers Featuring Intracrystalline Aurophilic Interactions with Novel Electronic and Optical Properties Qisheng Wu, Wen Wu Xu, Liang Ma, Jinlan Wang, and Xiao Cheng Zeng ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b02820 • Publication Date (Web): 24 Apr 2018 Downloaded from http://pubs.acs.org on April 24, 2018

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ACS Applied Materials & Interfaces

Two-Dimensional AuMX2 (M=Al, Ga, In; X=S, Se) Monolayers Featuring Intracrystalline Aurophilic Interactions with Novel Electronic and Optical Properties

Qisheng Wu,†, ,Δ Wen Wu Xu, ‡

‡,§,Δ

Liang Ma,‡ Jinlan Wang,†,□,* and Xiao Cheng Zeng‡,‖*

†

School of Physics, Southeast University, Nanjing 211189, P. R. China

‡

Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United

States §

Division of Interfacial Water and Key Laboratory of Interfacial Physics and Technology,

Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, P. R. China □

Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal

University Changsha, Hunan 410081, P. R. China ‖

Department of Chemical & Biomolecular Engineering and Department of Mechanical & Materials

Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States

Keywords: two-dimensional materials, aurophilicity, gold chemistry, first-principles calculations, global structure search

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ABSTRACT

Aurophilicity, known as aurophilic interaction, is a strong attractive van der Waals interaction between cationic gold(I) centers, whose strength is comparable to the hydrogen bond. Here, we show that aurophilicity can serve as an engineering approach to expand structural dimensionality for nanomaterials design. Specifically, based on a global-structure search method and density functional theory calculations, we predict a series of stable two-dimensional (2D) AuMX2 (M=Al, Ga, In; X=S, Se) structures featuring intracrystalline aurophilic interactions. All AuMX 2 monolayers designed are semiconductors with moderate bandgaps, excellent carrier mobilities, and good optical properties. The intriguing chemistry of aurophilicity coupled with novel electronic properties render AuMX2 monolayers a potentially new series of 2D materials that are of fundamental importance in gold chemistry and technology importance for nanoelectronics.


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INTRODUCTION Gold (Au), as the noblest of all the metal elements, can form a variety of compounds for broad applications in catalysis,1 electronics,2 luminescence,3 and medicine owing to its unique chemistry.4,5 The chemical properties of Au are quite different from other metals, stemming from its strong relativistic effects.6,7 In general, the outer 6s electrons of Au tend to be transferred to other nonmetal elements, e.g., sulfur (S) or selenium (Se), in many molecular gold compounds, making the Au(I) center positively charged.8 However, contrary to the expected repulsion between the remaining cationic Au(I) centers with closed d10 shells,9 strong attraction is commonly observed between Au(I) centers, termed aurophilicity or aurophilic interaction.10 Previous studies suggested that the aurophilicity arises from the relativistic and correlation effects of Au.11,12 The aurophilic Au-Au distance is around 3.0 Å,13 shorter than twice of the van der Waals radii of Au (1.66 Å).14 Thus, aurophilic bond can be treated as a kind of exceptionally strong van der Waals attraction with same directional character15 and comparable strength (5~15 kcal/mol)10,16 as hydrogen bond.17 On account of the bond strength and directionality, the aurophilic interaction has the potential to enrich the structures and dimensionality, as well as to promote the properties of the gold compound based materials.18 Plenty of experiments have been conducted to prepare polymers and three-dimensional (3D) structures by making use of aurophilic interactions,19-23 which demonstrate that the aurophilic bond does play an important role in the structure diversity of Au compound. Furthermore, previous studies revealed that the aurophilic interactions show significant impact on their properties and functionalities.24 In many molecular Au(I) complexes, photoluminescence was observed, which was believed to be highly correlated to the aurophilic interactions. 13,25-29


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In view of the marked effect of the aurophilic interactions on Au-based clusters, polymers and 3D molecular crystals, one would be curious if 2D atomic layers of Au compounds with featuring aurophilicity could be synthesized in laboratory. If so, what role the aurophilic interaction would play in the 2D structures? To address these questions, herein, we present ab initio computation based design of 2D aurophilic systems. Our recent work30 has predicted two free-standing Au6S2 monolayers, both showing novel gold chemistry and properties for desired application. The GAu6S2 monolayer can be viewed as a series of [-S-Au-]n and [-Au4(2e)-]n chains packed together in parallel, while the T-Au6S2 monolayer can be viewed as replacing each Mo atom in the T-MoS2 monolayer by an octahedral Au6 cluster. In both of the systems, the neighboring Au atoms have the distances of ~2.80 Å, indicating chemical bonding. The aurophilic Au-Au distance is usually 3.0 Å13. Thus the aurophilic interactions are not observed in both G-Au6S2 and T-Au6S2 monolayers.

Compared to binary compounds, ternary compounds can offer additional

composition degree of freedom, thereby offering much more structure variability31, intriguing properties, and flexible functionality.32 First, we present a search of 2D ternary Au based compounds with aurophilicity feature by using particle swarm optimization scheme. To induce cationic Au(I) centers and aurophilic interactions, we select S as the nonmetal element bonded to Au and set the Au:S ratio to be 1:2, a ratio commonly observed in previous aurophilic systems.10,13,18 The valence states of Au and S are usually +1 and -2, respectively, in the chemical compounds. As a result, valence state of the third element M for the ternary system should be +3 to meet the chemical octet rule.33 Thus, a chemical formula of AuMS2 is resulted accordingly. Gallium (Ga) is firstly considered as the third element, in view of the synthesized 2D gallium sulfide structures.34,35 After conducting the global structural search based on particle swarm optimization (PSO) algorithm, three stable phases of AuGaS2


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monolayers are identified, namely α, β and γ phases. The 2D ternary systems are then extended to AuMX2 (M=Al, Ga, In; X=S, Se) monolayers through element replacement within the same group in the periodic table. The aurophilic interaction widely exists in the α and β phases of AuMX 2 monolayers, which have outstanding stabilities. All of AuMX2 monolayers, especially the α phases, display excellent electronic and optoelectronic properties, entailing them great potential for future electronic and optoelectronic applications. COMPUTATIONAL METHODS The 2D crystal structure search was performed by using the PSO algorithm36 implemented in the CALYPSO code,37, which has been successful in predicting a number of new 2D structures.3842

In our PSO simulations, both the population sizes and the number of generation were set to be

30. Unit cells containing 1-4 times of chemical formula AuMX2 (M=Al, Ga, In; X=S, Se; up to 16 atoms) were considered. All structural relaxations and electronic calculations were carried out within the framework of density functional theory (DFT) as implemented in VASP 5.4.43 Projector-augmented wave (PAW)44 potentials and the exchange-correlation interactions formulated within the PerdewBurke-Ernzerhof generalized gradient approximation (PBE-GGA) were employed.45 The planewave cutoff energy was set to be 500 eV and the product of lattice constants and k points was set to be as close to 40 for sampling the first Brillouin zone. Van der Waals interactions were included by using DFT-D3 method,46 and spin-orbit coupling (SOC) was considered in all calculations (except for phonon dispersion calculations) due to the aforementioned relativistic effects of Au. All systems were completely relaxed until the energy and force were converged to 10-5 eV and 103

eV/Å. Vacuum space of 15 Å was adopted to eliminate possible artificial interactions between


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adjacent layers. Tested spin-polarized calculations prove that all AuMX2 monolayers are nonmagnetic. To examine the dynamic stabilities of the AuMX2 monolayers, we first performed phonon dispersion calculations on the basis of density functional perturbation theory (DFPT) with linear response as implemented in QUANTUM ESPRESSO package.47 Then ab initio molecular dynamics (AIMD) simulations was employed with the canonical (NVT) ensemble and the NoséHoover thermostat48 as implemented in CP2K package.49 We have also computed optical properties of the AuMX2 monolayers based on the dielectric constants, ε(ω)= ε1(ω)+iε2(ω), where ε1(ω) and ε2(ω) are the real and imaginary part, respectively. The same k point samplings, as used in the electronic structure calculations, and 216 empty bands were adopted. The absorption coefficient is given by50

 ( ) 

2E ( 12 ( )   22 ( )  1 ( ))1/2 h

in which E represent phonon energy and ħ is reduced Planck constant. RESULTS AND DISCUSSION Three ground-state structures, named as α, β and γ phases (Figure 1a-c), in the order of ascending total energy (Table 1) of the AuGaS2 monolayers are obtained via the comprehensive structural search and DFT relaxations. Table 1. Lattice parameters, bond lengths and angles, and band gaps for AuGaS2 monolayers. “D” indicates direct band gap, whereas “I” means indirect band gap. phase s

relative energy (eV/Au2Ga2S4)

α

0.00

a (Å) 6.13

b (Å) 6.43

θ (°)

dAu-Au (Å)

Au-S (Å)

Ga-S (Å)

S-Au-S (°)

band gaps (eV)

90.0

3.06

2.34

2.34

180

2.20 (D)


6

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β

0.44

6.15

7.43

65.6

3.66

2.30

2.33

162

γ

0.65

5.38

5.38

90.0

5.29

2.29

2.40

159

3.62 (I) 3.60

D)

Primitive cell of the α-AuGaS2 monolayer is orthogonal and its in-plane lattice constants are 6.13 Å and 6.43 Å (Figure 1a), respectively. Each unit cell contains two Au, two Ga, and four S atoms. Ga atoms are tetra-coordinated with four S atoms, as in bulk Ga2S3 crystal.51 Nanochains formed by Ga@S4 units are parallel to those by Au atoms, each of which is bonded with two S atoms in a tight linear bicoordination. The adjacent S-Au-S units are crossed to each other, which can be seen in the side view. Whereas in the β-AuGaS2, the adjacent S-Au-S units are parallel to each other. This structural nuance gives rise to a completely different symmetry with an angle of 65.6° between two lattice vectors (Figure 1b). The S-Au-S turns to be nonlinear with a bond angle of 162°, which is probably determined by the bonding character of μ3-tricoordinate sulfur. Due to the rearrangement of Ga@S4 units in the γ-AuGaS2 monolayer, which has tetragonal symmetry with lattice constants of 5.38 Å (Figure 1c), distances between the nearest Au atoms increase sharply.


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Figure 1. Top and side views of atomic structures for α-AuGaS2 (a), β-AuGaS2 (b) and γ-AuGaS2 (c). Solid blue lines indicate primitive cells. Gold, dark brown and red spheres represent Au, Ga and S atoms, respectively. Dashed lines indicate aurophilic interactions in α and β phases.

The dynamic stabilities of AuGaS2 monolayers were confirmed through phonon spectrum computations, on the basis of density functional perturbation theory. As shown in Figure 2a-c, no imaginary frequency is observed in their phonon spectra, indicating the dynamic stabilities of all AuGaS2 phases. The highest vibration frequencies of α-, β- and γ-AuGaS2 reach up to 466 cm-1, 426 cm-1 and 393 cm-1, respectively. These frequencies are comparable to those of single-layer MoS2 (473 cm-1)52 and Cu2Si monolayer (420 cm-1),53 indicating strong interatomic interactions in AuGaS2 monolayers and their synthetic feasibility. AIMD simulations were performed to further assess the thermal stabilities of AuGaS2 monolayers with a large 3×3 supercell (72 atoms). At room temperature (300 K), all structures retain their integrity after 10 ps AIMD simulations with a time step of 1.0 fs. By elevating the temperature to 500 K, AuGaS2 monolayers (Figure 2d-f) are still intact, suggesting their good thermal stability at the elevated temperatures.


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Figure 2. Phonon dispersions (a-c) and snapshots of ab initio molecular dynamics (AIMD) simulations (df) at 500 K for α-AuGaS2, β-AuGaS2 and γ-AuGaS2, respectively.

In order to further investigate the bonding nature in AuGaS2 systems, we calculated the electron localization function (ELF),54-56 which can well describe electron localization in molecules and solids. Generally, large ELF values correspond to covalent bonds and inner shell or lone pair electrons, whereas electron deficiency and ionic or metallic bonds are indicated by smaller values.57,58 Here, ELF maps and ELF line profiles connecting bonding atoms are plotted for AuGaS2 systems to highlight the bonds between Au and S, Ga and S, as well as Au and Au.


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Figure 3. (a, b, c) Electron localization functions (ELF) maps sliced along planes containing specified bonding atoms for α-AuGaS2 (a), β-AuGaS2 (b) and γ-AuGaS2 (c). For examples, [001] represents the plane perpendicular to z axis and neighboring Au atoms, whereas [S-Au-S] denotes the plane that contains one Au and two S atoms which bond with each other. Atoms are marked with corresponding chemical symbols. In the ELF maps, the highest value (red) and the lowest value (blue) indicate accumulation and depletion of electrons, respectively. (d, e, f) ELF line profiles along color lines in panel a-c. The lengths of horizontal axis correspond to those of color lines in panel a-c. Black, green, and magenta lines indicate ELF values in α-AuGaS2, β-AuGaS2, and γ-AuGaS2, respectively. Aurophilic interactions in α-AuGaS2 and β-AuGaS2 are denoted in (f). Since there is no interaction between Au atoms in γ-AuGaS2 any more, ELF line profile connecting them is omitted here.

The ELF values around the Au atoms are 0.0, suggesting electron deficiency of Au atoms in these AuGaS2 systems. Accordingly, electrons are obviously transferred from Au atoms to Ga@S4 units. This has been confirmed by the Bader charge analyses (Table S1), with Bader charge being calculated by partitioning the space into Bader basins around each atom based on stationary points in the charge density.59,60 For all three α-, β-, and γ-AuGaS2 monolayers, the ELF values are high (~0.85) in the intermediate regions between Ga and S atoms, indicative of strong covalent bonding.


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Au and S atoms interact in relatively weak covalent bond,61 as indicated by medium ELF values (~0.47). Interestingly, the plotted ELF line profiles in Figure 3d and 3e demonstrate that the bonding strength for both of Ga-S and Au-S is almost unchanged for different phases. Considering that the geometric structures of α and β phases are highly similar to each other (Figure 1a-b), a question arises: Why the total energy of α-AuGaS2 is notably lower than that of β-AuGaS2? Our analyses attribute the energy order to different aurophilic interactions in the α- and β-AuGaS2 systems. The plotted ELF line profiles between two neighboring Au atoms in Figure 3f show that there are obvious aurophilic interactions which form Au…Au chains with Au-Au distance of 3.06 Å (Table 1) in the α-AuGaS2, as reported in many aurophilic systems.10,13 On the other hand, the aurophilic interaction in β-AuGaS2 is largely reduced owing to the longer Au-Au distance (3.66 Å). Since the Au-Au distance in γ-AuGaS2 is very large (5.29 Å), aurophilicity is no longer present in γ-AuGaS2. Considering high stabilities and the vital aurophilic interactions in AuGaS2 monolayers, it is natural to construct a series of AuMX2 (M=Al, Ga, In; X=S, Se) monolayers by simply taking element substitution within the same group in periodic table. There are α, β, and γ phases for each compound of AuMX2 monolayers. Their atomic structures resemble those of AuGaS2 monolayers. Hence their geometric structures are not displayed here, instead their lattice constants and atomic positions are listed in Table S2. Relative energies for different phases are given in Figure S1. The α phase is the energetically most favorable structure for most AuMX2 monolayers except for γAuInSe2, whose stability could be influenced by other geometric parameters. Moreover, the α phase is always lower than the β phase in energy, which further proves that stronger aurophilic interactions stabilize the α-AuMX2 systems.


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Extensive structural searches on the basis of PSO algorithm verify that the global minimum is either α or γ phase for all AuMX2 monolayers. Other generated low-energy structures are not discussed here because they are either amorphous or featureless in structure. Phonon dispersion calculations and AIMD simulations have been conducted, which demonstrate that all low-lying structures as indicated in Figure S1 have no imaginary frequency in their phonon spectra (Figure S3), and they can keep their structures unbroken at 500 K after being annealed for 10.0 ps (Figure S4).

Figure 4. Band gaps calculated at HSE06 level of theory for all phases of AuMX2 (M=Al, Ga, In; X=S, Se) monolayers. Visible spectrum is marked in the figure.

The electronic properties of AuMX2 monolayers are investigated using the HSE06 functional62 since the PBE functional usually underestimates bandgaps of semiconductors.63 As listed in Figure 4, all AuMX2 monolayers exhibit semiconducting features, while most of them have direct bandgaps, within the range of 2.06 eV to 4.07 eV. The electronic band structures and projected density of states (PDOS) of α-AuMX2 monolayers are plotted in Figure 5, while the band structures for β- and γ-AuMX2 monolayers are given in Figure S5. Bandgaps for all α phases are located within the visible spectral range, making them possible candidates for optical applications (see


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below for more discussion). It can be seen from Figure 5 that, in α-AuMX2 monolayers, the bandgaps for sulfides are very close to corresponding selenides, which are reflected in PDOS as well.

Figure 5. Band structures and projected density of states (PDOS) calculated at the HSE06 level for α phases of AuMX2 (M=Al, Ga, In; X=S, Se) monolayers. Fermi levels are labelled as EF. Band gaps are indicated with gray regions.

Considering that all low-lying α phases exhibit high stabilities and direct bandgaps, we further compute their effective masses and carrier mobilities, which largely govern the electronic properties of the AuMX2 monolayers. As shown in Table 2, both small effective electron and hole masses (less than 1.0 m0, where m0 is the electron mass) along x and y directions remain in most α-AuMX2 monolayers. Some are even as low as ~0.1 m0. According to the deformation potential theory,64 the mobiliity is given by65,66

2D 

eh3C2 D k BTme*md ( E1 ) 2

where e is the electron charge, ħ is the reduced Planck constant, m*e is the effective mass in the transport direction, md is the average effective mass and kB is the Boltzmann constant. The 2D


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elastic modulus C2D and the deformation potentials E1 are the most relevant factors to the mobility64,67, and their values are given in Table S4. The temperature T is chosen to be 300K. Our predicted mobilities vary significantly, depending on the system. Most of them are around 1000 cm2V-1S-1, comparable to that of monolayer black phosphorus.68,69 Since the deformation potential E1 takes quadratic term, it has stronger effect than other terms on the mobility. Most systems have an order of 1.0 eV for deformation potentials. However, the α-AuAlSe2 monolayer has a small deformation potential (0.10 eV) for the hole along the b (x) direction, which leads to an extremely high carrier mobility up to tens or hundreds of thousands cm2V-1S-1, a novel feature highly desirable for applications in electronic devices. Table 2. Effective electron and hole masses and mobilities along both x and y directions for α phases of AuMX2 (M=Al, Ga, In; X=S, Se) monolayers. electron System

hole

m*e,x

μ*e,x

m*e,y

μ*e,y

m*h,x

μ*h,x

m*h,y

μ*h,y

(me)

(103 cm2V-1S-1)

(me)

(103 cm2V-1S-1)

(me)

(103 cm2V-1S-1)

(me)

(103 cm2V-1S-1)

α-AuAlS2

0.23

9.30

0.30

0.29

0.13

0.25

0.71

2.91

α-AuGaS2

0.20

13.55

0.30

0.31

0.13

0.20

0.87

28.79

α-AuInS2

0.27

0.29

1.30

0.09

0.49

0.62

0.44

0.09

α-AuAlSe2

0.29

3.26

0.40

0.14

0.14

0.14

0.73

111.35

α-AuGaSe2

0.22

1.80

0.29

0.37

0.13

0.12

0.92

1.46

α-AuInSe2

0.54

3.47

0.43

0.09

0.31

0.05

1.31

0.28

The computed band structures and moderate bandgaps of the AuMX2 monolayers suggest their potential applications in optoelectronics. The optical absorption properties of the AuMX2 monolayers are explored by computing the complex dielectric constants at a specified frequency based on the HSE06 functional. The absorption spectra for light linearly polarized along the x, y and z directions for the α-AuMX2 monolayers are displayed in Figure 6, while the optical


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absorption properties of β and γ phases are given in Figures S6 and S7, respectively. The calculated optical absorption coefficients are consistent with our calculated band gaps. Since all AuMX2 monolayers have band gaps larger than 2.0 eV, they usually have obvious absorption in the range (2.5-3.5 eV). Hence the AuMX2 monolayers may be practically utilized in optoelectronic devices.

Figure 6. Calculated optical absorption coefficients that are polarized in the x direction (a), y direction (b) and z direction (c) based on the HSE06 functional for the α phases of AuMX2 (M=Al, Ga, In; X=S, Se) monolayers.

CONCLUSION In summary, we predict several highly stable 2D AuMX2 (M=Al, Ga, In; X=S, Se) monolayers via combining advanced global structure search scheme and DFT calculations. All AuMX2 monolayers are shown to be dynamically and thermally stable. Three phases, i.e., α, β and γ, are identified for each AuMX2 monolayer compound. Importantly, the aurophilic interaction is found to exist in all AuMX2 monolayers, and it plays an important role in the structure and property diversity of the 2D AuMX2. All AuMX2 monolayers are semiconductors with moderate bandgaps, high carrier mobilities, and good optical properties. These novel properties are not only fundamentally intriguing, but also point to new directions in 2D material research for advanced electronic and optoelectronic applications.


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ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. Relative energies of different phases (α, β, γ) for AuMX2 (M=Al, Ga, In; X=S, Se) monolayers; ELF line profiles connecting bonding atoms in AuMX2 systems; Phonon dispersion for some lowlying AuMX2 monolayers; AIMD snapshots for some low-lying AuMX2 monolayers; Band structures for β and γ phases of AuMX2 monolayers; Calculated optical absorption coefficients for β and γ phases of AuMX2 monolayers; Bader charges in AuMX2 systems; Lattice parameters and fractional coordinates for AuMX2 monolayers; Bond lengths and angles in AuMX2 systems. (PDF) AUTHOR INFORMATION Corresponding Author *E-mail (J. Wang): [email protected] *E-mail (X. C. Zeng): [email protected] Author Contributions Δ

These authors contributed equally to this work.

ORCID Qisheng Wu: 0000-0001-9123-1864 Wen Wu Xu: 0000-0002-0651-9562 Liang Ma: 0000-0003-4747-613X Jinlan Wang: 0000-0002-4529-874X Xiao Cheng Zeng: 0000-0003-4672-8585 Notes


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Δ

The authors declare no competing financial interest.

ACKNOWLEDGMENT This work is supported by the National Key Research and Development Program of China (No. 2017YFA0204800), Natural Science Funds of China (21525311, 21373045, 21773027), Jiangsu 333 project (BRA2016353) and the Fundamental Research Funds for the Central Universities of China. Q.W. is supported by China Scholarship Council (CSC, 201606090079) and the Scientific Research Foundation of Graduate School of Southeast University (YBJJ1720). W.W.X. is supported by CSC (201604910285) and NSFC (11504396). X.C.Z. is supported by a grant from Nebraska Center for Energy Sciences Research and a fund from Beijing Advanced Innovation Center for Soft Matter Science & Engineering for summer visiting scholar. The computational resources utilized in this research were provided by Shanghai Supercomputer Center, National Supercomputing Center in Tianjin and Shenzhen, NC3 computer facility and Holland Supercomputing Center in University of Nebraska-Lincoln.

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Two-Dimensional AuMX2 (M = Al, Ga, In; X = S, Se) Monolayers

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