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Cite this: J.Mater. Chem. C, 2019,

7, 2589

Prediction of phonon-mediated superconductivityin two-dimensional Mo2B2

Luo Yan,†abcd Tao Bo,†ab Peng-Fei Liu, ab Bao-Tian Wang, *abef

Yong-Guang Xiao*cd and Ming-Hua Tang cd

Superconductivity has attracted much interest in two-dimensional (2D) compounds because of their

application in constructing nano-superconducting devices. Based on the crystal structure prediction

method and first-principles calculations, we obtain two new 2D molybdenum boride structures of tetr- and

tri-Mo2B2. Then, we calculate their electronic structures, phonon spectra, electron–phonon coupling (EPC),

and superconducting properties. The results show that both tetr- and tri-Mo2B2 are intrinsic phonon-

mediated superconductors with superconducting transition temperatures (Tc) of 3.9 and 0.2 K, respectively.

We demonstrate that the EPC is mainly from the low-frequency phonon vibrations of Mo atoms. Our

findings will enrich 2D superconducting materials and stimulate more efforts in this field.

I. Introduction

Rapid advancements in nanotechnology have allowed varioustypes of two-dimensional (2D) materials to be fabricated withatomic-scale precision and to be characterized in unprecedenteddetail, including molecular beam epitaxy,1 atomic layer deposition,2

pulsed laser deposition,3 magnetron sputtering4 etc. The greatsuccess of graphene,5 monolayer hexagonal boron nitride,6 2Dtransition-metal dichalcogenides7 and many others has expandedour knowledge of their morphology and properties. However,although many bulk transition metal borides (TMBs) are widelyapplied in various fields based on their unique combination ofhigh melting points, hardness, good electrical and thermalconductivities, chemical inertness and superconductivity,8 asfar as we know, few 2D forms of the TMBs have been reportedexperimentally and theoretically to date.8–10 Nanomaterialschemists dealing with boron must always struggle with the B sourceand harsh synthesis conditions,8 which has greatly limited thelandscape of the 2D TMBs. However, the 2D TMBs may, like theirbulk counterparts, exhibit properties of hardness, mechanicalstability, chemical inertness, and even superconductivity.

Since 2D TMBs have potential advanced applications, continuingattention is being paid to them. For example, LaB6 nanowires wereinvestigated as field emitter materials because of their low workfunction, low volatility at high temperature, high conductivity,high chemical inertness, and high mechanical strength.11 HfB2

films, deposited by single source chemical vapor deposition,were demonstrated to possess high hardness, elastic modulus,and wear resistance on the macroscale as well as on thenanoscale.12 Three graphene-like FeB6 monolayers, namely a-,b- and g-FeB6, were predicted by density functional theory (DFT)computations, which have sound thermodynamic, kinetic andthermal stabilities.13 Shortly afterwards, 2D tri-FeB6 as a globalminimum ground state structure with sandwich structure wasexplored and found to have remarkable mechanical properties.14

Most recently, Shao et al. reported the 2D pentagonal TMBs (TaB,WB) with sandwich structure and showed that they exhibitmetallic nonmagnetic ground states.15

Superconductivity in 2D or low-dimensional systems hasattracted much attention in recent years. The possibility of asuperconducting state in metal-coated graphene was discussed in2007,16 and then the superconducting transition temperature (Tc)of Li-decorated monolayer graphene was reported to be 5.9 K.17,18

MoS2, an archetypal band insulator, was reported to possesselectric-field-induced superconductivity.19 Subsequently, the Tc

of Ca-intercalated bilayer MoS2 was calculated to be 13.3 K.20 Inaddition, Saito et al. reported an ion-gated ZrNCl surface, exhibitinga dome-shaped phase diagram with a maximum Tc of 14.8 K.21 Theinterface-induced superconductivity of FeSe films, grown on SrTiO3,was also explored.22,23 By means of magnetotransport measure-ments, Xi et al. reported the observation of superconductingmonolayer NbSe2 with an in-plane upper critical field.24 Then,the Tc of 2H-NbSe2 was reported to be 7.8 K at 16 GPa,25 in

a Institute of High Energy Physics, Chinese Academy of Sciences (CAS),

Beijing 100049, China. E-mail: wangbt@ihep.ac.cnb Dongguan Institute of Neutron Science (DINS), Dongguan 523808, Chinac Key Laboratory of Key Film Materials & Application for Equipments (Hunan

Province), School of Material Sciences and Engineering, Xiangtan University,

Xiangtan, Hunan, 411105, China. E-mail: ygxiao@xtu.edu.cnd Hunan Provincial Key Laboratory of Thin Film Materials and Devices,

School of Material Sciences and Engineering, Xiangtan University, Chinae Institute of Applied Physics and Computational Mathematics, Beijing 100088, Chinaf Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan,

Shanxi 030006, China

† The first two authors contributed equally to this work.

Received 5th December 2018,Accepted 24th January 2019

DOI: 10.1039/c8tc06123h

rsc.li/materials-c

Journal ofMaterials Chemistry C

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accordance with previous experimental studies.26 Most recently,the zero-resistance state was found in Ca-intercalated bilayergraphene C6CaC6 with the onset temperature of 4 K,27 inaccordance with subsequent theoretical studies.28 These meaningfuldiscoveries prompt us to explore the superconductivity of novel2D TMBs, which are rarely reported.

In the present work, we predict two new 2D structures ofMo2B2 [labeled as tetr-Mo2B2 and tri-Mo2B2 and presented inFig. 1(a), (b) and (d), (e), respectively] and present a detailedstudy by accurate first-principles calculations. These 2D phasesof Mo2B2 exhibit a metallic electronic state inherently andhence inspire us to explore their superconductivity. The Tc oftetr-Mo2B2 is calculated to be 3.9 K and tri-Mo2B2 has an extremelylow Tc of 0.2 K. In the main text, we will discuss to some extent thereason for the difference in superconductivity between these twostructures. Our work provides an important clue to explore novelsuperconductive materials.

II. Theoretical methods

We searched the crystals of Mo2B2 using the swarm-intelligence-based CALYPSO structure prediction method,29,30 which hasbeen certified in predicting stable or metastable crystal structuressuccessfully.31,32 Structural optimizations are performed in theframework of DFT as implemented in the VASP.33 The Perdew–Burke–Ernzerhof form of the generalized gradient approximationis chosen for the exchange–correlation potentials.34 The electron–ion interaction is described by projector-augmented-wave potentialswith the 4d55s1 and 2s22p1 configurations treated as valenceelectrons for Mo and B, respectively. A kinetic cutoff energy of550 eV and a 10 � 10 � 1 Monkhorst–Pack (MP) k-point meshare adopted. All the geometries are optimized until the forceson all the atoms are smaller than 0.01 eV Å�1.

The calculations of the electronic structures, latticedynamics, and electron–phonon coupling (EPC) are performedat the DFT level, employing the local density approximation(LDA) and norm-serving pseudopotentials35,36 as implementedin the QUANTUM-ESPRESSO (QE) package.37 We adopt avacuum layer with 15 Å between the periodically repeated slabs,which is enough to avoid the nonphysical coupling. The plane-waves kinetic-energy cutoff and the charge-density cutoff arechosen as 80 and 320 Ry, respectively. The self-consistentelectron densities are evaluated on a 32 � 32 � 1 k-point grid.We adopt the Hermitian-Gaussian smearing method and thevalue of degauss is set as 0.02 Ry. The phonon modes arecomputed within the density-functional perturbation theory38

(DFPT) on 8 � 8 � 1 and 4 � 4 � 1 q meshes for tetr- and tri-Mo2B2, respectively. The Tc is evaluated by using the Allen–Dynes modified McMillan formula39 with a typical Coulombpseudopotential of m* = 0.1.

III. Results and discussion

Our optimized global minimum structure of the Mo2B2 mono-layer crystallizes in a tetragonal phase with a space group of

P4/nmm (no. 129). For simplicity, we label it as tetr-Mo2B2. Thisstructure can be viewed as a distortion NaCl-type structure. Wepresent its structure and 2D Brillouin-zone (BZ) in Fig. 1(a)–(c).In this work, we also want to present the results of another2D Mo2B2 monolayer: the trigonal Mo2B2 with a space groupof P%3m1 (no. 164). The formation energy of this metastablestructure is higher by 41.2 meV per atom than that of the globalminimum one. We label it as tri-Mo2B2 and present its structureas well as 2D BZ in Fig. 1(d)–(f). One can see that there are threesublayers stacked in order of Mo–B–Mo within its unit cell. Thetwo Mo sublayers are located at the valley sites of the puckered Bplane. The high-symmetry paths of the tetr- and tri-Mo2B2 mono-layers are along G–X–M–G and G–M–K–G, respectively.

In order to explore the bonding properties of the tetr- andtri-Mo2B2, we calculate the charge density and difference chargedensity and plot them in Fig. 2. Here, the difference chargedensity is calculated by subtracting the density of noninteractingcomponent systems, r(Mo) + r(B), from the density of Mo2B2. Wealso calculate the line charge density distribution along thenearest B–B, Mo–Mo, and Mo–B bonds and perform the Baderanalysis.40 The results of the Bader charges (QB), bond lengths,and line charge density at the corresponding bond point (CDb)are listed in Table 1.

From Fig. 2 and Table 1, we can deduce the followingcharacters for tetr-Mo2B2: (i) the two typical Mo–B bond lengthsof about 2.2 Å are greatly shorter than that of the Mo–Mo andB–B bonds, indicating that the stability and the mechanicalproperties of this structure are mainly governed by the Mo–Bbonds; (ii) the Mo–B bonds show mixed features of ionic andcovalent characters. The CDb value for the Mo–B bond of0.038 e au�3 is prominently higher than 0.007 e au�3 foundfor the Na–Cl bond in the typical ionic crystal NaCl, but smallerthan 0.104 e au�3 found for the Si covalent bond. As for tri-Mo2B2, we find that the puckered B layer is strongly bonded by

Fig. 1 (a) Top and (b) side views of the 2D tetr-Mo2B2. (d) Top and (e) sideviews of the 2D tri-Mo2B2. 2D BZs of (c) tetr- and (f) tri-Mo2B2, respectively.The square in (a) and rhombus in (d) enclosed by solid black lines denotethe unit cell for tetr- and tri-Mo2B2, respectively.

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very short bonds of B–B covalent bonds with a large CDb valueof 0.116 e au�3. At both sides of the puckered B layer, Mo atomsbond to each other with relatively weak metal bonds. Theadjacent Mo and B layers are bonded by Mo–B bonds withmixed features of ionic and covalent. Here, one may wonderwhy tri-Mo2B2 with strong B–B bonding is not that energeticallystable. After reviewing the structures of these two systems, wefind that there are ten Mo–B bonds in one unit cell of tetr-Mo2B2

while there are only three B–B bonds and two Mo–B bonds intri-Mo2B2. Thus, the fact that tetr-Mo2B2 is more stable thantri-Mo2B2 is understandable.

The isosurfaces of the difference charge density of 2D Mo2B2

indicate that the electrons are accumulated at each B atomfrom the vertical direction of the Mo atoms. For tetr-Mo2B2, theelectron transfer is along its Mo–B bonds to strengthen theirbonding while for tri-Mo2B2, the electrons are substantially movedfrom Mo to B. By analyzing the ionicity according to the Badercharges, the ionic charges of tetr- and tri-Mo2B2 are also different.In tetr-Mo2B2, each Mo atom transfers 2.82 electrons to the B atomwhile in tri-Mo2B2, it transfers 2.35 electrons. The ionic charge fortetr- and tri-Mo2B2 can be represented as tetr-Mo2

2.82�B22.82+ and

tri-Mo22.35�B2

2.35+, respectively. Based on these analyses, it is easyto conclude that the electron transfer of tetr-Mo2B2 is strongerthan that of tri-Mo2B2.

We calculate the electronic structures of these two 2D Mo2B2

monolayers. The orbital-resolved band structures, the electronicdensity of states (DOSs), and the Fermi surfaces are presented inFig. 3. We find that both tetr- and tri-Mo2B2 monolayers exhibit

intrinsic metallic features with many bands crossing the Fermilevel [see Fig. 3(a) and (c)]. For tetr-Mo2B2, there are threecrossings along the G–X and G–M paths, which is in agreementwith the Fermi surface shown in Fig. 3(e). For tri-Mo2B2, thereare three and two crossings along the G–M and G–K high-symmetry paths, respectively. These crossings clearly indicatethat these 2D systems are good electronic conductors. Besides,for these two monolayers, the 4d orbitals of Mo atoms contributedominantly around the Fermi energy level while the contributionfrom the B-2p orbitals is limited. The results of the Fermi surfacealso support this conclusion. Thus, we can conclude that themetallic nature of these 2D Mo2B2 monolayers is mainly controlledby their Mo-4d orbitals.

Fig. 2 (a and c) Top and (b and d) side views of the charge density (toppanels) and difference charge density (bottom panels) for tetr-Mo2B2.(e and g) Top and (f and h) side views of the charge density (top panels)and difference charge density (bottom panels) for tri-Mo2B2. The yellowand cyan areas represent electron gains and losses, respectively. The Moand B atoms are denoted by blue and red spheres, respectively.

Table 1 The Bader charges (QB), bond lengths, and line charge density at the corresponding bond point (CDb) for tetr- and tri-Mo2B2. In tetr-Mo2B2,there are two typical kinds of Mo–B bonding: one is within the xy plane and another along the c direction. The bonding along the c direction is indicatedby the data within parentheses

Compounds QB (M) (e) QB (B) (e) B–B (Å) Mo–Mo (Å) Mo–B (Å) CDb (B–B) (e au�3) CDb (Mo–Mo) (e au�3) CDb (Mo–B) (e au�3)

tetr-Mo2B2 3.18 5.82 3.07 3.07 2.19(2.27) 0.043 0.038 0.077(0.070)tri-Mo2B2 3.65 5.34 1.74 2.85 2.17 0.116 0.027 0.080

Fig. 3 Orbital-resolved band structures with the contributions of Mo andB atoms for (a) tetr- and (c) tri-Mo2B2, respectively. The total and theorbital-resolved local electron DOSs for (b) tetr- and (d) tri-Mo2B2,respectively. The Fermi surfaces for (e) tetr- and (f) tri-Mo2B2, respectively.The blue color indicates Mo-d orbitals and the red color indicates B-porbitals. The Fermi energy levels are all set to zero.

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We now focus on the vibration properties and electron–phononcoupling (EPC) in tetr- and tri-Mo2B2. Fig. 4a and e show thephonon dispersions. The absence of the imaginary modesindicates that they are dynamically stable.41 From the decom-position of the phonon spectra with respect to the Mo and Batomic vibrations, as indicated in Fig. 4(a), we find that one out-of-plane mode of Moz and two in-plane modes of Moxy constitute thethree acoustic branches for tetr-Mo2B2. The main contributionsbelow 260 cm�1 are from the Mo atomic vibrations. In theintermediate-frequency region from 350 to 460 cm�1, the vibrationsare mainly from the out-of-plane modes of the B atoms. The in-plane modes of the B atoms occupy the high frequencies above580 cm�1. As for tri-Mo2B2 (see Fig. 4(e)), the Mo atomicvibrations (Moz and Moxy modes) dominate the low frequencybelow 280 cm�1. Interactions between out-of-plane and in-planemodes of B atoms contribute to the intermediate-frequency regionfrom 400 to 660 cm�1 as well as the high-frequency regionabove 720 cm�1.

The phonon dispersions weighted by the magnitude of theEPC lqv, the phonon density of states (PhDOSs), the Eliashbergspectral function a2F(o), and the cumulative frequency-dependentof EPC l(o) are exhibited in Fig. 4(b–d) and (f–h) for tetr- andtri-Mo2B2, respectively. We calculate lqv according to the Bardeen–Cooper–Schrieffer (BCS) theory:44

lqv ¼gqv

phN EFð Þoqv2

(1)

where gqv is the phonon linewidth, oqv is the phonon frequency,and N(EF) is the electronic density of states at the Fermi level.

The Eliashberg spectral function a2F(o) is calculated based onthe Eliashberg equation:43

a2FðoÞ ¼ 1

2pNðEFÞXqv

gqvoqv

d o� oqv

� �: (2)

The total EPC constant is calculated by the frequency-spaceintegration:

lðoÞ ¼ 2

ða2FðoÞ

odo; (3)

while the logarithmic average frequency olog is calculated by

olog ¼ exp2

l

ðdooa2FðoÞ logo

� �: (4)

We find that the low-frequency phonons in tetr-Mo2B2 arekey to achieving its EPC. They account for 0.33 (67%) of thetotal EPC (l = 0.49). The phonons in the intermediate-frequencyregion contribute 0.06 (12%) while the high-frequency phononscontribute 0.04 (8%) of the total EPC. In the frequency rangeof 100–260 cm�1, the large values of lqv along the X–M–Gdirections are visible. These lead to the two largest peaks ofthe PhDOS and a2F(o). As a consequence, l(o) increases rapidlyin this frequency range. As for tri-Mo2B2, we find that thelow-frequency phonons contribute 0.25 (83%) of its total EPC(l = 0.3). The phonons in the intermediate-frequency regiononly contribute 0.01 (3%).

Apparently, the most significant contributions to the EPC oftetr- and tri-Mo2B2 come from the low-energy phonon modes,as with bilayer C6CaC6.28 The difference between tetr- and

Fig. 4 The phonon dispersions, PhDOS, Eliashberg spectral function a2F(o), and cumulative frequency-dependent of EPC l(o) of (a)–(d) tetr- and (e) and(f) tri-Mo2B2. The phonon dispersions are weighted by the motion modes of B and Mo atoms as well as the magnitude of the EPC lqv in the first-left andthe second-left panels, respectively. The yellow, blue, green, and red hollow circles in (a) and (e) indicate Mo vertical, Mo horizontal, B vertical and Bhorizontal modes, respectively.

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tri-Mo2B2 may come from the flat acoustic phonon vibrationswith large EPC for tetr-Mo2B2 along the X–M–G directions.Overall, the small EPC constants for tetr- and tri-Mo2B2 indicatethat they are both weak conventional superconductors.

Based upon the above results and according to the BCStheory,44 the Tc of tetr- and tri-Mo2B2 can be calculated by usingthe McMillian-Allen–Dynes formula:39

Tc ¼olog

1:2exp � 1:04 1þ lð Þ

l� m�ð1þ 0:62lÞ

� �(5)

where m* is the effective screened Coulomb repulsion constant.This value can be generally set between 0.1 and 0.15.45,46

We explore the sensitivity of the critical temperature to thechoice of m* by varying it from 0.08 to 0.15 (see Fig. 5). As expected,increasing m* results in a clear decrease of Tc for both our studiedTMB monolayers. With a typical value of m* = 0.1, our calculatedvalues of Tc are 3.9 and 0.2 K for tetr- and tri-Mo2B2, respectively.

In Table 2, we list the superconductive parameters of N(EF),olog, l, and Tc for tetr- and tri-Mo2B2. For comparison, we alsopresent the results of some recent phonon-mediated 2D super-conductors. We can see that the BCS theory is suitable forpredicting the superconducting properties of these phonon-mediated 2D superconductors, as verified by the good agreementsbetween experimental and theoretical investigations of LiC6,17,18

2H-NbSe2,25,26 C6CaC6.27,28 For a more detailed overview,

we redirect the readers to ref. 9, 10 and 42. We can see that the Tc

of tetr-Mo2B2 is larger than that of silicene,47 stanene48 andtri-Mo2B2, while it is smaller than that of LiC6,17,18 2H-NbSe2,25,26

C6CaC6,27,28 B2C,49 B (a sheet),50 B (b12),51 Li2B752 and Mo2C.53

Comparing with the intrinsic B (a sheet and b12), the 2D Mo2B2

systems constrain the vibrations of the B atoms and result in smallvalues of EPC and Tc, especially for tri-Mo2B2.

Experimentally, high-quality graphene54 and MoS255 have

been successfully grown on substrates in their intrinsic strainlimit (B15% for graphene and B11% for MoS2) without sub-stantially damaging their crystal structures. Thus, we expectedthat tetr- and tri-Mo2B2 can also be fabricated or transferred onsome potential substrates. As a guide, we theoretically explorepossible substrates for the epitaxial growth of tetr- and tri-Mo2B2.After extensive searching, we select the widely used semiconductorsof CuI, SiC and InAs as ideal candidate substrates. The detailedstructures of tetr- and tri-Mo2B2 on substrate systems are illustratedin Fig. 6. The adsorption energy is calculated according to thefollowing equation:

Eads ¼Emolþslab � Emol þ Eslabð Þ

n; (6)

where Emol+slab denotes the total ground state energy of theoptimized configuration of 2D Mo2B2 adsorbed on the slab

Fig. 5 Calculated superconducting critical temperature Tc as a functionof Coulomb pseudopotential parameter m*. The red squares and the bluetriangles represent the results of tetr- and tri-Mo2B2, respectively.

Table 2 The superconductive parameters of N(EF) (in unit of states/spin/Ry/cell), olog (in K), l, and Tc (in K) for some 2D monolayer-phonon-mediatedsuperconductors. The values of Tc from experiments are indicated by datawithin parentheses

Compounds m* N(EF) olog l Tc calc.(expt.) Ref.

B2C 0.1 314.8 0.92 19.2 49B (a sheet) 0.05 5.85 262.2 0.52 6.7 50B (b12) 0.1 8.12 425.0 0.69 14 51Silicene 0.1 338.10 0.44 1.7 47Li2B7 0.12 462.8 0.56 6.2 51Mo2C 0.1 0.63 5.9 53Stanene 0.13 60.57 0.65 1.3 48LiC6 0.14 0.55 5.9 (5.9) 17 and 182H-NbSe2 0.16 189.23 0.91 7.8 (7.8) 25 and 26C6CaC6 0.207 0.71 6.8 (4) 27 and 28tetr-Mo2B2 0.1 16.02 344.84 0.49 3.9 This worktri-Mo2B2 0.1 16.81 295.0 0.3 0.2 This work

Fig. 6 Top and side views of tetr-Mo2B2 on (a) CuI(100), (b) SiC(100),and (c) InAs(100) surfaces and tri-Mo2B2 on (d) CuI(111), (e) SiC(111), and(f) InAs(111) surfaces.

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surface, Eslab is the total energy of the slab with a clean surface,Emol is the energy of 2D Mo2B2 and n is the 2D Mo2B2 atomnumber. To correctly describe the van der Waals interaction, arapidly dispersion-corrected DFT method (optB86b-vdW) hasbeen used.56–58 The lattice mismatch (d) is calculated through

d ¼ Lmol � Lslab

Lslab� 100% (7)

where Lmol and Lslab are the corresponding lattice parameters of2D Mo2B2 and the slab, respectively. Results of the adsorptionenergy and the lattice mismatch are listed in Table 3. Theadsorption energies of tetr-Mo2B2 on the three substrates ofCuI(100), SiC(100), and InAs(100) surfaces as well as tri-Mo2B2

on the two substrates of CuI(111) and SiC(111) surfaces are allnegative, indicating that our predicted Mo2B2 monolayers maybe grown on such substrates. Only the adsorption energy oftri-Mo2B2 on InAs(111) is positive. Besides, a small latticemismatch is required in the real growing of 2D materials.59

Considering the lattice mismatches and adsorption energies ofthe five promising monolayer–substrate schemes, the growth oftetr-Mo2B2 on CuI(100) and tri-Mo2B2 on CuI(111) should be thetwo most possible cases.

IV. Conclusions

In summary, combining the crystal structure prediction techniqueand the first-principles method, we obtained two new 2D structuresof tetr- and tri-Mo2B2 and investigated their electronic structures,phonon spectra and superconductivity. Both these TMB monolayersexhibit inherent metallic state and intrinsic superconductivity. Thelow-frequency vibrations of the Mo atoms and the electronicoccupations of the Mo-4d orbitals near the Fermi level are foundto be crucial for the superconductivity. We believe that our findingswill provide a reference for searching for new 2D superconductors.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors would like to acknowledge the financial supportfrom the National Natural Science Foundation of China underGrant No. 11835008, 51872250, and 51472210, the State KeyLaboratory of Intense Pulsed Radiation Simulation and Effect(Northwest Institute of Nuclear Technology) under Grant No.SKLIPR1606 and SKLIPR1814, and Key Laboratory of LowDimensional Materials & Application Technology of Ministry

of Education (Xiangtan University) under Grant No. KF20180203.We also acknowledge the China Postdoctoral Science Foundationunder Grant No. 2018M641477 and the Guangdong ProvincialDepartment of Science and Technology, China (No. 2018A0303100013). The calculations were performed at SupercomputerCentre at the China Spallation Neutron Source.

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Table 3 The adsorption energies and the lattice mismatches (d) for tetr-and tri-Mo2B2 on various substrates

tetr-Mo2B2 Eads (eV) d (%) tri-Mo2B2 Eads (eV) d (%)

CuI(100) �3.78 1.95 CuI(111) �4.72 0.35SiC(100) �0.38 �6.4 SiC(111) �3.73 �7.94InAs(100) �0.25 �0.55 InAs(111) 0.77 �5.66

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