Uncovering a Stable Phase in Group V Transition-metal Dinitride (MN

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C: Physical Processes in Nanomaterials and Nanostructures

Uncovering a Stable Phase in Group V Transitionmetal Dinitride (MN, M= Ta, Nb, V) Nanosheets and Their Electronic Properties via First-principles Investigations 2

Yanli Wang, and Yi Ding J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08885 • Publication Date (Web): 31 Oct 2018 Downloaded from http://pubs.acs.org on November 5, 2018

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The Journal of Physical Chemistry

Uncovering a Stable Phase in Group V Transition-metal Dinitride (MN2, M= Ta, Nb, V) Nanosheets and Their Electronic Properties via First-principles Investigations Yanli Wang∗,† and Yi Ding∗,‡ †Department of Physics, Zhejiang Sci-Tech University, Xiasha College Park, Hangzhou, Zhejiang 310018, People’s Republic of China ‡Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, People’s Republic of China E-mail: [email protected](Y.Wang); [email protected](Y.Ding)

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Abstract Owing to the fast developments of transition-metal dichalcogenides (TMDs), their cousins, i.e. layered transition-metal dinitrides (TMDNs), have also drawn appreciable research interests. Generally, these TMDNs nanosheets are expected to share similar geometries to the TMDs ones with trigonal prismatic (H-phase) or octahedral (T phase) structures. However, in this work, through first-principle calculations, a different geometry is identified as the most stable structure of group V MN2 (M= Ta, Nb, V) nanosheets so far. In this new phase (M -phase), the upper and lower N atoms are alternately bonding and staggering to each other, which significantly enhances the energetic stability and leads to robust mechanical, dynamical, and thermal stabilities. Unlike the metallic H- and T -phases, these M -MN2 nanosheets are indirect-gap semiconductors, which account for the experimental observation on the TaN2 system. Particularly, the band edges of M -TaN2 can straddle the redox potentials of water, and the carrier mobilities of M -TaN2 and M -NbN2 nanosheets are much larger than the MoS2 nanosheet, which enable these TMDNs promising optoelectronic and green-energy applications. Our study demonstrates that new geometrical structures will emerge in the transition-metal dinitrides, which bring distinct electronic properties from the TMD systems.

Introduction Layered transition-metal dichalcogenides have attracted extensive scientific attention due to their peculiar electronic, magnetic, optical and catalytic properties. 1–5 The general formula of TMD material is MX2 (M=transition metal and X=S/Se/Te), which adopts an X-M-X sandwich structure. Depending on the arrangement of X atoms, there are two common geometries for the MX2 nanosheets, which are the H-phase where the metal atoms form trigonal prismatic coordination with six X neighbors, as well as the T -phase in which the metal atoms form octahedral coordination. It has been revealed that different geometries

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will lead to diverse electronic properties in the MX2 nanosheets. 6 Taking the MoS2 as an example, the H-MoS2 nanosheet is a normal semiconductor, 7 but the T -MoS2 is a metal, which can further transform to a Td -phase that becomes a quantum spin Hall insulator. 8,9 Similar geometry-dependent electronic properties are also present in other TMDs nanosheets, such as MoSe2 , WS2 and WSe2 ones. 10,11 As a cousin of TMDs, layered transition metal dinitrides have also gained lots of interests from the experimenters and theorists. Through the solid-state ion-exchange reaction, the MoN2 compound with a 3R-MoS2 geometry has been synthesized. 12 The H-phase MoN2 nanosheet is a ferromagnetic metal, 13 which will undergo a structural transition under tensile strain and become an antiferromagnetic metal. 14 Through the surface decoration, a topological nodal-line state will exist in the K-functionalized H-MoN2 nanosheet. 15 However, different from the MoS2 one, the MoN2 nanosheet prefers T -phase to the H-case, and the corresponding T -MoN2 is a semiconductor with a small band gap. 16,17 When the T MoN2 is hydrogenated, a distorted Td -phase is obtained and the system exhibits a Dirac-like semimetallic behavior. 17 Besides these MoS2 -type geometries, other types of structures are also present in the MoN2 nanosheet. Zhang et al. have proposed a tetra-MoN2 geometry by the particle swarm optimization method, which is energetically more stable than the HMoN2 and T -MoN2 ones. 18 We have discovered a bilayer hexagonal structure (BHS) for the MoN2 , which is the ground-state structure of MoN2 nanosheet. 19 In addition to MoN2 , the YN2 nanosheet also prefers a different geometry from the MoS2 ones, i.e. the O-YN2 , as the ground-state structure. 20 These results motivate us to explore the possible novel geometrical structures in the TMDNs, which will exhibit distinct characteristics from the TMDs. Besides the MoN2 , the layered TaN2 compound has also been reported in the experiment, which is prepared by deintercalating Na ions from the ternary NaTaN2 . 21 In the NaTaN2 material, the TaN2 layers adopt the octahedral T -phase structure. By first-principles calculations, it has been found that such T -TaN2 nanosheet displays a half-metallic feature due to the unpaired p electrons of N atoms. 22 However, this result is inconsistency with

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the experimental measurement, which indicates that the synthesized TaN2 system is a semiconductor. 21 It suggests that the group V TMDNs nanosheet will have different geometries from the ones in the ternary bulk. However, there is no study on the stable structures of group V TMDNs nanosheets yet. What are their most stable geometries? How do their electronic properties behave? Can we explain the semiconduting behavior of TaN2 in the experiment? To solve these issues, we have performed a comprehensive first-principles study on the structural and electronic properties of group V TMDNs (MN2 , M= Ta, Nb, V)) nanosheets.

Method The first-principles calculations are performed by the VASP code, 23,24 which utilizes the projector augmented wave pseudopotentials and plane-wave basis sets. The Perdew-BurkeErnzerhof (PBE) functional is used and the cut-off energy is set to 500 eV. The Γ-centred k-meshes of 24×24×1 and 18×24×1 are used in the relaxation of hexagonal and orthogonal supercells, which are increased to 36 × 36 × 1 and 24 × 36 × 1 in the static calculations, respectively. In order to simulate the isolated nanosheet, a vacuum layer of more than 15 Å is adopted in the calculations. All the geometrical structures are fully relaxed until the maximum residual force is less than 0.005 eV/Å. Since the traditional PBE functional will underestimate the band gaps of semiconductors, a hybrid Heyd-Scuseria-Ernzerhof (HSE) functional is used to check the obtained electronic properties. This is performed by the FHIaims code, 25 which adopts the HSE06 form with a screening parameter of 0.11 bohr−1 . 26 The dynamical stabilities of investigated nanosheets are studied by the phonon calculations using the Phonopy code. 27 To determine the relative energetic stabilities of different structures, the cohesive energies (Ecoh ), which are the energy differences between the compound and its constituents under the isolated case, are calculated. Here, for the MN2 nanosheets, the Ecoh are calculated as

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Ecoh = −(EM N 2 − nM EM − nN EN )/(nM + nN ), where EM N 2 is the total energy of MN2 nanosheet, nM /nN is the number of metal/nitrogen atoms in the system, and EM /EN is the energy of an isolated metal/nitrogen atom from the spin-polarized calculation. According to this definition, the more positive the Ecoh value, the more energetically favourable the corresponding structure.

Results and Discussion (a)

(b)

H

(c)

Hb

T (e) 800 Frequency (cm-1)

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(f) Frequency (cm-1)

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600

400

200

800

600

400

200

-200 -400

M

G

K

M

0

M

G

K

M

0

M

G

K

M

Figure 1: The atomic structures and phonon dispersions of [(a), (d)] H-TaN2 , [(b), (e)] T -TaN2 , and [(c), (f)] Hβ -TaN2 nanosheets. The big balls are Ta atoms and the small ones are N atoms.

Firstly, the common MoS2 -type structures are examined for the group V TMDN nanosheets. Taking the TaN2 as an example, its H- and T -phases are illustrated in Figs. 1(a) and (b), whose lattice constants are 3.11 and 3.17 Å and the thicknesses are 2.20 and 2.01 Å, respectively. The calculated Ecoh of H- and T -TaN2 nanosheets are 6.23 and 6.43 eV, which indicates the T -phase is energetically more favorable. The phonon calculations show that the T -TaN2 nanosheet is dynamically stable while the H-TaN2 is not. It would be noted that in the dinitride system, another H-phase (Hβ ) structure, where the N dimers are formed between the upper and lower N layers, could also exist. 14 As shown in Fig.

1(c), due to

the N-N bonding, the layer thickness is decreased to 1.69 Å while the lattice constant is elongated to 3.31 Å. Meanwhile, the Ecoh of Hβ -TaN2 is enhanced to 6.27 eV, which is larger 5



than the H-TaN2 . Besides that, the dynamical stability is recovered in this Hβ -TaN2 as indicated in Fig. 1(f). (a)

(b)

T

E E

-462

Hb

-456

-458

-464 1

2

3

Time (ps)

Hg N1 y

top

Ta1

N3 N2

0

5

z

1

2

3

4

5

Time (ps)

(d)

900

N4 Ta2

x

N1 lateral

4

Frequency (cm-1)

0

(c)

E E

-454

E(eV)

-460

E(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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N3

Ta1 Ta2 N2 N4 x

600

300

0

-300

Hg G X

S

Y

G

Figure 2: The variations of total energy versus time for the (a) T -TaN2 and (b) Hβ -TaN2 nanosheets in the AIMD simulations. For clarity, the average values of adjacent data in 1 ps are depicted as dotted lines in (a) and (b), and the final configuration of Hβ -TaN2 after the AIMD simulation is also displayed in the inset of (b). (c) The top and lateral views of Hγ -TaN2 nanosheet. (d) The phonon dispersions of Hγ -TaN2 nanosheet, in which the atomic displacement of imaginary mode at the Γ point is also illustrated. Then, ab initial molecular dynamics (AIMD) calculations are performed to check the thermal stabilities of Hβ -TaN2 and T -TaN2 nanosheets, which adopt a Nosé thermostat of 300 K and a supercell of 4 × 4 units. The step time is set to 1 fs, and total simulated time is 5 ps. In accordance with the previous result, 22 the T -TaN2 nanosheet could maintain the structural integrity during the AIMD simulations. On the other hand, the Hβ -TaN2 can not keep its structural integrity. As shown in Fig.

2, the total energy of Hβ -TaN2 gradually

descends at the first 2 ps, and then fluctuates during the left 3 ps. After scrutinizing the final configuration, it is found that the descending of total energy is attributed to the breaking of some N-N bonds in the structure. Considering that the group V metals may have a +5 oxidation state in the TMDNs, this inspires us to construct a Hγ -phase, which is made up by 6


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doubling the primitive cell of Hβ -TaN2 and opening half of the N dimers. As depicted in Fig. 2(c), after the structural relaxation, the Ta basal plane becomes buckled in the Hγ -TaN2 . The buckling height is 0.59 Å between the Ta1 and Ta2 atoms. The N1 and N2 atoms are still bonded together, while the N3 and N4 atoms are separated by a distance of 2.39 Å. Compared to the Hβ -TaN2 , the Hγ -TaN2 nanosheet has a larger Ecoh of 6.39 eV, which is 0.12 eV stronger than that of Hβ -TaN2 . However, this Hγ -TaN2 nanosheet is dynamically unstable as shown in Fig. 2(d). There is a noticeable imaginary mode in its phonon bands, which has a negative frequency of -107 cm−1 at the Γ point. By analyzing the eigenvector of this imaginary mode, we find it corresponds to the relative displacement of N3 and N4 atoms. Thus, we manually add this displacement and reoptimize the structure. Finally, a new phase is obtained for the TaN2 nanosheet. As shown in Fig. 3, the N1 and N2 atoms are still bonded together, but the N3 and N4 atoms are staggered to each other. This new phase structure can be viewed as a mixture of Hβ - and T -phase from the top side in Fig. 3(a). Thus, it is referred to as the M -phase in the following. In the M -TaN2 nanosheet, the lattice constants are lx =5.57 and ly =3.19 Å, and the buckling height of Ta atoms is 0.80 Å. Due to the low symmetry of Pm(6) space group, the Ta-N bond lengths are no longer uniform, which are varied in the range of [1.95-2.17] Å. Figure 3(c) depicts the phonon bands of M -TaN2 nanosheet. Different from Hγ -TaN2 , there are no imaginary modes in the M -TaN2 . Although some negative frequencies appear near the Γ point, they are less than -5 cm−1 that will be attributed to the numerical artifact. 28 Thus, it demonstrates that the M -TaN2 nanosheet is dynamically stable. The AIMD simulations are performed on a supercell of 2 × 4 × 1 units for the M -TaN2 . As shown in Fig. 3(d), under the Nosé thermostat of 300 K, the total energy is just fluctuated during the AIMD simulation. The final configuration in Fig. 3(d) shows that there is only a slight distortion in the M -TaN2 nanosheet, while the whole structural integrity is well retained. In fact, when the simulated temperature is raised to 1000 K, the whole structure is still maintained. This verifies the good thermal stability of M -TaN2 nanosheet. Besides that,

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(b)

(a)

N1

N3 N1 Ta1

y

N2 Ta

N4ly 2

lx

N3 Ta2 N4

x

900

(d)

-473

600

E(eV)

(c)

Ta1 N2

z

x

Frequency (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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300

-474

E E

-475 0

X

G

S

Y

-476

G

0

1

2

3

4

5

Time (ps)

Figure 3: [(a), (b)] The top and lateral views of M -TaN2 nanosheet. (c) The phonon dispersions and (d) the variations of total energy versus time for the T -TaN2 nanosheet during the AIMD simulation. The final configuration of M -TaN2 after the AIMD simulation is also displayed in the inset of (d). the elastic constants of M -TaN2 are calculated by the energy-vs.-strain method, 29,30 which are C11 = 157, C22 = 157, C12 = 41, C44 = 19 N/m. These constants satisfy the Born criteria 2 (C11 > 0, C22 > 0, C44 > 0, and C11 C22 − C12 > 0), 31 which proves the mechanical stability

of M -TaN2 . Thus, combining the dynamical, thermal, and mechanical analysis, the robust structural stability is confirmed in the M -TaN2 nanosheet. Now, we compare the energetic stability of this M -TaN2 to the other ones. The calculated Ecoh of M -TaN2 nanosheet is 6.67 eV, which is larger than those of T -TaN2 and Hβ -TaN2 in Fig. 4(a). Besides that, the previously proposed structures for other TMDNs nanosheets, such as the tetra-phase and BHS-phase in the MoN2 nanosheet 18,19 as well as the orthogonal O-phase in the YN2 nanosheet, 20 are also tested in the TaN2 nanosheet. The Ecoh are 6.20, 6.40 and 5.99 eV in the tetra-TaN2 , BHS-TaN2 , O-TaN2 nanosheets, which are all smaller than that of M -TaN2 . Furthermore, the distorted T -MoS2 (Td ) and hybridized T -MoS2 (Th ) structures are also checked 8,32 for the TaN2 nanosheet. It is found that the initial Td -TaN2 nanosheet will return to the ideal T -phase after the structural relaxation, while the Th -TaN2 8


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nanosheet has a Ecoh of 6.60 eV, still smaller than that of M -TaN2 . Therefore, the M -phase is the most energetically stable structure of TaN2 nanosheet as we know. (a)

7.0

(b)

Ecoh (eV/atom)

6.67

6.5

6.43

6.60 6.40

6.39 6.27

6.23

DCD

6.20 5.99

6.0

5.5

H

T

Hb

Hg

M TetraBHS O

Th

ELF

TaN2

(c)

(d)

6.03 5.95 5.70 5.73

5.5

Ecoh (eV/atom)

6.0

Ecoh (eV/atom)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5.80 5.70 5.53

5.54

5.5

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Hb

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M Tetra BHS

O

5.38 5.30

5.29 5.20

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5.00

5.0

4.5

Th

5.44 5.35

T

Hb

Hg

M Tetra BHS

O

Th

VN2

NbN2

Figure 4: Cohesive energies of different structures in the (a) TaN2 , (c) NbN2 and (d) VN2 nanosheets. It would be noted that the H-phase will spontaneously evolve to the Hβ -phase in the NbN2 and VN2 nanosheets. Thus, only the data of Hβ -NbN2 and Hβ -VN2 are provided in (c) and (d). The deformation charge density (DCD) and electron localization function of M -TaN2 are depcited in (b), where the isosurfaces are 0.025 e/Å3 and 0.675, respectively. For the DCD, the yellow and blue isosurfaces stand for the charge accumulation and charge depletion, respectively. To understand the strong energetic stability of M -TaN2 nanosheet, the deformation charge density (DCD) and electron localization function (ELF) are depicted in Fig. 4(b), where the DCD is calculated by substracting the atomic charge densities from the charge density of compound. It can been seen that the electrons are mainly accumulated around the N atoms, while the electron-deficient region concentrates around the Ta atoms. The Bader charge analysis shows that Ta atoms transfer about 2.46 electrons to the neighboring N atoms, which are bigger than those in Hβ -TaN2 and T -TaN2 counterparts (1.94 and 2.23 electrons). The bigger charge transfer will lead to stronger ionic Ta−N bonds, enhancing the

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stability of M -TaN2 nanosheet. The ELF analysis indicates that besides the ones around the N atoms, the electrons are also localized in the middle of N1 and N2 dimer. This corresponds to a covalent bond between them. In the primitive cell of M -TaN2 , the two Ta atoms can provide 10 valence electrons to the neighboring N atoms. But for the four N atoms, it needs a total number of 12 valence electrons to fulfill their p states. With the 10 valence electrons from Ta atoms, there will be still two unpaired electrons left on the N atoms. In the T -TaN2 nanosheet, this results in a spontaneous spin-polarization phenomenon. Here, in the M -TaN2 nanosheet, the formed N1 -N2 covalent bond can accommodate two electrons. Consequently, the M -TaN2 nanosheet can be assigned as a formula of (Ta+5 )2 (N2 )−4 (N−3 )2 , where the Ta atoms are d0 metals and the N atoms have fulfilled p states. It meets the requirement of octet rule, which result in the high stability of M -TaN2 nanosheet. In addition to TaN2 nanosheet, we also investigate other group V TMDN nanosheets. Akin to TaN2 , the NbN2 and VN2 nanosheets also prefer the M -phase in Figs. 4(c) and (d), whose Ecoh are 6.03 and 5.44 eV, respectively. Comparing to the experimentally synthesized 2D nanosheets, these data are close to the values of MoS2 (5.07 eV/atom) 33 and TaS2 (5.92 eV/atom) nanosheets, 33 and much larger than those of silicene (3.90 eV/atom) 34 and phosphorene (3.48 eV/atom) cases, 35 which suggests the M -phase group V TMDN nanosheets are possibly synthesized in the experiment. For these MN2 nanosheets, their formation energies Ef orm are calculated by the formula of Ef orm = EM N 2 − EM −bulk − EN 2 , where EM N 2 is the total energy of MN2 nanosheet, EM −bulk is the energy of metal atom in its elementary bulk structure and EN 2 is the energy of an isolated N2 molecule. The obtained Ef orm are -1.30, 0.80, and -0.60 eV per f.u. for the M -TaN2 , M -NbN2 and M -VN2 nanosheets (1 f.u. contains one group V metal and two N atoms). Here, the negative values of Ef orm suggest that the formation of M -MN2 nanosheets are exothermic reactions from the elementary substances. Thus, it is feasible to prepare them by appropriate experimental techniques. It is worth mentioning that in the experiment, 21 the layered TaN2 compound is prepared by deintercalating Na ions from the NaTaN2 , where the TaN2 layers adopt the T -phase struc-

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ture. During the synthesis, there is a small amount of Na ions left in the TaN2 compound, 21 which will affect the relative stability of T -TaN2 and M -TaN2 nanosheets. To this end, we study the Na adsorption on them with a stoichiometry of Nax TaN2 (x =0.083, 0.167, 0.25, 0.33, 0.417 and 0.5). Our calculations show that the energy differences between the M -TaN2 and T -TaN2 are −0.53, −0.36, −0.17, −0.05, 0.05 and 0.20 eV per f.u. at x =0.083, 0.167, 0.25, 0.33, 0.417 and 0.5, respectively. It can be seen that the relative stability of M -TaN2 is enhanced with the decrease of Na content, and it becomes more favourable when the Na content x 4d > 3d for the group V transition-metals. Finally, the carrier mobilities are calculated for these M -MN2 nanosheets. In view of their anisotropic structural feature, the carrier mobilities are estimated by the recently proposed formula for anisotropic systems, 37 which is

µα =

5Cα +3Cβ ) 8 2 +7E E +4E 2 9E α β α β 0.5 kB T m1.5 ) α mβ ( 20

e¯h3 (

(α, β = x, y).

Here C, m, and E are the elastic moduli, effective carrier mass, and deformation potential constant of band edge in the corresponding transport direction. Considering the large computational resource acquired by the HSE calculation, the carrier mobilities are just performed by the PBE one. The obtained parameters for M -MN2 nanosheets are listed in Tab.

1. It can be seen that the m and E values are quite anisotropic, which results in

orientation-dependent mobilities in these M -MN2 nanosheets. In the M -TaN2 nanosheet, the hole and electron carriers have different preferred transport directions, which possesses a high µh /µe of 1281/684 cm2 /Vs in the x/y direction under the room temperature of 300

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K. Similar large mobilities are also found in the M -NbN2 nanosheet, whose µh /µe is as high as 673/1001 cm2 /Vs in the x/y direction. In the M -VS2 nanosheet, the µh and µe values are prominently reduced due to the heavier carrier mass, which only reach up to 61 and 344 cm2 /Vs as shown in Tab.

1. However, these mobility data are still larger than the

ones of MoS2 nanosheet, whose maximum hole and electron mobilities are merely µh = 47 and µe = 25 cm2 /Vs, respectively. 38,39 The higher carrier mobilities in the M -TaN2 and M -NbN2 nanosheets are even comparable to monolayer phosphorene, whose mobilities are µh = 2370 and µe = 690 cm2 /Vs by the same formula. 37 This suggests the group V TMDNs are promising semiconducting materials, which have potential applications in nano-electrics and nanodevices. Table 1: The elastic constants, effective masses, deformation potential constants and carrier mobilities of holes and electrons in the M -TaN2 , M -NbN2 , and M -VN2 nanosheets under the room temperature of 300 K .

M -TaN2 M -NbN2 M -VN2

x y x y x y

C N/m 157 157 136 137 125 104

mh m0 0.70 1.76 1.01 1.18 1.52 3.34

me m0 1.09 0.70 0.73 0.83 1.14 1.78

EV BM eV 0.79 3.31 0.97 3.43 3.50 3.39

ECBM eV -3.33 -2.51 -3.43 -1.23 -1.45 -3.13

µh µe 2 cm /Vs cm2 /Vs 1281 383 289 684 673 722 339 1001 61 344 27 147

Conclusion In summary, we have investigated the stable geometries and electronic structures of group V TMDN nanosheets. We find that (1) in the stable geometry of TaN2 , NbN2 , and VN2 nanosheets, the N atoms are alternately bonding and staggering to each other, forming a mixed structure of H and T phases. Such M -phase is the most energetically stable structure of these group V TMDNs, which also possess robust dynamical, thermal and mechanical stabilities. (2) Different from the metallic H-and T -phases, the M -phase group V TMDNs 14


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are all semicondutors, which agrees well with the experimental observation on the TaN2 ststem. (3) The band edges of M -TaN2 nanosheet can straddle the redox potentials of water, and the carrier mobilities of M -TaN2 and M -NbN2 systems are much larger than the MoS2 nanosheet. Our study demonstrates that new geometrical structures will emerge in the transition-metal dinitrides, which enable them potential optoelectronic and green-energy applications.

Author information Corresponding Author E-mail: [email protected] (Yanli Wang), E-mail: [email protected] (Yi Ding). ORCID Yanli Wang: 0000-0002-1255-0937 Yi Ding: 0000-0001-7461-0213 Notes The authors declare no competing financial interest.

Acknowledgement The authors thank the supports from National Natural Science Foundation of China (11774312 and 11474081), and Zhejiang Provincial Natural Science Foundation of China (LY15A040008). Parts of the calculations were performed in the Tianhe-2 at National Supercomputer Center in Guangzhou (NSCC-GZ), China.

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Uncovering a Stable Phase in Group V Transition-metal Dinitride (MN

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