A unique pentagonal network structure of the NiS2 monolayer ...n11.iphy.ac.cn/wj/pdf/2020-PCCP-WCT.pdfhis ournal is ' the Owner Societies 2020 Phys. Chem. Chem. Phys. , 22 22, 7483--7488

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Cite this:Phys.Chem.Chem.Phys.,2020, 22, 7483

A unique pentagonal network structure of theNiS2 monolayer with high stability and a tunablebandgap†

Chang-Tian Wang ab and Shixuan Du *abcd

Two dimensional atomic crystals with pentagonal building blocks have attracted extensive interest in

recent years for their fundamental significance and potential applications in nanoscale devices. Here,

with the help of ab initio calculations based on density functional theory, we report a unique pentagonal

structured NiS2 monolayer in P %421m symmetry, named P-NiS2. Its dynamic stability has been confirmed

by phonon mode analysis. Molecular dynamics simulations and total-energy calculations show that this

new P-NiS2 has robust thermal stability and energetically more stable than all other reported NiS2monolayer structures. Electronic band structure calculations show that it is a semiconductor with an

indirect band gap of 1.94 eV. Furthermore, we find that small strain triggers a transition from the indirect

to direct band gap for this P-NiS2, suggesting its great potential for applications based on strain-

engineering techniques.

1 Introduction

Discovery of graphene1 has triggered considerable interest inexploring novel two-dimensional (2D) nanomaterials. In particular,2D transition metal dichalcogenides (TMDs) have attractedtremendous interest recently due to their tunable electronicproperties with layered structures, and can be applied in opto-electronic devices and transistors.2–4 For instance, when MoS2crystals are thinned to a monolayer, a strong photoluminescenceemerges, indicating an indirect to direct band gap transition frommultilayer to monolayer MoS2.

2 Meanwhile, some 2D TMDs canhold the bulk properties with novel potential applications innanoscale devices. The superconductivity of bulk NbSe2 remainsin its monolayer;5 few-layered VS2 is metallic and can be used forconstructing the electrodes of in-plane supercapacitors;6 monolayerWSe2 is a semiconductor and its applicability has been demon-strated for logic-circuit integrations.7

Most of the 2D TMDs have two main crystal phases, i.e., 2Hand 1T phases, depending on the coordination sphere of the

transition metal atom that can have either trigonal prismatic orantiprismatic symmetry, respectively.2,5,8–36 For instance, the2H phase of MoS2,

2 NbSe2,5 WS2,

9 MoSe2, MoTe210 monolayers,

and the 1T phase of TiSe2,11 NiTe2,

13 PtS2,15 PtSe2

16 monolayershave been reported experimentally. Meanwhile, the multilayer1T phase of NiSe2,

12 PdTe2,14 and PtTe2

17 has been successfullysynthesized under laboratory conditions.

In addition to 2H and 1T phases, TMDs with pentagonalnetwork structures have attracted tremendous interest recentlydue to their unique configurations and interesting properties.37–44

So far, two typical pentagonal network monolayer structures havebeen reported.37–60 One is the tetragonal pentagonal building blocksin P%421m symmetry, which have been theoretically predicted ingraphene,51,52 B2C,

53 CN2,55 AlN2,

56 SiX (X = B, C, and N),57 BP558

and CdS2.59 The other is the monoclinic pentagonal network

structures in P21/c symmetry, which have been theoreticallypredicted in PdS2,

40 PdSe2,39 PdTe2,

41,42 and O-NiS2.43,44

Recently, the monoclinic penta-PdSe2 monolayer has beenexfoliated from the bulk crystals with high air stability,37 andthe bilayer penta-PdSe2 has been grown on a graphene–SiC(0001)substrate by molecular beam epitaxy.38

In this paper, we report a new pentagonal NiS2 monolayer inP%421m symmetry with a tetragonal lattice (named P-NiS2 here-after) for the first time by using ab initio calculations based ondensity functional theory. We find that this P-NiS2 is energeticallymore stable than all the reported NiS2 monolayers. Moleculardynamics simulations show that P-NiS2 is thermally stable up to500 K. Its dynamical stability has been confirmed by phononspectrum simulations. Electronic band structure calculations reveal

a Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,

Chinese Academy of Sciences, Beijing 100190, China. E-mail: [email protected] School of Physics, University of Chinese Academy of Sciences, Beijing 100049,

Chinac CAS Center for Excellence in Topological Quantum Computation, Beijing 100190,

Chinad Songshan Lake Materials Laboratory, Dongguan, Guangdong 523803, China

† Electronic supplementary information (ESI) available: The bulk structures ofmarcasite- and pyrite-type NiS2, the monolayer structures of O-, T- and H-NiS2,and the total energy of NiX2 and PdX2 (X = S, Se, Te) monolayers. See DOI:10.1039/d0cp00434k

Received 26th January 2020,Accepted 6th March 2020

DOI: 10.1039/d0cp00434k

rsc.li/pccp

PCCP

PAPER

http://orcid.org/0000-0001-8785-5105http://orcid.org/0000-0001-9323-1307http://crossmark.crossref.org/dialog/?doi=10.1039/d0cp00434k&domain=pdf&date_stamp=2020-03-27http://rsc.li/pccp

7484 | Phys. Chem. Chem. Phys., 2020, 22, 7483--7488 This journal is©the Owner Societies 2020

that the P-NiS2 pentagonal network structure is a semiconductorwith an indirect band gap of 1.94 eV. Moreover, investigation of thestrain effect on the band structures reveals an indirect to directband gap transition under a tensile strain of 0.55%.

2 Computational method

The calculations are carried out using the density functionaltheory as implemented in the Vienna ab initio simulationpackage (VASP).61 The exchange–correlation interactions areconsidered in the generalized gradient approximation (GGA)using the Perdew–Burke–Ernzerhof (PBE) functional.62 Theinteractions between the valence electrons and ionic cores weredescribed by the projector augmented wave (PAW) method,63

with valence electrons employed as 3d84s2 for Ni and 3s23p4 forS, respectively. A plane-wave basis set with a large energy cutoffof 550 eV is used. We construct the P-NiS2 by cleaving themarcasite-type structure. The lattice is set with a fixed value of20 Å along the Z-axis to simulate the 2D monolayer structures.The Brillouin zone is sampled with a 12 � 12 � 1 G-centeredMonkhorst–Pack k-point grid. Convergence criteria employedfor both the electronic self-consistent relaxation and the ionicrelaxation are set to 10�8 eV and 0.0001 eV Å�1 for energy andforce, respectively. A hybrid density functional method basedon the Heyd–Scuseria–Ernzerhof scheme (HSE06)64 is used tocalculate the band structure. The phonon spectra are calculatedusing a DFPT method as implemented in the VASP combinedwith the phonopy code.65 The ab initio molecular dynamics

simulations are performed in the canonical (NVT) ensemblewith a Nosé thermostat.66 The transformation from the O-NiS2

43,44

toward P-NiS2 monolayer is simulated at the atomic scale using amodified climbing image nudged elastic band (CI-NEB) method.67–69

3 Results and discussion3.1 Structural stability

Pentagonal network structures exist in marcasite and pyriteTMDs.70,71 We can obtain two typical 2D pentagonal networksby cleaving the bulk NiS2 in marcasite- and pyrite-type structures(Fig. S1, ESI†). The one cleaved from pyrite NiS2, termed O-NiS2 inP21/c symmetry (Fig. S2, ESI†), has been reported as a semi-conductor with an indirect band gap.43,44 Fig. 1 shows a newpentagonal network structure of monolayer NiS2 cleaving frommarcasite NiS2 in P%421m symmetry with a tetragonal lattice,named P-NiS2. Two Ni atoms and four S atoms occupy the 2b(0.0, 0.0, 0.5) and 4e (0.1430, 0.6430, 0.5338) Wyckoff positions,respectively. Each Ni atom is four-fold coordinated with four Satoms, while each S atom is three-fold coordinated with two Niatoms and one S atom, forming an intriguing pentagonal ringnetwork known as the Cairo pentagonal tiling. The calculatedlattice parameters are a = b = 5.28 Å, the buckling heighth = 0.68 Å, with the bond lengths of dNi–S = 2.14 Å and dS–S =2.14 Å. Besides P- and O-NiS2, there are NiS2 monolayers with2H and 1T configurations (Fig. S2, ESI†).34–36 The calculatedstructural parameters are summarized in Table 1.

Fig. 2(a) presents the total energy per atom for P-NiS2 incomparison with those for O-, T- and H-NiS2 monolayers. Theenergetic stability sequence is estimated to be: H-NiS2 o T-NiS2 oO-NiS2 o P-NiS2. Thus, P-NiS2 is the most stable structure amongthe four NiS2 monolayers. We have also shown the total energy peratom for NiX2 (X = Se and Te) and PdX2 (X = S, Se, and Te)monolayers in Fig. S3 in the ESI.† It is found that, among thepentagonal network structures, P-NiX2 is always more favourablein energy than O-NiX2, while O-PdX2 is always more favourablein energy than P-PdX2. If we consider all four possible structures,the T-structure becomes more stable in NiSe2, NiTe2, andPdTe2 monolayers. Experimentally, mutilayer O-PdSe2,

37 T-NiSe2,12

T-NiTe2,13 and T-PdTe2

14 have been successfully synthesized,and are in good agreement with our calculated results shown inFig. S3 in the ESI.†

Fig. 1 Top (a) and side (b) views of P-NiS2 in P %421m symmetry. Dashedlines represent the unit cell of the square lattice. h is the buckling height.The blue and yellow balls represent the Ni and S atoms, respectively.

Table 1 Calculated equilibrium structural parameters (space group, lattice parameters a, b and c, the buckling height h, bond lengths dNi–S and dS–S),total energy per atom E, and HSE06 band gap Eg for P-, O-, T-, H-NiS2 monolayers and bulk NiS2 in the marcasite- or pyrite-type structure

Structure Space group Method a (Å) b (Å) c (Å) h (Å) dNi–S (Å) dS–S (Å) E (eV per atom) Eg (eV)

P-NiS2 P%421m PBE 5.28 5.28 — 0.68 2.14 2.14 �4.870 1.94O-NiS2 P21/c PBE 5.22 5.33 — 0.57 2.17, 2.18 2.13 �4.823 2.41

PBE43 5.22 5.33 — 0.57 2.17, 2.18 — — 2.40T-NiS2 P%3m1 PBE 3.35 3.35 — 1.17 2.26 3.03 �4.781 1.11

PBE43 3.35 3.35 — 1.17 2.26 — — 1.10H-NiS2 P%6m2 PBE 3.54 3.54 — 1.05 2.30 2.10 �4.633 Metal

LDA34 3.40 3.40 — — 2.24 2.14 — —

Marcasite (bulk) Pnnm PBE 4.60 5.57 3.55 — 2.38 2.09 �4.811 MetalPyrite (bulk) Pa%3 PBE 5.62 5.62 5.62 — 2.37 2.08 �4.815 Metal

Exp.75 5.69 5.69 5.69 — — — — —

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We have examined the kinetic stability of the typical pentagonalP-NiS2 network structure. The transformation from the O-NiS2toward P-NiS2 monolayer is simulated at the atomic scale usinga modified climbing image nudged elastic band (CI-NEB)method.67–69 In the CI-NEB calculations, the initial and finalstates are set with the calculated equilibrium lattice parametersof O-NiS2 and P-NiS2, respectively, and the energy convergencecriterion for electronic self-consistent calculations is set to10�6 eV. The energy pathway of the transformation from theO-NiS2 toward P-NiS2 monolayer (Fig. 2b) shows that the energybarrier is 86 meV per atom. We note that the main change of thestructure is that the S1 atom goes down while the S3 atom goes upfrom the side views shown in Fig. 2b. The low transformation barriersuggests that O-NiS2 can easily convert to P-NiS2, and thus P-NiS2 isthe most stable from both kinetic and energetic points of view.

We have also calculated the total energies of the marcasite-and pyrite-type bulk NiS2 structures (Table 1). We find that theP-NiS2 monolayer is 0.059 and 0.055 eV per atom more stablethan the marcasite-type and pyrite-type bulk NiS2, respectively. Asmentioned above, the P-NiS2 and O-NiS2 monolayers can beobtained by cleaving the marcasite-type and pyrite-type structures,respectively. However, the bulk NiS2 is generally considered to havea pyrite structure,72–76 no marcasite-type bulk NiS2 exist in nature.Thus, we cannot directly obtain the P-NiS2 monolayer by cleavingthe bulk structures. Nevertheless, we can expect that the P-NiS2

monolayer could be synthesized experimentally on a suitablesubstrate by chemical vapor deposition or molecular beam epitaxy.

To investigate the dynamical stability of the P-NiS2 mono-layer, we have calculated the phonon spectrum along the highsymmetric directions in the first Brillouin zone. The phononband structure and density of states (DOS) are shown in Fig. 3.The absence of any imaginary frequency in the phonon spectraconfirms the dynamical stability of the P-NiS2 monolayer.

The stability of the P-NiS2 monolayer with a pentagonalnetwork structure against mechanical strains is also investigatedby calculating the elastic constants. The calculated componentsof the elastic modulus tensors C11, C22, C12 and C44 are 92.3, 92.3,20.1, and 22.6 GPa, respectively. For a mechanically stablematerial, the elastic constants should satisfy the followingequations according to the Born criteria:77 C11C22 � C122 4 0and C44 4 0. The positive values of C11C22 � C122 and C44confirm the mechanical stability of P-NiS2.

To examine the thermal stability at finite temperature, wehave performed ab initio molecular dynamics (AIMD) simulationswith a step of 1 fs in a 3 � 3 � 1 supercell for the P-NiS2monolayer at 300, 400 and 500 K in comparison with O-NiS2. Theenergy fluctuations at 300 K are presented in Fig. 4. We found

Fig. 3 Calculated phonon band structure and density of states (DOS) forP-NiS2.

Fig. 4 Energy fluctuations in AIMD simulations for P-NiS2 in comparisonwith the O-NiS2 monolayer at 300 K. Insets are the configurations after thesimulations. The dotted lines represent the average energy for each case.

Fig. 2 (a) Energy as a function of area per atom for the P-NiS2 pentagonalnetwork structure (red) in comparison with those for O-, T- and H-NiS2monolayers. (b) Energy pathway for the transformation from the O-NiS2toward P-NiS2 monolayer.

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that P-NiS2 has an average energy of �4.831 eV, which is lowerthan that of O-NiS2 (�4.782 eV). After heating up to 500 K for5 ps, P-NiS2 almost retains its configuration with some atomsdeviating from the equilibrium positions. These atoms willmove back after further relaxation. On the other hand, uponincreasing the temperature up to 500 K for 5 ps, the O-NiS2structure becomes unstable and some planar building blockscomposed of S and Ni atoms are largely distorted, showing atendency of phase transformation to P-NiS2. These resultsfurther confirm the stability of P-NiS2 and, once synthesized,P-NiS2 has robust thermal stability at room temperature.

3.2 Electronic properties

The electronic band structure and density of states (DOS)projected on different obitals of P-NiS2 are calculated basedon the hybrid density functional method (HSE06)64 and plottedin Fig. 5(a) and (b), respectively. Our results show that P-NiS2 isa semiconductor with an indirect band gap of 1.94 eV. Theconduction band minimum (CBM) is located at the G pointand the valence band maximum (VBM) is located at the Mpoint. More importantly, a direct band gap of 2.01 eV at the Gpoint is quite close to the indirect band gap, revealing thatthe P-NiS2 monolayer is a semiconductor with a quasi-directband gap.

From the projected density of states, we find that the statesaround the Fermi level of P-NiS2 are almost contributed by S-3pzand Ni-3dxz,yz orbitals [see Fig. 5(b)], while the states around theCBM are almost contributed by Ni-3dxy,x2�y2 orbitals [seeFig. 5(b) and (e)]. Since the VBM is very close in energy to theband top at the G point, we have plotted the band decomposedcharge density of P-NiS2 at the highest occupied band at G andM points in Fig. 5(c) and (d), respectively. It is found that thehighest occupied band at the G point [Fig. 5(c)] is mainlycontributed by the S-pz and Ni-dxz,yz orbitals, while that at theM point [Fig. 5(d)] is mainly contributed by the Ni-dxz,yz andS-px,y orbitals.

We have further investigated the effect of strain on theelectronic band structures for P-NiS2. The calculated bandstructures with isotropic lattice strains of �3% and +3% forP-NiS2 are plotted in Fig. 6(a) and (b). It is shown that the CBMis always located at the G point for each case. Meanwhile, theVBM is located at the M point under compression strain, whileit moves to the G point under tensile strain, resulting in anindirect to direct band gap transition at the G point. Thecorresponding direct and indirect energy gaps versus strainfrom �5% to +5% are plotted in Fig. 6(c). We find that theenergy gap Eg(M � G) increases as Eg(G � G) decreases and thetransition from indirect to direct band gap occurs at a smalltensile strain of 0.55%. These results suggest that the P-NiS2monolayer is a semiconductor with a strain-engineeredindirect-to-direct band gap transition.78

Fig. 5 (a and b) Electronic band structure and density of states (DOS) ofthe P-NiS2 monolayer using hybrid density functional HSE06. The Fermilevel is set to zero eV. The valence band maximum and conduction bandminimum are at the M and G point, respectively. (c–e) The band-decomposed partial charge densities for the highest occupied band atthe G point (c), the highest occupied band at the M point (d) and the lowestunoccupied band at the G point (e). The isosurfaces are 0.05 e Å�3.

Fig. 6 Strain-induced electronic band structures for the P-NiS2 monolayer. (a) Band structure under a compression strain of 3%. (b) Band structureunder a tensile strain of 3%. The Fermi energy was set to zero. (c) Energy gaps versus strain. The indirect energy gaps (black line) are given between thehighest occupied band at the M point and the lowest unoccupied band at the G point, Eg(M � G). The direct energy gaps (red line) are shown between thehighest occupied band and the lowest unoccupied band at the G point, Eg(G � G).

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4 Conclusions

In conclusion, we have identified by ab initio calculations a newtype of 2D atomic crystal with a pentagonal network, P-NiS2.Our calculations show that it is energetically more stable thanall previously reported NiS2 monolayers. Its dynamic stabilityhas been confirmed by phonon mode analysis. Moleculardynamics simulations show that the P-NiS2 monolayer hasrobust thermal stability at room temperature. Electronic bandstructures reveal that P-NiS2 is a semiconductor with an indirectband gap of 1.94 eV. More interestingly, the P-NiS2 monolayerundergoes a band gap transition from indirect to direct when asmall tensile strain of 0.55% is applied, revealing promisingapplications in optoelectronics.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We acknowledge financial support from the National KeyResearch & Development Projects of China (No. 2016YFA0202300),the National Natural Science Foundation of China (No. 61888102),the Strategic Priority Research Program of Chinese Academy ofSciences (No. XDB30000000), and the K. C. Wong EducationFoundation (No. GJTD-2019-02). MD simulations were carried outon TianHe-1A at the National Supercomputer Center in Tianjin.

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Paper PCCP

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