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C: Physical Processes in Nanomaterials and Nanostructures

Distorted Janus Transition Metal Dichalcogenides: Stable Two Dimensional Materials with Sizable Band Gap and Ultrahigh Carrier Mobility Xiao Tang, Shengshi Li, Yandong Ma, Aijun Du, Ting Liao, YuanTong Gu, and Liangzhi Kou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04161 • Publication Date (Web): 26 Jul 2018 Downloaded from http://pubs.acs.org on August 2, 2018

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The Journal of Physical Chemistry

Distorted Janus Transition Metal Dichalcogenides: Stable Two Dimensional Materials with Sizable Band Gap and Ultrahigh Carrier Mobility

Xiao Tang1, Shengshi Li2, Yandong Ma2, Aijun Du1, Ting Liao1, Yuantong Gu1, Liangzhi Kou1* 1

School of Chemistry, Physics and Mechanical Engineering, Science and Engineering Faculty, Queensland

University of Technology, Gardens Point Campus, Brisbane, QLD 4001, Australia 2

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Str. 27,

250100 Jinan, People's Republic of China [email protected]

1 ACS Paragon Plus Environment

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ABSTRACT Transition metal dichalcogenides (TMDs) are ideal layered materials to fabricate field effect transistors (FETs) due to sizable band gaps and high stability, however the low carrier mobility limits the response speeds. Here, based on recent experimental progress, we employed first principle calculations to reveal a distorted phase of the Janus TMD, 1T’ MoSSe, which is highly stable, exhibiting moderate band gap and ultrahigh carrier mobility. We show that 1T’ MoSSe can be obtained via structural transition from the synthesized 2H phase after overcoming an energy barrier of 1.10 eV, which can be significantly reduced with alkali metal adsorption, thus proposing a feasible approach for experimental fabrications. 1T’ MoSSe is predicted to a semiconductor with trivial band gap of 0.1 eV (based on HSE calculations), which can be closed to form Dirac nodes and then reopened under strain deformation. Due to the almost linear dispersion of the band states, an ultrahigh electron (hole) mobility up to 1.21×105 (7.24×104) cm2 V−1 s −1 is predicted for the new phase, which is three orders of magnitudes higher than traditional counterparts and close to the value of graphene. The high stability, sizable band gap and ultrahigh carrier mobility in the new Janus systems are expected to be used in high performance electronics applications.


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INTRODUCTION The successful exfoliation of graphene1 has inspired extensive investigations of two-dimensional (2D) materials due to the outstanding mechanical, high carrier mobility (2×105 cm2V−1s−1)2, excellent electronic properties, and the promising applications.3-4 However, the zero band gap of graphene limits its applications in semiconducting electronics. Monolayer transition metal dichalcogenides (TMDs with formula of MX2; M=W, Mo; X=S, Se, Te) have been regarded to be one of perfect candidates to replace graphene, because of the high structural stability, easy fabrication and large band gaps.5-8 Especially, the semiconducting properties of 2H TMDs with the gap over 1 eV have opened a realm of photonic and electronic possibilities and revealing a wide range of functionalities such as photodetectors, transistors and electroluminescent devices.9-11 The FETs based on MoS2 have been demonstrated to exhibit an ultrahigh room temperature on-off ratio of 1×108 and ultralow standby

power dissipation due to the sizable band gaps12. However, the relatively low carrier mobility of 200410 cm2 V−1s−1 is the bottleneck to determine the performance, which severely limits the response speed. Looking for a 2D layered material which combines the three merits of sizable band gap, high carrier mobility and high stability is therefore desirable and essential to move the low-dimensional electronics forward. Structural phase transition is a possibly feasible approach to improve the low carrier mobility of TMDs as the corresponding electronic/transport properties can be effectively modulated. Meanwhile the unique triple layer sandwiched structure of TMDs provides an excellent platform for structural phase modulations. A variety of polytypic crystal structures with distinct properties originated from the different atomic stacking sequences has been revealed, such as 2H, 1T, and 1T’ phase. 2H TMDs are semiconductors and can be easily fabricated via mechanical exfoliation or chemical growth, the structure is featured with chalcogen atoms from two sides on top of each other. When the chalcogen atom at one side is shifted, it can be transferred into metallic 1T phase, but typically unstable under ambient condition.13 It experiences a lattice distortion spontaneously to form a period-doubling 2×1 structure with higher stability— 1T’ structures14-17, showing non-trivial topological states.18-19 The three structural phases are reversibly transferrable with the aids of external stimuli like strain, annealing, electron-beam irradiation,20-21 and chemical methods like doping with Re atoms22 or adsorption of alkali metal atoms.

6, 23-25

The intriguing phase engineering has been used for TMDs based device design. For

example, the locally induced 1T MoS2 in semiconducting 2H phase nanosheets can be engineered to build FETs with metallic 1T phase MoS2 as electrodes to achieve low-resistance contacts.26 The structural phase transitions in TMDs provide the possibilities for exploring novel material properties and practical device applications. Here, we reveal a new phase of TMDs via structural transition which possess high structural stability, semiconducting properties and ultrahigh carrier mobility, based on the recent successful synthesized 2H MoSSe, a Janus TMD monolayer.27 The Janus MoSSe exhibits hexagonal lattices as observed from 3 ACS Paragon Plus Environment


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experimental measurements,28 but different electronic properties from conventional MX2 owing to the broken out-of-plane structural symmetry.29-30 For instance, Janus MXY monolayers possess the highly desired vertical piezoelectric effect, which could greatly increase the flexibility and compatibility in piezoelectric device operations. The out-of-plane piezoelectricity also provides platform to design nanoelectromechanical devices and future spintronics.

27, 30

However, these researches are based on the 2H phase of the Janus TMD, the

possible new phases, like 1T or distorted 1T’ phases which are important for device design and expected to occur as in MX2, and corresponding physics, are unclear yet. In this paper, we systematically investigated the phase stability and electronic properties of a new phase of the Janus TMD, 1T’-MoSSe, and proposed a feasible approach to achieve the structural phase transition. It is found that this new phase 1T’ is thermally and dynamically stable. The energy barrier for 2H to 1T’ phase transition is around 1.10 eV, which can be remarkably reduced with Li adsorption to 0.55eV. 1T’ MoSSe is found to be a semiconductor with gap of 0.10 eV which is effectively tunable with strain, and closed at strain of 1% to form the Dirac nodes. Most importantly, 1T’ MoSSe shows ultrahigh carrier mobility which is up to 1.2×105 cm2 V−1 s −1, it is 3 magnitude higher than traditional TMDs and close to that of graphene. Furthermore, the other 1T’ MXY (M= Mo, W, X/Y =S, Se, Te, and X≠Y) are shown to be stable, and exhibit metallic or semiconducting properties depending on the composed elements. The investigations paved the way for applications of the new phase TMDs in high performance electronics and pointed out feasible synthesis approaches.

COMPUTATIONAL DETAILS All calculations based on density functional theory (DFT) were carried out using the Vienna ab initio simulation package (VASP)31 with projector augmented wave method32 and the plane wave energy cutoff was set to 400 eV. The exchange-correlation energy is used by the Perdew-Burke-Ernzerhof (PBE) function33 within the generalized-gradient approximation (GGA)34-35 for the calculation of geometries and band structures of Janus monolayers of transition metal dichalcogenides. A dispersion correction of total energy (DFT-D3 method) was used in order to incorporate the long-range van der Waals interaction.36 The hybrid DFT based on the HeydScuseria-Ernzerhof (HSE) exchange-correlation functions wad adopted to correct the well-known underestimation of the band gap in the PBE calculations. A vacuum thickness at least 15Å was set to minimize interactions from periodic boundary condition. The Brillouin zone was represented by Monkhorst-Pack special k-point mesh37 of 9×9×1 for geometry optimization. All the atoms were fully relaxed until the residual force and energy converged to 0.01eV/Å and 10-5eV, respectively. Moreover, first-principles calculations of the phonon spectrum were carried out using VASP31 and Phonopy.38 We constructed a 4×4×1 supercell with


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3×3×1 k-mesh points for both 2H-MoSSe and 1T-MoSSe (4×8×1 supercell with 2×2×1 k-mesh points for 1T’MoSSe) for calculating the phonon spectrum accurately.

RESULTS AND DISCUSSION As a benchmark, we firstly calculated the structural parameters of the trigonal prismatic 2H-MoSSe with GGAPBE. The relaxed model of 2H-MoSSe monolayer is shown in Figure 1(a). Each Mo is coordinated by three neighboring S atoms on one side and another three Se atoms on opposite side, with Se atoms lying directly above those S atoms. The calculated lattice constants are a=b=3.24 Å, which are consistent with the experimental values (a=b=3.22 Å)39-40 as well as previous theoretical results (a=b=3.23-3.25 Å).27-28 Due to the differences of electrostatic potential on both sides, the length of Mo-S bond and Mo-Se bond are different, which are 2.42 and 2.53 Å, respectively. The thickness, namely the distance between top Se layer and bottom S layer is 3.25 Å. These results are also well consistent with the previous reports.27 Similar to MoS2, where the metallic 1T phase can be obtained by shifting one side of S atoms with 1/3 lattice constant with aid of annealing, doping, strain or electron-beam irradiation, we built 1T Janus MoSSe using the same strategy, where all the Se atoms on top surface are shifted with 1/3 lattice constant. As 1T-MX2 is unstable and typically undergoes a lattice distortion spontaneously to form a period-doubling 2×1 distorted 1T’-MX2 configuration, we therefore built three models of (1×1), (1×1), (2×1) supercells for 2H-MoSSe, 1TMoSSe, 1T’-MoSSe in our work, respectively. Figure 1(b) and Figure 1(c) show the side and top views of optimized atomic structure of 1T-MoSSe and distorted octahedral coordinated 1T’-MoSSe. Three Se atoms and three S atoms form a distorted octahedron around each Mo atom in 1T phase and the Mo-Se bond length is slightly elongated as compared to 2H phase. The lattice constant is slightly reduced to 3.20 Å. For 1T’-MoSSe, the lattice constants along two directions are 3.21 and 5.84 Å shown as in Figure 1c, the length of Mo-S and Mo-Se bond ranges from 2.39-2.54Å and 2.51-2.62 Å, respectively. Due to the reconstruction and distortion, the Se (or S) atoms of one side are not at the same plane.



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Figure 1. Side and top view for the optimized geometries of (a) 2H-MoSSe, (b) 1T-MoSSe, and (c) 1T’-MoSSe unit cell. The cyan, yellow and brown balls represent Mo, S and Se atoms, respectively. The dashed lines indicate the unit cell used for the calculations.

As the 1T and 1T’ phase of Janus MoSSe are artificially built and theoretically proposed based on synthesized 2H MoSSe following the idea of MoS2, we firstly checked the structural stability of these phases before the investigations of the electronic properties. From the energy calculations, it is found that the experimental synthesized 2H-MoSSe has the lowest total energy among the three phases, the energy is lower than the 1T-MoSSe by 0.71eV for a unit cell, and 0.44eV than 1T’-MoSSe. These phases thus have the stability order of 2H > 1T’ > 1T from the energetic perspective. To assess the experimental feasibility of these materials, we then evaluate the dynamical stabilities of the three structures by calculating phonon band structures along the high-symmetry lines. Imaginary modes are found for 1T phase (Figure S1), indicating that 1T-MoSSe is unstable similar to the 1T-MX2.14 Due to the kinetic structural instability, we will not pay much attention to the phase. In contrast, the imaginary frequency in the phonon spectrum in 2H-MoSSe is absent which not only confirms the kinetic stability of this recently synthesized phase (Figure S2), but also demonstrated the validity of the used methods. The highest frequency of 2H-MoSSe reaches up to 12.93 THz, which is close to the recent theoretical results (~ 13THz).27 Except 2H phase, the 1T’-MoSSe is also kinetically stable from phonon spectrum (Figure 2a) due to the absence of the imaginary frequency. The highest frequency of newly predicted structure is 12.73THz, which is within the range ~10THz (for 1T’-MoSe2) to ~14THz (for 1T’-MoS2).18 We also calculated the formation energy (Eform) of 1T’-MoSSe with the formula: Eform = (Etot - nEMo-nES-nESe)/3n, where Etot is the total energy of the 1T’-MoSSe, EMo, ES, ESe are the energies of a Mo, S, Se atoms in their bulk phases, respectively; n is the number of atoms of each element in the supercell. The formation energy for 1T’MoSSe is -4.77 eV/atom, indicating this phase is energetically favorable. The thermal stabilities are further examined by performing Ab-initio molecular dynamics (AIMD) simulations at the temperature of 500K using (5×5) supercell for 2H-MoSSe and (3×6) supercell for 1T’-MoSSe. It is found that the total energies for both structures fluctuate smoothly with small amplitudes. Moreover, no evident structure destructions are observed after 1.5 ps, see the snapshot structures of 1T’-MoSSe at Figure 2b, which suggests their high thermal stabilities at mild environment of 500K, therefore should be experimentally observable at room temperature. 6 ACS Paragon Plus Environment

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Figure 2. (a) Phonon dispersion of the fully optimized 1T’-MoSSe. (b) Snapshot of 1T’ MoSSe at the temperature of 500K after 1.5 ps

After the structural stabilities were confirmed, we investigated the possibilities to fabricate 1T’ Janus MoSSe through phase transition from experimental synthesized 2H-MoSSe. The energy barriers between 2H and 1T or 1T’ phases are therefore calculated from climbing-image nudged elastic band (CI-NEB) method41 to provide the kinetic insights for the phase transition, see Figure 3. Two possible transition pathways were proposed to fabricate the 1T’ MoSSe as discussed following: 2H-1T-1T’ and 2H-1T’. For the indirect pathway (2H-1T-1T’), 1T phase is regarded as the metastable intermediate state although it is not stable as indicated from the phonon calculations. As calculated from CI-NEB method, the energy barrier is 1.27eV from 2H to 1T phase transition which is slightly lower than the corresponding value (1.59 eV for 2H-1T phase transition) of MoS2.21 Due to the structural instability, there is no energy barrier between 1T and 1T’ phases, it will be automatically transferred to the distorted structure, 1T’ MoSSe. For the second pathway, the distorted phase 1T’ can be obtained directly via 2H to 1T’ phase transition after overcoming an energy barrier of 1.10 eV. In either case, a large energy barrier need to be overcome, which leads to a major experimental challenge. Inspired by previous reports that the doping, strain and electron-beam irradiation are effective approaches to induce the phase transition in MX2,

23-24, 42-43

we also checked the effects of strain and alkali metal adsorption on the

energy barrier and propose a feasible way to achieve the new phase. Firstly, the in-plane tensile strain of 5% is applied to Janus MoSSe, however it is found that the effect of applied strain is ignorable, the energy barrier of 2H-1T keeps unchanged while the barrier of 2H-1T’ is slightly reduced by 0.07 eV. In contrast, alkali metal adsorption (with Li as a representative example) on the surface significantly reduces the energy barriers. For instance, the barrier of 2H to 1T phase transition is reduced to 0.98 eV while the barrier for 2H to 1T’ is only 0.55 eV when Li is adsorbed on the S side of 1T’ MoSSe, see Figure 3. When Li atom is placed on the Se side, the barrier for 2H-1T is reduced to 0.79 eV while that for 2H-1T’ is 0.60 eV. The barrier difference between Li on Se and S sides is originated from the intrinsic polarization along thickness direction induced by asymmetric 7 ACS Paragon Plus Environment


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structure of MoSSe, which will lead to different amount electron transfer. It is worthy to note that the ground energy of 1T’ with Li is even lower than other two phases (2H and 1T), which means such new Janus distorted phase is observable in experiments when alkali metals are adsorbed on the surface. The similar findings have been observed in MoS2, 6, 23-24, 42 or InSe monolayers,20 the energy barrier of phase transition after Li, Na or K adsorption can be significantly reduced. It is worth mentioning that the structural transformation between MoS2 2H and 1T phase has been verified in experiments,44 therefore distorted 1T’ Janus MoSSe is highly expected to be experimentally synthesized with doping or electron-beam irradiation like the success example in MoS2.

Figure 3. The energetic barrier between Janus MoSSe under different phases. The effects of strain deformation and Li adsorption on different sides are presented.

After the phase transition, 1T’-MoSSe displays different electronic features. As shown in Figure 4a, 2HMoSSe is a semiconductor with a direct band gap of 1.53 eV at K point based on the PBE functional, obvious band splitting can be seen for all band states due to the Rashba effects induced by out-plane symmetry breaking in the Janus system27. This calculated value is well consistent with the recent predicted result (1.56 eV)27 and also experimental measurements. For the unstable 1T-MoSSe, it is metallic like most 1T-MX2 compounds (See Figure S3). After the distortion, 1T’-MoSSe become a semiconductor with a band gap of 0.02 eV near Γ point (PBE calculations), while the conduction band minimum (CBM) and valance band maximum (VBM) exhibit Dirac-like linear band dispersions near the Fermi level as in graphene. We notice that the band gap of 1T’ MoSSe is remarkably smaller than the corresponding values of 1T’ MoS2 (0.044 eV) or MoSe2 (0.031 eV) from the standard DFT calculations,18 this results from the significant band splitting near the Fermi level induced by Rashba effects in the asymmetric structure, see Figure 4b. Meanwhile, in contrast to the topological insulating properties of 1T’ MoS2 and MoSe218, the Janus 1T’ MoSSe is a trivial semiconductor as confirmed from the topological invariant index Z2 (Figure S4) due to the intrinsic electric field along thickness direction (see following discussions). To clearly see the band dispersion of the bands near the Fermi level in the first Brillouin Zone, we plotted the 3D bands (see the inset of Figure 4b), it can be seen the CBM and VBM are located at two points along Γ-Y direction, which will meet with each other to form two Dirac nodes under proper strain 8 ACS Paragon Plus Environment

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deformation. It is known that PBE exchange correlation functional generally underestimates the band gap,45 a hybrid functional (HSE06) were thus performed to correct the gap value. Our result clearly shows that the general curves for the valence band (VB) and conduction band (CB) are similar for both PBE and HSE06 functionals, except the enlarged band gap value. Due to the shifts of the VB and CB positions, the band gaps of 2H-MoSSe and 1T’-MoSSe are corrected to 1.95 and 0.10 eV (Figure 4), respectively. The band gap of 1T’ phase is very close to a recent theoretical result (0.07 eV)46.

Figure 4. Band structures calculated by PBE (black line) and HSE06 (red line) functionals of (a) 2H-MoSSe, (b) 1T’MoSSe, respectively. The inset is the 3D band structure near the Fermi level. The spin orbit coupling effect is included for band structure calculations. The Fermi level was set to zero.

The Dirac-like linear dispersion of the band states along Γ-Y direction (Figure 4b) implies the small

effective mass of the carriers ∗ and expected large carrier mobility. From the energy-moment

dispersion relation, it is estimated that the effective electron mass along a direction is 0.13 me while the effective hole mass is -0.17 me. In contrast, the corresponding values along b direction are much larger, which are 0.77 and -0.61 me respectively due to the anisotropic band dispersions along Γ-Y and Γ-B directions, see Figure 4. The carrier mobility of 1T’ MoSSe was then calculated based on the deformation theory47, which has been widely used to predict the carrier mobility of 2D layer materials48-49 although it generally tends to overestimate the values. According to the deformation theory, the carrier mobility of 2D systems can be calculated by the formula: μ

∗

. Here, C2D is the elastic modulus and defined as C

/" #/$%, in which " is the applied uniaxial strain, and $% is the area of the optimized 2D structure. m∗ is the effective mass, T is the temperature (300K), and KB is the Boltzmann constant; E1 is the deformation potential constant, which is defined as ∆E=E1(∆l/l0), in which ∆E is the energy shift of the band edge position with respect to the lattice dilation ∆l/l0 along the direction a or b. The energy-strain relation and CBM & VMB variations as a function of strain are presented in Figure S7. Table 1 Carrier Effective Mass (m*), Elastic Module (C2D), Deformation Potential Constant (E1), and Carrier Mobility (µ) of the 1T’ MoSSe 9 ACS Paragon Plus Environment


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Carrier type

E1 (eV)

C2D (J/m2)

m* (me)

µ (×103cm2V-1s-1)

electron (a)

0.90

116.08

0.13

121.02

hole (a)

0.89

116.08

-0.17

72.36

electron (b)

-1.48

102.42

0.77

1.12

hole (b)

-1.21

102.42

-0.61

2.68

Our results for effective masses, elastic module, deformation potential and carrier mobility are summarized in Table 1. For the 1T’ MoSSe, the elastic moduli along a and b directions are 116.08 and 102.42 J/m2 respectively, which are remarkably larger than the values of recent reported 2D materials (~60 J/m2: CaP3;48 ~43 J/m2: InP350). E1 values for electron and hole are almost the same along a direction as 0.9 and 0.89 eV, but they are anisotropic along b direction (1.48 and 1.21 eV, respectively). Due to the small effective masses of carriers and large elastic module, an ultrahigh carrier mobility is induced along a direction, which is calculated as 1.21×105 (7.24×104) cm2 V−1 s −1 for electron (hole). The values are quite close to that of suspended graphene (2×105 cm2 V−1 s

−1

) at room temperature, and ~3 magnitude orders higher than MoS2 (200-410 cm2 V−1 s−1)12

while 1~2 magnitude order higher than phsosphorene (5,200-10,000 cm2 V−1 s−1)51. In contrast, the carrier mobility along b direction are much smaller due to the larger effective carrier masses, they are estimated as 1.12×103 and 2.68×103 cm2 V−1 s −1 for electron and hole, but the values are still obviously larger than these of MoS2. The large carrier mobility in 1T’ phase is originated from the modified band structures, see Figure 4, and small effective mass. It can be seen that the newly revealed 1T’ MoSSe not only has inherited the merits of TMDs (high stability and semiconducting properties), but also significantly improved the weakness (carrier mobility). The ultrahigh carrier mobility, high stable structure together with semiconducting properties render it promising for high performance electronics applications with high speed response. We then check the robustness of band gap in 1T’ MoSSe under stain deformation as strain engineering is an effective and economic approach to modulate the electronic properties of nanomaterials.52-53 Here we investigate the band gap variations of two stable phase 2H- and 1T’-MoSSe as a function of biaxial tensile strain (compressive strain is not studied as 2D materials would be buckled). The spin-orbit coupling (SOC) effect, which is originated from the d orbitals of the heavy Mo atom,54 is switched on and off to check its effect on band topology. For 2H-MoSSe, the band gap is reduced by biaxial tensile strain linearly regardless of inclusive or exclusive the effect of SOC, see Figure S5. In contrast, the band gap variation of 1T’ MoSSe as a function of strain is non-linear as in 2H phase. Figure 5(a) shows the band gap variation of 1T’-MoSSe calculated by PBE as a function of biaxial strain. When SOC is exclusive, the band gap (0.04 eV at free standing situation) is firstly reduced, but soon closed at critical strain of 2%, and then reopened under increased strain deformation, reaches up to 0.12 eV in 5%. As SOC is switched on, the band states near the Fermi level are split, the CBM and VBM states come closer, reducing the gap to 0.02 eV, see Figure 5c. Under the strain 10 ACS Paragon Plus Environment

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deformation, the gap is also reduced firstly, and closed at strain of 1% to form two Dirac nodes, then reopened at 2%, see Figure 5c. Note that the gap variation after the critical strain of 1% is quite gentle, because the second conduction band (CBM-1) is shifted downwards under strain deformation. The SOC gap is opened as 0.07 eV at strain of 5%. It should point out the electronic variation under strain is calculated from standard PBE functional, the values are underestimated as shown in Figure 4, however the variation trend is expected to be the same even under hybrid functional calculation although the critical strain to close the band gap will be different. The band gap closure and reopening is generally a signal of the topological phase transition; however it is not the case here. To confirm the statement, we calculated the edge states of 1T’ MoSSe at strain of 0% and 3%, which can well reflect the possible topological phase change. For free standing 1T’ MoSSe, the edge state has even times crossing the Fermi level, see Figure S6, indicating it is a trivial semiconductor, which is consistent with Z2 calculations. Under strain of 3%, the edge band states almost keep the same except slightly shifting, rendering the strained 1T’ MoSSe remaining as trivial.

Figure 5. (a) Band gap variation as a function of applied strain; (b) Workfunction variation under strain. (c) Zoomed band structures near Γ point under different strain deformation with (red solid line) and without (black solid line) spin-orbital coupling. The Fermi level was set to zero.

To understand the band gap variation and trivial phenomena which is different from topological 1T’ MoS2 and MoSe2, we have calculated the electrostatic potential distribution along z direction. Different from 1T’ MoS2 or MoSe2, the different chalcogen atoms at opposite surface of 1T’ MoSSe will lead to the electrostatic potential difference along the thickness direction, and induce an intrinsic interior electric field. From the work function calculation, the electrostatic potential difference for free standing 1T’ MoSSe is 1.36 eV, and 11 ACS Paragon Plus Environment


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significantly reduced to 0.91 eV at the strain of 5% due to the electron redistributions, see Figure 5b. The intrinsic electric field can be estimated to reduce from 0.42 V/Å to 0.29 V/Å (thickness of MoSSe is 3.20Å). At the free-standing situation, 1T’ MoSSe can be approximately regarded as 1T’ MoS2 under the electric field of 0.42 V/Å, which is much larger than the critical value for nontrivial-trivial phase transition (0.14 V/Å).18 Under strain deformation of 5%, although the interior electric field is reduced to 0.29 V/Å, it is still above the critical value, rendering the Janus 1T’ MoSSe keep as the trivial state. Two times’ band closure and reopening in Figure 5 are from the combination effects of interior electric field and SOC. On one hand, the strain induced interior electric field can reduce, close and reopen the band gap of 1T’ MoSSe when SOC is not considered, see Figure 5a (black lines); on the other hand the gap inversion is switched back by the SOC effect (red lines). The synergetic effects from both interior electric field and SOC render strained 1T’ MoSSe keep in the trivial state even there is band gap closure and reopening phenomena as shown in Figure 5a. In order to give a comprehensive picture and also see if the same phenomena can be observed in all distorted Janus TMDs, we also checked the stabilities and electronic properties of other 1T’ MXY (M=Mo, W; X, Y=S, Se, Te; X≠Y) although there is currently no corresponding experimentally progress except MoSSe. However, the 2H phases of all the Janus MXY have been theoretically studied and the stabilities are confirmed, they are semiconductors with significant band splitting.55 For the corresponding Janus 1T’ MXY, we investigated the structures, stability and electronic properties, and summarized the results as in Table 2. It is found that all these Janus 1T’ MXY are stable from phonon frequency investigations, see Figure S8. However, the cohesive energies are generally lower than corresponding phase by 0.03-0.12 eV/atom. Due to the increased SOC strength in heavy elements (like Te, W), the stronger Rashba effect and spin splitting for the states near Fermi level are produced, and therefore the band gaps for some of the materials are closed, leading to the metallization of the 1T’ MXY except WSSe and WSTe, see Figure S9-10. Table 2. Lattice constants, band gaps and cohesive energiesa of other MXY monolayer.

WSSe MoSTe WSTe MoSeTe WSeTe 2H 1T’ 2H 1T’ 2H 1T’ 2H 1T’ 2H 1T’ 3.24 5.83 3.35 6.07 3.35 6.04 3.41 6.18 3.41 6.14 3.24 3.23 3.35 3.29 3.35 3.32 3.41 3.33 3.41 3.37 1.76 0.07 1.14 0.11 1.32 0.04 1.34 -b 1.43 -

Phase a (Å) b (Å) Band gap (eV) Band gap with SOC 1.45 0.03 1.12 1.18 0.01 1.22 1.10 (eV) Ecoh (eV/atom) 5.52 5.39 4.59 4.51 5.15 5.09 4.38 4.32 4.92 4.89 a

Ecoh is the cohesive energy [Ecoh= (nEM+nEX+nEY-EMXY)/3n, where EM, EX, EY, EMXY are the total energies of a single M atom, a single X atom, a single Y atom and MXY, respectively; n is the number of atoms of each element in the unit cell]. bThe “-”sign in the table means there is no gap, it is a metal.


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In conclusion, we have revealed a new phase of Janus MoSSe based on the recent experimental progress, namely distorted 1T’ MoSSe, and proposed a feasible approach to induce the structural phase transition from 2H to 1T’ after overcoming a reasonable low energy barrier. The electronic investigations indicate that the new distorted phase exhibit semiconducting feature with band gap of 0.10 eV, which is tunable with strain deformation and exhibits a pattern of gap closing and reopening originated from synergetic effects of intrinsic interior electric field and SOC. Most importantly, an ultrahigh carrier mobility in the structure has been predicted. Distorted 1T’ phases are also revealed in other Janus TMDs family. The proposed feasible approach to induce structural phase transition and novel electronic properties render the new revealed 1T’ TMDs promising in electronics applications.

ASSOCIATED CONTENT Supporting Information The phonon dispersions and band structures of 2H MoSSe and 1T’ MXY (M=Mo, W; X, Y=S, Se, Te; X≠Y) are presented. The edge states of 1T’ MoSSe under 0 and 3% strain deformation, and Z2 calculations are also shown.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; Tel; 07-31382771 Notes The authors declare no competing ﬁnancial interest.

ACKNOWLEDGMENTS We acknowledge the grants of high-performance computer time from computing facility at the Queensland University of Technology, the Pawsey Supercomputing Centre and Australian National Facility. L.K. gratefully acknowledges financial support by the ARC Discovery Early Career Researcher Award (DE150101854).

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Figure 1. Side and top views for the optimized geometries of (a) 2H-MoSSe, (b) 1T-MoSSe, and (c) 1T’MoSSe unit cells. The cyan, yellow and brown balls represent Mo, S and Se atoms, respectively. The dashed lines indicate the unit cell used for the calculations. 82x28mm (300 x 300 DPI)

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Figure 2. (a) Phonon dispersion of the fully optimized 1T’-MoSSe. (b) Snapshot of 1T’ MoSSe at the temperature of 500K after 1.5 ps. 82x28mm (300 x 300 DPI)


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Figure 3. The energetic barrier between Janus MoSSe under different phases. The effects of strain deformation and Li adsorption on different sides are presented. 82x28mm (300 x 300 DPI)



Figure 4. Band structures calculated by PBE (black line) and HSE06 (red line) functionals of (a) 2H-MoSSe, (b) 1T’-MoSSe, respectively. The inset is the 3D band structure near the Fermi level. The spin orbit coupling effect is included for band structure calculations. 82x28mm (300 x 300 DPI)


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Figure 5. (a) Band gap variation as a function of applied strain; (b) Workfunction variation under strain. (c) Zoomed band structures near Γ point under different strain deformation with (red solid line) and without (black solid line) spin-orbital coupling. 82x28mm (300 x 300 DPI)



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Distorted Janus Transition Metal Dichalcogenides ... - ACS Publications

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