Electronic and magnetic properties of MoS2 nanoribbons with sulfur line vacancy defects

Accepted Manuscript Title: Electronic and Magnetic Properties of MoS2 Nanoribbons with Sulfur Line Vacancy Defects Author: Yang Han Jian Zhou Jinming Dong PII: DOI: Reference:

S0169-4332(15)00311-6 http://dx.doi.org/doi:10.1016/j.apsusc.2015.02.016 APSUSC 29695

To appear in:

APSUSC

Received date: Revised date: Accepted date:

15-11-2014 31-1-2015 2-2-2015

Please cite this article as: Y. Han, J. Zhou, J. Dong, Electronic and Magnetic Properties of MoS2 Nanoribbons with Sulfur Line Vacancy Defects, Applied Surface Science (2015), http://dx.doi.org/10.1016/j.apsusc.2015.02.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Electronic and Magnetic Properties of MoS2 Nanoribbons

Yang Han1, Jian Zhou2 and Jinming Dong1,a) 1

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with Sulfur Line Vacancy Defects

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Group of Computational Condensed Matter Physics, National Laboratory of Solid State

Microstructures and Department of Physics, Nanjing University, Nanjing 210093, P. R. China 2

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Engineering, Nanjing University, Nanjing 210093, P. R. China

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National Laboratory of Solid State Microstructures and Department of Materials Science and

ABSTRACT

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Motivated by the recent experimental result that single sulfur vacancies in monolayer MoS2 are mobile under the electron beam and easily agglomerate into the sulfur line

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vacancy defects [Physical Review B 88, 035301(2013)], the structural, electronic and

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magnetic properties of one dimensional zigzag (ZZ) and armchair (AC) edge MoS2

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nanoribbons with single or double staggered sulfur line vacancy defects (hereafter, abbreviated as SV or DV, respectively), parallel to their edges, have been investigated systematically by density functional theory calculations. It is very interesting to find that the bond strains induced by the sulfur line vacancy defect can cause a much larger out-of plane distortions in the ZZ edge MoS2 nanoribbon than in the AC edge counterpart. Besides, the defective ZZ edge MoS2 nanoribbons with SV or DV are both metals, having their two respective degenerate ground states with the same energy, among which one is ferromagnetic (FM “++”) and the other is antiferromagnetic (AFM “+”). But the AC edge MoS2 nanoribbons with SV or DV are both nonmagnetic semiconductors, having very different gap values. Finally, the sulfur line vacancy defects would induce some defect states in the electronic structures of the defective MoS2 nanoribbons. All these important

a)

Corresponding author: [email protected]

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results could provide a new route of tuning the electronic properties of MoS2 nanoribbons and its derivatives for their promising applications in nanoelectronics and optoelectronics. KEY WORDS: electronic and magnetic; out-of plane distortion; MoS2 nanoribbon; sulfur

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line vacancy defect

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I. INTRODUCTION The new novel two dimensional (2D) graphene-like monolayer MoS2 [1] has

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stimulated a great interest of researchers working in different fields in the world due to its promising applications in nanoelectronics and optoelectronics [2]. Its intrinsic direct

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band-gap[1] and good photoluminescence[3-5] have made it a good complementary material to the semimetal graphene with an intrinsic zero band-gap [6], thus suggesting its

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practical applications in the next generation of nanoelectronics and optoelectronics

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devices.

Monolayer MoS2 has a layered structure, containing three atomic layers composed of

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one Mo layer sandwiched between two S layers, which is different from those of plane-like graphene [7] and h-BN [8]. Correspondingly, its bulk structure can be formed by stacking monolayer MoS2 through weak van der Waals interaction. Recently, very thin MoS2 films

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and even monolayer structure, prepared on a substrate [9-12] or freely suspended [1, 13]

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have been successfully realized in experiments by several methods, such as through the

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micromechanical cleavage technique [1, 13], chemical exfoliation of the bulk sample[3, 14], as well as by chemical vapor deposition (CVD) [9, 15-17]. In addition, the one dimensional (1D) MoS2 nanoribbons have been fabricated experimentally by a two-step electrochemical/chemical synthetic method [18, 19]. Following the experimental fabrication, an explosion of theoretical studies have been

done [20, 21]. Previous first-principles calculations have shown that the zigzag (ZZ) edge MoS2 nanoribbons, as shown in Fig. 1(a), are ferromagnetic (FM) metal, whereas the armchair (AC) edge ones, as shown in Fig. 1(b), are nonmagnetic semiconductors with a width-dependent band gap [20, 21]. Additionally, their magnetic and electronic properties can be tuned by several ways, such as applying an external electric field, elastic strain, or introducing some defects etc.[22-26]. For example, in 2012, Dolui et al. showed that the 3/3

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band gap of AC edge MoS2 nanoribbon can be significantly reduced by applying an external transverse electric field, even leading to a metal-insulator transition beyond a certain critical field value[24]. In the same year, Pan et al. studied the strain effects on the

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electronic and magnetic properties of MoS2 nanoribbons[25]. Shortly after that, the effective modulation of physical properties of ZZ edge MoS2 nanoribbons by a

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combination of strain engineering and electric field has been investigated[26]. The similar

nanoribbons has also been studied recently[27].

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combination effect on the electronic and magnetic properties of the AC edge MoS2

On the other hand, the topological defects, such as the line defects, dislocations and

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grain boundaries, exist inevitably in the graphene, h-BN and monolayer MoS2, which have an important effect on their physical properties, and correspondingly already been

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investigated theoretically and experimentally[28-30]. For instance, the grain boundaries composed of the sets of squares and octagons (4−8) or pentagons and heptagons (5−7)

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defects in the MoS2 sheet have been recently proposed and observed in experiments by the

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CVD method [15, 28, 31]. Recently, Duy Le et al. have investigated the vacancy structures on one side of monolayer MoS2 by the density functional theory calculations, finding that

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the formation energy per sulfur vacancy is the lowest (energetically favorable) if the vacancies form a row. And the longer the vacancy row, the lower the formation energy value[32].

Besides, one or two lines of single sulfur vacancies (here, SV or DV) have been

recently proposed from both experimental results and corresponding theoretical calculations [33], whose geometric structures are shown in Figs. 1(c) and 1(d). Also, the production, diffusion, and agglomeration of the single sulfur vacancies in monolayer MoS2 under electron irradiation have been studied in Ref.[33], in which, the single sulfur vacancies are particularly found to be mobile under the electron beam, tending to agglomerate into SV lines, which must have a big effect on the electronic and magnetic properties of MoS2 nanoribbons. 4/4

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Therefore in this paper, we have explored the fascinating electronic and magnetic properties of 1D MoS2 nanoribbon with one or two staggered sulfur line vacancy (SV or DV) defects along the zigzag (ZZ) or armchair (AC) directions by the first-principles

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calculations. For simplicity, we have only considered the normal ZZ and AC edge types of MoS2 nanoribbons without the complicated edge reconstructions. It is found that the

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defective ZZ edge MoS2 nanoribbon with the SV or DV defects are both metal with a FM coupling along the same edge, but the AC edge ones with the SV or DV defects are

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nonmagnetic semiconductors with a similar or a much smaller band gap value, compared with that of the pristine AC edge MoS2 nanoribbons. And some defect states are found to

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appear in the electronic structures of the defective MoS2 nanoribbons due to existence of the sulfur line vacancy defects. All these important results could provide a new route of

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tuning the electronic properties of MoS2 nanoribbons and its derivatives for their promising applications in nanoelectronics and optoelectronics.

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II. MODELS AND METHOD By cutting a perfect monolayer MoS2 along the zigzag (ZZ) or armchair (AC)

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direction into the ribbons with different widths, the quasi-one dimensional (Q1D) MoS2 nanoribbon can be obtained, which can be denoted by a symbol of “xx-MoS2-RB-N”, where xx= ZZ or AC indicates its edge type (zigzag or armchair one), and the number N represents the number of zigzag or armchair Mo-S chains in the ZZ or AC edge MoS2 ribbon. For example, the geometrical structures of the ZZ-MoS2-RB-10 and AC-MoS2-RB-18 are shown in Figs. 1(a) and 1(b), with their top and side views, lying on the top and bottom panels, respectively. In this paper, following the previous experimental and theoretical results, only two types of sulfur line vacancy defects are considered, among which one is single sulfur vacancy (SV) line defect and the other is double sulfur vacancy (DV) line defect in a staggered configuration[33]. Because the line vacancy defect orientation can be taken 5/5

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along the ZZ or AC direction, there can be four types of sulfur line vacancy defects, denoted by ZZ-SV, ZZ-DV, AC-SV and AC-DV, respectively. The geometric structures of both the ZZ and AC edge MoS2 nanoribbons with SV or DV line defect, parallel to

ZZ-SV-MoS2-RB-(n,m),

ZZ-DV-MoS2-RB-(n,m),

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their edges, are shown in Figs. 1(c) and 1(d), respectively, which will be denoted as the AC-SV-MoS2-RB-(n,m)

and

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AC-DV-MoS2-RB-(n,m), respectively, in the following. All of them are still a quasi-one dimensional (Q1D) periodic system along their line vacancy defect directions. Here, a pair

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of integers n and m represents the numbers of zigzag or armchair Mo-S chains in two sides of the line vacancy defect, respectively. If n=m, the Q1D MoS2 nanoribbon with

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sulfur line vacancy defect is called as the symmetrical one. Otherwise, it is unsymmetrical (nm). In the following, we only focus on the the symmetrical ones at

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different ribbon widths because the electronic and magnetic properties of the unsymmetrical ones are found to be similar to those of symmetrical ones so long as they

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are wide enough.

Fig. 1 (Color online) Schematic shows of (a) the ZZ-MoS2-RB-10 and (b) the AC-MoS2-RB-18 with their top and side views, lying on the upper and lower panels, respectively. Here, the two black solid lines in (a) and (b) indicate their unit cells. (c) Geometric structures of the ZZ-SV-MoS2-(4,5) and 6/6

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ZZ-DV-MoS2-(4,4), shown in the upper and lower panels, respectively. (d) Same as (c), but now for both the AC-SV-MoS2-(8,9) and AC-DV-MoS2-(8,8). In both (c) and (d), the red opened circles denote the initial S vacancy positions. The Mo and S atoms in the blue rectangle box are selected as those

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atoms nearby the S vacancy, which will be used for analyzing the PDOS. Here, the Mo atoms are represented by big purple balls, but the S atoms on the top and bottom layers denoted by the small

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yellow and green balls, respectively.

We performed both the spin unpolarized and polarized density functional theory (DFT)

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calculations in the generalized gradient approximation (GGA) by the Perdew–Burke– Ernzerhof (PBE) exchange-correlation[34], implemented with the Vienna Ab-initio

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Simulation Package (VASP)[35-38], in which the projected augmented wave method [39, 40] is adopted. A kinetic energy cutoff of 350 eV for the plane-wave basis set is employed.

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The 5s14d5 orbitals of the Mo atom and the 3s23p4 orbitals of the S atom are treated as valence ones. The ribbon is placed along the Y direction, with a large enough vacuum

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region in both X and Z directions (>15 Å ) in order to make spurious interactions between

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two nearest samples negligible. We utilize the Monkhorst–Pack k-point meshes of the 1211 unit cells for the first Brillouin zone (BZ) summation, in order to ensure energy

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convergence in optimizing structures and total energy calculations. All atoms and the simulation box in y direction are fully relaxed. Geometric structure optimizations were performed by using the conjugate-gradient algorithm with the maximum residual force at each atom less than 0.02 eV/Å. The allowed error in total energy for the electron self-consistent loop is 10-5 eV. A much denser k points are used to calculate the band structure.

The similar level of calculations (VASP, GGA-PBE) has been made to study the physical properties of the MoS2 system with defects in previous works [32, 33, 41]. We have further validated our calculations by improving the calculation precision, but found no any change for our conclusions.

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III. RESULTS AND DISCUSSIONS A. Geometric structures of MoS2 nanoribbon with sulfur line vacancy

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defect

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We have investigated the Q1D MoS2 nanoribbon with the sulfur line vacancy defect only in the symmetric configuration, in which the sulfur line vacancy defect locates in the

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middle of the ribbon. For the AC edge ones, the AC-SV-MoS2-RB-(8,9) and the AC-DV-MoS2-RB-(8,8) are taken as examples, whose optimized geometrical structures

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are shown in Figs. 2(a) and 2(b), respectively. It can be seen that both of them lie almost in a plane structure with only a little bit out-of-plane distortion (wrinkle), especially for the

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AC-DV-MoS2-RB-(8,8). But for the ZZ edge ones, both of the optimized ZZ-SV-MoS2-RB-(4,5) and the ZZ-DV-MoS2-RB-(4,4) are found to exhibit severe out-of

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plane distortions, as seen from the left panels of Figs. 2(c) and 2(d).

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For example, the optimized ZZ-SV-MoS2-RB-(4,5) bends around the sulfur line vacancy defect, making the left and right sides of its SV form a certain angle  of about

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137.2o, as seen in Fig. 2(c), which is much smaller than the angle  of the AC-SV-MoS2-RB-(8,9) at about 173.8o, as shown in Fig. 2(a). Besides, the DV line defects in ZZ-DV-MoS2-RB-(4,4) can induce a dislocation between the left and right sides of its DV at a distance of about d=1.86 Å near the DV line defect, as shown in the left panel of Fig 2(d), which is also much bigger than that of the AC-DV-MoS2-RB-(8,8), as seen in Fig. 2(b), because the latter almost keeps its plane structure.

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Fig. 2 (Color online) The side views of the optimized geometric structure of (a) the AC-SV-MoS2-RB-(8,9) and (b) the AC-DV-MoS2-RB-(8,8). (c) and (d) show those of the ZZ-SV-MoS2-RB-(4,5) and ZZ-DV-MoS2-RB-(4,4) in the left panels, respectively. And their

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spin-polarized charge densities in the FM ‘++’ and AFM ‘+-’ ground states have also been shown at the middle and right panels, respectively. Here, the Mo and S atoms are represented by big purple and small

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yellow balls, respectively. The yellow and cyan represent the spin-up and -down charge densities,

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respectively. The isovalues for these isosurfaces are taken as 0.01 e·Å-3. The  and d denote the

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bending angle and dislocation distance d, respectively.

B. Strain distribution in confined MoS2 nanoribbon with sulfur line vacancy defect

It is noted from Figs. 2(a) and 2(c) that the out-of-plane distortion of the

ZZ-SV-MoS2-RB-(4,5) is more severe than that of the AC-SV-MoS2-RB-(8,9). To get a more in-depth understanding of the deformation mechanism, we have quantified the strain distributions of the Mo-S bonds in the optimized ZZ-SV-MoS2-RB-(4,5) and AC-SV-MoS2-RB-(8,9) under a constraint of all Mo atoms lying in the xy plane. A bond strain could be defined as s 

l  l0 , where l is the Mo-S bond length of the l0 9/9

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optimized defective MoS2 nanoribbon under the constrained condition, and l0 is that in a perfect monolayer MoS2. Therefore, the s value, being larger, smaller than or equal to zero, will indicate that the bond is strained, compressed or not changed, compared with that of a

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perfect monolayer MoS2, which will be colored by red, blue and white, respectively.

The calculated bond strain distributions in the ZZ-SV-MoS2-RB-(4,5) and

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AC-SV-MoS2-RB-(8,9), optimized under the constraint, are given in Fig. 3, from which it

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can be seen that the severely compressed or strained bonds, shown respectively by blue and red colors, mainly locate at or near the SV line defects and the ribbon edges. In contrast, the

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larger area between the line vacancy defect and the edge is mainly colored in white, indicating that the Mo-S bond lengths in the area are almost not changed. Due to the dangling bonds at the armchair edge, we have noted that there is an obvious structure

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reconstruction at the edges of the AC-SV-MoS2-RB-(8,9), which is found to be almost the same as the reconstructed edges of pristine armchair MoS2 nanoribbons. It is easy to

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understand that the bond length change at the edges would not have big influence on the

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out-of-plane distortion near the central SV line defect due to the wide transition region

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from the line defect to the edge in white color. So those bond strains in the middle part of the ribbon, induced by the SV line defect, must be dominant in deciding the out-of plane distortion in the defective nanoribbon.

Fig. 3 (Color online) The bond strain distributions of the optimized (a) ZZ-SV-MoS2-RB-(4,5) and (b) 10 / 10

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AC-SV-MoS2-RB-(8,9) under a constraint of all Mo atoms lying in xy plane. The red and blue colors represent the tensile and compressive Mo-S bonds, respectively, and the white ones mean almost unchanged ones, compared with the value of 2.41 Å in a perfect monolayer MoS2. The color bar is

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shown at the bottom of (a) and (b) with the maximum bond tension and compression values at its two ends. The corresponding maximum deformed bonds in defective area are marked by black arrows. Here,

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the Mo and S atoms are represented by big purple and small yellow balls, respectively.

In the defective area of the constrained ZZ-SV-MoS2-RB-(4,5), shown in Fig. 3(a), as

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outlined in the blue rectangle box, the most severely strained bonds are elongated by 4.6%, numbered by 1 in red color, in contrast to the most severely compressed bonds which are

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shortened by 2.5%, denoted by 2 in blue color. In comparison, the maximum bond strain and compression values (denoted by 1’ and 2’ in Fig. 3(b)) in the defective area of the

smaller absolute

values

than

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constrained AC-SV-MoS2-RB-(8,9) are 1.3% and 2%, respectively, both of which have those (4.6% and 2.5%) of the constrained

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ZZ-SV-MoS2-RB-(4,5). Therefore, in the case of no constraint, releasing of both the bond

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strain and compression in the defective area of defective MoS2 plane will cause the out-of-plane distortion, which will be more severe in the ZZ-SV-MoS2-RB-(4,5) than in the Besides,

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AC-SV-MoS2-RB-(8,9).

the

bond

strain

and

compression

in

the

AC-SV-MoS2-RB-(8,9) satisfies the mirror symmetry to the sulfur vacancy line due to its intrinsic symmetric defective structure.

C. Electronic and magnetic properties of zigzag edge MoS2 nanoribbons with sulfur line vacancy defects We have further studied the electronic and magnetic properties of the ZZ-SV-MoS2-RB-(4,5) and ZZ-DV-MoS2-RB-(4,4), whose optimized geometrical structures are shown in Figs. 2(c) and 2(d). Both of them are found to have two respective degenerate magnetic ground states with the same energy and FM coupling at the same 11 / 11

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edge. One is still the FM coupling ‘++’ between two opposite edges, and the other is antiferromagnetic (AFM) coupling ‘+-’ at two opposite edges, which is similar to the situation of the pristine ZZ-MoS2-NR. The ground state energies of the FM ‘++’ and AFM

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‘+-’ configurations of the ZZ-SV-MoS2-RB-(4,5) and ZZ-DV-MoS2-RB-(4,4) are found to be 93.5 meV and 80.4 meV per supercell (with one Mo atom at the edge) lower than their

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nonmagnetic ones, respectively. The spin-polarized charge densities of both the configurations are shown in the middle and right panels of Figs. 2(c) and 2(d), respectively.

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There are no magnetic moments on the sulfur line vacancy defects. For the ZZ-SV-MoS2-RB-(4,5) in the FM ‘++’ configuration, the total magnetic moments in a unit

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cell is about 1.29 μB. But the value is 0.22 μB for the AFM ‘+-’ one because the total magnetic moments at the opposite Mo and S edges are different. The corresponding two

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values for the ZZ-DV-MoS2-RB-(4,4) are 1.36 μB and 0.29 μB, respectively. The magnetic moments are mainly localized on the Mo and S atoms at its zigzag edges. The absolute

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respectively.

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values of the magnetic moments of the edge Mo and S atoms are about 0.6 μB and 0.3 μB,

The calculated spin-polarized band structures of both the ZZ-SV-MoS2-RB-(4,5) and

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the ZZ-DV-MoS2-RB-(4,4) in their ground state FM ‘++’ or AFM ‘+-’ coupling configurations are given in Fig. 4, showing that all of them are metallic. That is because some edge bands denoted by symbols a and c split now and pass through the Fermi level, which are contributed by the zigzag edge Mo and S atoms, respectively. On the other hand, there are two defect states, denoted by the symbol b, in the band structure of the ZZ-SV-MoS2-RB-(4,5), as shown in Figs. 4(a) and 4(b), in contrast to its DV counterpart ZZ-DV-MoS2-RB-(4,4), which has four defect states, doubled than those of ZZ-SV-MoS2-RB-(4,5), as shown in Figs. 4(c) and 4(d). However, the number of the edge states of a and c keeps the same in both the DV and SV cases, and their positions are hardly changed.

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Fig. 4 (Color online) The spin-polarized band structures, total density of states (DOSs), and projected density of states (PDOSs) of the ZZ-SV-MoS2-RB-(4,5) in their ground states of FM ‘++’ and AFM ‘+-’

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are plotted in (a) and (b), respectively, and those of the ZZ-DV-MoS2-RB-(4,4) are shown in (c) and (d), respectively. The black and red lines represent the spin-up and down channels in the band structures.

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The states a, b and c are denoted by blue solid circles, red solid squares, and cyan solid circles,

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respectively. In the DOS panel on the right, the black and red lines represent the total DOS and PDOS of the atoms on the line vacancy defect. And the blue and cyan ones represent PDOS of the Mo and S edge

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atoms, respectively. The Fermi level is set to zero.

In the band structure of the ZZ-SV-MoS2-RB-(4,5) in the FM ‘++’ configuration,

shown in Fig. 4(a), the edge bands of a1, a2 and a3 are all contributed by the Mo edge atoms, which split in the spin-polarized calculations, making the spin-up channel much more occupied than the spin-down one, and thus inducing its FM magnetism with the magnetic moments lying on the Mo edge atoms. The two split edge c states are contributed by the edge S atoms, among which the spin-up channel is also more occupied than the spin-down one, enhancing then more its FM magnetism with additional spin-up charges from the edge S atoms. In the band structure of its AFM ‘+-’ configuration shown in Fig. 4(b), the positions of 13 / 13

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spin-up and spin-down edge band c are reversed to each other, compared with them in its FM ‘++’ configuration in Fig. 4(a), thus causing the residual net spin-down charges at the edge S atoms, as shown in the right panel of Fig. 2(c). Similarly, both the spin-up and

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spin–down edge c bands are exchanged in Fig. 4(d), compared with them in Fig. 4(c). On the other hand, it is noted that the line vacancy defect bands (denoted by b) of the

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ZZ-SV-MoS2-RB-(4,5) and ZZ-DV-MoS2-RB-(4,4), all contributed by d orbitals of the Mo atoms on the line vacancy defects. The SV line defect bands (denoted by b1 and b2 in Figs.

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4(a) and 4(b)) do not split in their spin-polarized band structures, which would thus not induce a net spin-polarized charge on the line vacancy defects. While for the DV line

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defect states (from b1 to b4 in Figs. 4(c) and 4(d)), only b4 splits a little bit far away from the BZ center. However, the two split b4 bands at there have the higher energies above the

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Fermi level, which thus have neither any contribution to the magnetism at the line vacancy defect.

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From the spin polarized band structures in Fig. 4, it is found that all defect states

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(denoted by b) are not across the Fermi level, and the metallic properties and all spin

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splitted bands across the Fermi levels come from the edge Mo and S atoms (denoted by a and c), respectively. Besides, there exists a wide transition region between the line defect in the middle and the edges, as shown in white color in Fig. 3(a). Therefore, it is obvious that as the ribbon width increases, the coupling between the defect states and those edge ones becomes weaker and weaker, leading to less and less effects of the SV (or DV) defect states on the electronic and magnetic properties of the defective MoS2 ribbons with either the SV or DV.

D. Electronic properties of armchair (AC) edge MoS2 nanoribbons with sulfur line vacancy defects Now let’s turn to the case of a sulfur line vacancy defect along the AC direction. The 14 / 14

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optimized

geometric

structures

of

the

AC-SV-MoS2-RB-(8,9)

and

the

AC-DV-MoS2-RB-(8,8) are shown in Figs. 2(a) and 2(b), respectively. Their calculated electronic structures indicate that both of them are nonmagnetic semiconductors with their

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direct band gap values of about 0.564 eV and 0.238 eV, respectively. The former is nearly equal to the gap value (0.569 eV) of the perfect AC-MoS2-RB-18, but the latter one is

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much smaller than that of 0.569 eV. What is the reason to cause the large difference between the gap values in the SV and DV cases?

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From the band structure of the AC-SV-MoS2-RB-(8,9), shown in Fig. 5(a), it is noted that all the defect states of b1, b2 and b3, contributed by the d-orbitals of the Mo atoms at

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the line vacancy defect, are far away from the Fermi level. Thus, its direct band gap is determined by the two edge states of a2 and a4 at the  point, which would not be changed

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by the existence of a SV line defect in the ribbon. Further analysis indicates that the a1 band is contributed mainly by pz orbitals of the edge S atoms, and the bands from a2 to a5

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are all mainly attributed to the d orbitals of the edge Mo atoms. All the edge bands are

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reconstructions.

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doubly degenerate, because they are contributed from two equal edges without edge

Fig.5 (Color online) The spin-unpolarized band structures, total density of states (DOSs), and projected density of states (PDOSs) of: (a) AC-SV-MoS2-RB-(8,9) and (b) AC-DV-MoS2-RB-(8,8). The states a and b are denoted by blue solid circles and red solid squares, respectively. In the DOS panel on the right, the black, red and blue lines represent the total DOS, PDOS of the line vacancy defect and that of the edge atoms, respectively. The Fermi level is set to zero.

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But the DV case is much different from the SV one. The gap value of AC-DV-MoS2-RB-(8,8) is greatly reduced, compared with that of its perfect counterpart. It can be seen from Figs. 5(a) and 5(b) that the edge bands of a2, a3 and a4, determining the

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band gap value in the SV case, are almost not affected by one more S line vacancy defect in the DV case, which but induces the doubled number of defect bands now, introducing

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three more defect bands, all contributed from the d orbitals of Mo atoms at the line vacancy defects. More importantly, a part of the defect bands, i.e. the b2 and b3, as shown in Fig.

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5(b), move deep into the original band gap of the perfect AC-MoS2-RB-18, which now decide the band gap of AC-DV-MoS2-RB-(8,8), thus greatly decreasing its band gap.

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Similar to the case of ZZ-SV-MoS2-RB-(4,5), there is also a wide transition region between the line defect in the middle and the edges in the armchair counterpart

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AC-SV-MoS2-RB-(8,9), as shown in white color in Fig. 3(b). As explained above, the band gap of AC-SV-MoS2-RB-(8,9) is decided by the bands coming from the edge atoms

d

(denoted by a in Fig. 5(a)), and the defect bands (denoted by b) are far away from the Fermi

AC-SV-MoS2-RB-(n,m).

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level. Therefore it is obvious that the ribbon width has no big effect on the band gap of the On

the

other

hand,

the

smaller

band

gaps

of

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AC-DV-MoS2-RB-(n,n) are decided by both the two defect states (denoted by b2 and b3 for AC-DV-MoS2-RB-(8,8) as shown in Fig. 5(b)). So, its gap value around 0.238 eV will keep almost unchanged and not vanish with the ribbon width increases. To further prove the above point, we have done some test calculations for more

AC-SV-MoS2-RB-(n,n+1) and AC-DV-MoS2-RB-(n,n) with narrower or wider ribbon widths by changing the number of n (n = 6, 7, 9 and 10). And the calculated band gap values of them at different values of number n are given in Fig. 6. It is clearly seen from Fig. 6 that the band gap keeps almost unchanged when the number n varies, indicating that the ribbon width has a very small effect on the calculated band gaps of both the AC-SV-MoS2-RB and AC-DV-MoS2-RB, as explained above.

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Fig.6 (Color online) The calculated band gaps of both the AC-SV-MoS2-RB-(n,n+1) and

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AC-DV-MoS2-RB-(n,n) versus different values of the number n, which are denoted by black solid

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IV. SUMMARY

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squares and red solid circles, respectively. The dashed lines are the corresponding fitting lines of them.

The structural, electronic and magnetic properties of 1D ZZ and AC edge MoS2

nanoribbons with the SV or DV, parallel to their edges, have been investigated systematically by the first-principles calculations. It is found that the large bond strains around the sulfur line vacancy defect can cause a much severer out-of plane distortion in the ZZ edge MoS2 nanoribbon than in the AC edge counterpart. The defective ZZ edge MoS2 nanoribbons with the SV or DV are both metals, which have two degenerate magnetic ground states with the same energy and FM coupling along the same edge. But the 1D AC edge MoS2 nanoribbons with the SV or DV are both nonmagnetic semiconductors with their direct band gap values of about 0.56 eV and 0.24 eV, respectively, due to different numbers of the vacancy states caused by the SV or DV. Thus, 17 / 17

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our obtained results will be helpful for applications of the defective MoS2-based materials in spintronics and electromechanical devices.

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ACKNOWLEDGEMENT The authors acknowledge financial supports from the State Key Program for Basic

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Research of China through the Grant No 2011CB922100Q. Our numerical calculations are performed on the High Performance Computing Center of Nanjing University. Y. Han

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gratefully acknowledged useful discussions with Doctors R. Li, W. S. Wang, Y. P. Du and Y.

an

F. Zhang.

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FIGURE CAPTIONS Fig. 1 (Color online) Schematic shows of (a) the ZZ-MoS2-RB-10 and (b) the AC-MoS2-RB-18 with their top and side views, lying on the upper and lower panels, respectively. Here, the two black solid lines in (a) and (b) indicate their unit cells. (c) Geometric structures of the ZZ-SV-MoS2-(4,5) and 20 / 20

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ZZ-DV-MoS2-(4,4), shown in the upper and lower panels, respectively. (d) Same as (c), but now for both the AC-SV-MoS2-(8,9) and AC-DV-MoS2-(8,8). In both (c) and (d), the red opened circles denote the initial S vacancy positions. The Mo and S atoms in the blue rectangle box are selected as those

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atoms nearby the S vacancy, which will be used for analyzing the PDOS. Here, the Mo atoms are represented by big purple balls, but the S atoms on the top and bottom layers denoted by the small

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yellow and green balls, respectively.

Fig. 2 (Color online) The side views of the optimized geometric structure of (a) the

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AC-SV-MoS2-RB-(8,9) and (b) the AC-DV-MoS2-RB-(8,8). (c) and (d) show those of the ZZ-SV-MoS2-RB-(4,5) and ZZ-DV-MoS2-RB-(4,4) in the left panels, respectively. And their

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spin-polarized charge densities in the FM ‘++’ and AFM ‘+-’ ground states have also been shown at the middle and right panels, respectively. Here, the Mo and S atoms are represented by big purple and small

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yellow balls, respectively. The yellow and cyan represent the spin-up and -down charge densities, respectively. The isovalues for these isosurfaces are taken as 0.01 e·Å-3. The  and d denote the

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bending angle and dislocation distance d, respectively.

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Fig. 3 (Color online) The bond strain distributions of the optimized (a) ZZ-SV-MoS2-RB-(4,5) and (b) AC-SV-MoS2-RB-(8,9) under a constraint of all Mo atoms lying in xy plane. The red and blue colors

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represent the tensile and compressive Mo-S bonds, respectively, and the white ones mean almost unchanged ones, compared with the value of 2.41 Å in a perfect monolayer MoS2. The color bar is shown at the bottom of (a) and (b) with the maximum bond tension and compression values at its two ends. The corresponding maximum deformed bonds in defective area are marked by black arrows. Here, the Mo and S atoms are represented by big purple and small yellow balls, respectively. Fig. 4 (Color online) The spin-polarized band structures, total density of states (DOSs), and projected density of states (PDOSs) of the ZZ-SV-MoS2-RB-(4,5) in their ground states of FM ‘++’ and AFM ‘+-’ are plotted in (a) and (b), respectively, and those of the ZZ-DV-MoS2-RB-(4,4) are shown in (c) and (d), respectively. The black and red lines represent the spin-up and down channels in the band structures. The states a, b and c are denoted by blue solid circles, red solid squares, and cyan solid circles, respectively. In the DOS panel on the right, the black and red lines represent the total DOS and PDOS of

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the atoms on the line vacancy defect. And the blue and cyan ones represent PDOS of the Mo and S edge atoms, respectively. The Fermi level is set to zero. Fig.5 (Color online) The spin-unpolarized band structures, total density of states (DOSs), and projected

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density of states (PDOSs) of: (a) AC-SV-MoS2-RB-(8,9) and (b) AC-DV-MoS2-RB-(8,8). The states a and b are denoted by blue solid circles and red solid squares, respectively. In the DOS panel on the right,

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the black, red and blue lines represent the total DOS, PDOS of the line vacancy defect and that of the edge atoms, respectively. The Fermi level is set to zero.

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Fig.6 (Color online) The calculated band gaps of both the AC-SV-MoS2-RB-(n,n+1) and AC-DV-MoS2-RB-(n,n) versus different values of the number n, which are denoted by black solid

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squares and red solid circles, respectively. The dashed lines are the corresponding fitting lines of them.

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