Aug 12, 2014 - Magnetic and electronic properties of α-graphyne nanoribbons. J. Chem. Phys. ... nite 2D sheets, which can also be synthesized by using an.
Electronic and magnetic properties of armchair MoS2 nanoribbons under both external strain and electric field, studied by first principles calculations Ting Hu, Jian Zhou, Jinming Dong, and Yoshiyuki Kawazoe Citation: Journal of Applied Physics 116, 064301 (2014); doi: 10.1063/1.4891997 View online: http://dx.doi.org/10.1063/1.4891997 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hydrogenation-induced edge magnetization in armchair MoS2 nanoribbon and electric field effects Appl. Phys. Lett. 104, 071901 (2014); 10.1063/1.4865902 Effects of edge hydrogenation on structural stability, electronic, and magnetic properties of WS2 nanoribbons J. Appl. Phys. 114, 213701 (2013); 10.1063/1.4829664 Tunable electronic and magnetic properties of WS2 nanoribbons J. Appl. Phys. 114, 093710 (2013); 10.1063/1.4820470 Magnetic and electronic properties of α-graphyne nanoribbons J. Chem. Phys. 136, 244702 (2012); 10.1063/1.4730325 First-principles study on electronic structures and magnetic properties of AlN nanosheets and nanoribbons J. Appl. Phys. 111, 043702 (2012); 10.1063/1.3686144
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JOURNAL OF APPLIED PHYSICS 116, 064301 (2014)
Electronic and magnetic properties of armchair MoS2 nanoribbons under both external strain and electric field, studied by first principles calculations Ting Hu,1 Jian Zhou,2 Jinming Dong,1,a) and Yoshiyuki Kawazoe3 1
Group of Computational Condensed Matter Physics, National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China 2 Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, People’s Republic of China 3 Institute for Materials Research, Tohoku University, 2-1-1 Katahira Aoba-ku, Sendai 980-8577, Japan
(Received 7 April 2014; accepted 22 July 2014; published online 12 August 2014) The electronic and magnetic properties of armchair edge MoS2 nanoribbons (MoS2-ANRs) underboth the external strain and transverse electric field (Et) have been systematically investigated by using the first-principles calculations. It is found that: (1) If no electric field is applied, an interesting structural phase transition would appear under a large tensile strain, leading to a new phase MoS2-A’NR, and inducing a big jump peak of the band gap in the transition region. But, the band gap response to compressive strains is much different from that to tensile strain, showing no the structural phase transition. (2) Under the small tensile strains (10%) after its monotonic decrease under the smaller tensile strain from 0 to 10%. A structural phase transition is also predicted under a large tensile strain. Moreover, when an external transverse electric field is simultaneously applied, a relative low critical field of about 4 V/nm for the S-M and diamagnetic-magnetic transition has been obtained because of the structural phase transition induced by tensile strain. The remainder of this paper is organized as follows. In Sec. II, the geometrical structure and computational details are described. In Sec. III, the main numerical results and some discussions are given. Finally, in Sec. IV, a conclusion is presented. II. MODEL AND METHOD
Similar to the graphene nanoribbon, the geometrical structure of a MoS2-ANR can be identified by a prefix integer n to label its width, denoted as n-MoS2-ANRs, where n represents the numbers of armchair chains along its width direction. For example, the optimized geometric structure of a 10-MoS2-ANR is shown in Fig. 1(a), which has two naked edges (without the hydrogen-terminations). The geometric, electronic, and magnetic properties are calculated using both the spin-unpolarized and spinpolarized density functional theory in the generalized gradient approximation (GGA), implemented by the VASP code,26,27 in which the projected augmented wave method28 and the Perdew–Burke–Ernzerhof (PBE)29 exchangecorrelation functional are employed. 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 y direction, and large vacuum regions are added in both x and z directions, making the closest distance between two adjacent MoS2˚. ANRs to be 15 A
J. Appl. Phys. 116, 064301 (2014)
Geometric structures of the MoS2-ANR were optimized by the conjugated- gradient minimization scheme. A planewave cut-off of 400 eV was used in our calculations, and the energies were converged to 106 eV/atom. Both the atomic positions and the lattice constant along the ribbon axis were fully relaxed until the maximum residual forces on atoms ˚ . The 1D Brillouin integration were less than 0.0005 eV/A was sampled with a 1 25 1 Monkhorst–Pack grid. III. RESULTS AND DISCUSSIONS A. Variation of electronic properties with an applied strain
We have first studied the geometric and electronic structures of the MoS2-ANR without an applied strain or external electric field by the first-principles calculations. Taking the 10-MoS2-ANR as an example, the optimized geometric structure is shown in Fig. 1, where the S–Mo bonds on the ˚ , in contrast to armchair edges are shortened to about 2.29 A ˚ in monolayer MoS2, which is consistent with prethe 2.42 A vious studies.21 The calculated electronic structure of the 10-MoS2-ANR is shown in Fig. 1(b), indicating that it is a nonmagnetic semiconductor with a direct band gap of 0.52 eV at the C point. The projected densities of states (pDOS) for p orbitals of the S atoms and d orbitals of Mo atoms at its edges are also calculated, which are given on the right side in Fig. 1(b). It can be seen from the pDOSs that near the Fermi level, its two conduction bands, labeled as a and b, and two valence bands, labeled as c and d, are dominated mainly by the d electrons of the Mo atoms at the edges, while its another doubly degenerate valence band, labeled as e, is contributed by the p electrons of the S atoms at the edges. These results are in good agreement with previous calculations.20,23 The strain effect on the electronic properties of 10MoS2-ANR is then investigated by applying an external tensile or a compressive strain along the ribbon direction, in which the corresponding shrinkage or expansion of the ribbon width and the distance between two S layers due to the Poisson’s ratio effect are automatically taken into account. The applied maximum strain is 18%, which is less than the ultimate tensile strength of the MoS2, predicted by the
FIG. 1. (a) The optimized geometrical structure of a 10-MoS2-ANR, viewed from the out-of-plane z axis (left) and in-plane x axis (right). The purple and yellow balls denote the Mo and S atoms, respectively. (b) The band structure (left side) and projected DOSs (right side) of the 4d orbital of Mo atom (Mo-d) and 3p orbital of S atom (S-p) at the edges of the 10-MoS2-ANR. The lines marked by red dots and blue triangles in the band structures represent the bands contributed mainly by the 4d-orbitals of Mo atoms and 3p-orbitals of S atoms, respectively.
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064301-3
Hu et al.
J. Appl. Phys. 116, 064301 (2014)
FIG. 2. (a) Band gap variations of 10-MoS2-ANR with an external tensile or a compressive strain. (b) The distorted geometric structure of 10-MoS2-ANR under a tensile strain of 13%. The atoms lying at the tetragons of one edge are labeled by different numbers in order to identify accurately their electron contributions to the band structures. (c) The stress-strain relations for a 10-MoS2-ANR under a tensile or compressive strain up to 18%.
previous theoretical studies.14–17 The band gap variation with the applied strains is presented in Fig. 2(a). It is found from Fig. 2(a) that the band gap decreases with increasing strain under a low external tensile strain from 1% to 10%, which is in accordance with the previous theoretical result.23 In contrast, however, when the tensile strain increases over 10%, the band gap experiences a big jump from 0.38 eV to 0.51 eV, keeping then almost unchanged until the strain increasing to 12.5%. Further increase of the tensile strain makes the band gap sharply decrease to 0.32 eV at the strain of 13%, followed by a slow linear increase to 0.38 eV until the tensile strain increases to 17%. Finally, the band gap decreases to 0.36 eV at a maximum tensile strain of 18%. Why does the gap experience a big jump in the large tensile strain range between 10% and 13%? It is interesting to notice that as the strain increases up to 13%, the 10-MoS2ANR undergoes a strong structural distortion, in which the Mo atoms at the edges move towards the hexagon centers, leading to an edge reconstruction from pristine armchair edges into S-terminated zigzag-like edges, as shown in Fig. 2(b). During the process, one edge hexagon transforms into two tetragons, inducing a new geometrical phase, which is named as MoS2-A’NR, as clearly seen in Fig. 2(b). The detailed analysis of stress-strain relation is presented in Fig. 2(c), from which it can be found that both the MoS2-ANR and new phase MoS2-A’NR exhibit a linear stress-strain relation under the applied tensile strains from 0% to 10% and from 13% to 18%, indicating clearly they lie in the elastic range. Thus, their band gap modulations are fully reversible in these two separate strain ranges. However, the structural transition between the MoS2-ANR and new phase MoS2-A’NR is fully irreversible. The band gap variation with applied strain can be understood from the band structures under different tensile strains, as shown in Fig. 3. At small tensile strains from 1% to 10%, the band gap variation with strain is consistent with the previous studies, showing the band gap reduction, as shown in Figs. 3(a) and 3(b), which is accompanied by a transition from direct character to indirect one.23 However, when the tensile strain further increases to 11%, the conduction bands a and b, contributed by d orbitals of Mo atoms at the edges shift up at C point, while the valence bands move down at X point, leading to a sudden enhancement of the band gap, as shown in Fig. 3(c).
It is worth noting that the structural phase transition into the MoS2-A’NR at 13% tensile strain makes its band structure change suddenly at this point, as shown in the left side of Fig. 3(d). The pDOSs for p orbitals of three S1, S2, and S3 atoms at the edge tetragons and d orbitals of three Mo1, Mo2, and Mo3 atoms at the edge tetragons, as shown in Fig. 2(b), were all calculated at the tensile strain of 13%. The obtained results are presented in the right side of Fig. 3(d). The calculated pDOSs reveal that the highest occupied molecular orbital (HOMO) corresponds to an edge state, localized strongly at S1 atom with a p orbital character, which is quite different from the electronic structures at small external strains (
