Effects of the Edge Structures and Defects on the Electronic Structure of Nanostructured MoS2 Monolayers
Guan-Hao Peng1*, Kuan-Fu Lee1, Yan-Chen Huang1, Shun-Jen Cheng1
1Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
* presenting author:Guan Hao Peng, email:bnm852i@gmail.com
Two-dimensional transition metal dichalcogenides (TMDs) have recently drawn great attention because of the fundamental interest of its physical and chemical properties and versatile technology applications. One of the most impressive physical property is the extra valley degrees of freedom of the electron in this material. This degree of freedom is associated with the large spin splittings of the low energy bands at the Brillouin zone (BZ) corners due to the strong spin-orbit coupling (SOC) of the transition metal atom. Due to this giant SOC, the electron spin and the valley degrees of freedom are locked together, and it turns out to be possible to manipulate the valley polarization by means of circularly polarized light[1,2]. But in the case of real sample and device, the symmetries of the electronic structure of bulk are further lowered by the symmetry breakings due to the presence of the boundary of the crystal structure and the vacancy defects. In this work, we use the density functional theory (DFT) in the VASP software package[3] and the tight-binding(TB) model both in the Slater-Koster(SK) scheme[4] and the symmetry-adapted scheme[5] to investigate the electronic structure of MoS2 in the cases of zigzag-edge nanoribbon, armchair-edge nanoribbon and the triangular flake with defects. We discuss the edge bands of the nanoribbon in different types of edge structure by inspecting their orbital components and studying their formulation process in the point of view of atomic orbital interactions. Remarkably, in the case of armchair-edge nanoribbon, there is a flat edge band near the fermi level and its orbital content is dominated by the dxz and dyz orbitals of Mo atom, which are not the relevant orbitals in the low energy region in the bulk case. In the case of triangular flake, there exist edge states inside the energy gap due to the presence of the crystal edge structure, and the energy distribution of these states also depend on the edge structure of the crystal. In the case of flake with defects, the energy level of these defect states emerges in the energy region between the bulk states and edge states, or in the energy region of the edge states, depending on the type of the edge structure.

[1] D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides, Phys. Rev. Lett. 108, 196802 (2012).
[2] G. Sallen, L. Bouet, X. Marie, G. Wang, C. R. Zhu, W. P. Han, Y. Lu, P. H. Tan, T. Amand, B. L. Liu, and B. Urbaszek, Robust optical emission polarization in MoS2 monolayers through selective valley excitation, Phys. Rev. B 86, 081301 (2012).
[3] G. Kresse, J. Furthmüller, Efficient iterative schemes for Ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186.
[4] E. Ridolfi, D. Le, T. S. Rahman, E. R. Mucciolo and C. H. Lewenkopf, A tight-binding model for MoS2 monolayers, J. Phys.: Condens.Matter 27 365501 (2015).
[5] G. B. Liu, W. Y. Shan, Y. G. Yao, W. Yao, and D. Xiao, Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides, Phys. Rev. B 88, 085433 (2013).

Keywords: 2D materials, transition metal dichalcogenides, band structure, tight-binding model