A First Principle Comparative Study of Three, Two and One-dimensional MoS$_2$ [Part:1]

This paper presents our comparative study on atomic, electronic, magnetic and phonon properties of three, two and one dimensional honeycomb structures of molybdenum disulfide (MoS$_2$) using first-principles plane wave method. The cohesion and interlayer interactions in graphitic MoS$_{2}$ are analyzed. Two dimensional, single layer MoS$_2$, which consists of a positively charged molybdenum atomic plane between two negatively charged sulfur atomic planes is a stiff semiconducting material with significant mechanical strength. Its band gap is calculated within density functional theory and then corrected by GW$_0$ self-energy method. Calculated phonon frequencies of bare armchair nanoribbon reveal the fourth acoustic branch and indicates the stability. Bare MoS$_2$ armchair nanoribbons are nonmagnetic, direct band gap semiconductors. Bare zigzag MoS$_2$ nanoribbons become half-metallic as a result of the (2x1) reconstruction of edge atoms and then attain net integer magnetic moment per unit cell. However, their magnetic moments and spin-polarizations at the Fermi level are reduced upon hydrogen passivation of edge atoms. In the harmonic elastic deformation range force constant and in-plane stiffness are calculated. Optimized lattice constants, energy band gap, dielectric constants, infrared and Raman active modes calculated for three and two dimensional MoS$_2$ are in agreement with the available experimental data.