First-principles calculations of structure optimization, phonon modes, and finite temperature molecular dynamics predict that silicon and germanium can have stable, two-dimensional, low-buckled, honeycomb structures. Similar to graphene, these puckered structures are ambipolar and their charge carriers can behave like a massless Dirac fermion due to their pi and pi(*) bands which are crossed linearly at the Fermi level. In addition to these fundamental properties, bare and hydrogen passivated nanoribbons of Si and Ge show remarkable electronic and magnetic properties, which are size and orientation dependent. These properties offer interesting alternatives for the engineering of diverse nanodevices.

Using first-principles plane-wave calculations, we investigate two-dimensional ͑2D͒ honeycomb structure of group-IV elements and their binary compounds as well as the compounds of group III-V elements. Based on structure optimization and phonon-mode calculations, we determine that 22 different honeycomb materials are stable and correspond to local minima on the Born-Oppenheimer surface. We also find that all the binary compounds containing one of the first row elements, B, C, or N have planar stable structures. On the other hand, in the honeycomb structures of Si, Ge, and other binary compounds the alternating atoms of hexagons are buckled since the stability is maintained by puckering. For those honeycomb materials which were found stable, we calculated optimized structures, cohesive energies, phonon modes, electronic-band structures, effective cation and anion charges, and some elastic constants. The band gaps calculated within density functional theory using local density approximation are corrected by GW 0 method. Si and Ge in honeycomb structure are semimetal and have linear band crossing at the Fermi level which attributes massless Fermion character to charge carriers as in graphene. However, all binary compounds are found to be semiconductor with band gaps depending on the constituent atoms. We present a method to reveal elastic constants of 2D honeycomb structures from the strain energy and calculate the Poisson's ratio as well as in-plane stiffness values. Preliminary results show that the nearly lattice matched heterostructures of these compounds can offer alternatives for nanoscale electronic devices. Similar to those of the three-dimensional group-IV and group III-V compound semiconductors, one deduces interesting correlations among the calculated properties of present honeycomb structures.

Semiconducting transition metal dichalcogenides consist of monolayers held together by weak forces where the layers are electronically and vibrationally coupled. Isolated monolayers show changes in electronic structure and lattice vibration energies, including a transition from indirect to direct bandgap. Here we present a new member of the family, rhenium disulphide (ReS 2 ), where such variation is absent and bulk behaves as electronically and vibrationally decoupled monolayers stacked together. From bulk to monolayers, ReS 2 remains direct bandgap and its Raman spectrum shows no dependence on the number of layers. Interlayer decoupling is further demonstrated by the insensitivity of the optical absorption and Raman spectrum to interlayer distance modulated by hydrostatic pressure. Theoretical calculations attribute the decoupling to Peierls distortion of the 1T structure of ReS 2 , which prevents ordered stacking and minimizes the interlayer overlap of wavefunctions. Such vanishing interlayer coupling enables probing of two-dimensional-like systems without the need for monolayers.

Recent studies have revealed that single-layer transition-metal oxides and dichalcogenides (MX 2 ) might offer properties superior to those of graphene. So far, only very few MX 2 compounds have been synthesized as suspended single layers, and some of them have been exfoliated as thin sheets. Using first-principles structure optimization and phonon calculations based on density functional theory, we predict that, out of 88 different combinations of MX 2 compounds, several of them can be stable in free-standing, single-layer honeycomb-like structures. These materials have two-dimensional hexagonal lattices and have top-view appearances as if they consisted of either honeycombs or centered honeycombs. However, their bonding is different from that of graphene; they can be viewed as a positively charged plane of transition-metal atoms sandwiched between two planes of negatively charged oxygen or chalcogen atoms. Electron correlation in transition-metal oxides was treated by including Coulomb repulsion through LDA + U calculations. Our analysis of stability was extended to include in-plane stiffness, as well as ab initio, finite-temperature molecular dynamics calculations. Some of these single-layer structures are direct-or indirect-band-gap semiconductors, only one compound is half-metal, and the rest are either ferromagnetic or nonmagnetic metals. Because of their surface polarity, band gap, high in-plane stiffness, and suitability for functionalization by adatoms or vacancies, these single-layer structures can be utilized in a wide range of technological applications, especially as nanoscale coatings for surfaces contributing crucial functionalities. In particular, the manifold WX 2 heralds exceptional properties promising future nanoscale applications.

We present our study on atomic, electronic, magnetic and phonon properties of one dimensional honeycomb structure of molybdenum disulfide (MoS 2 ) using first-principles plane wave method. Calculated phonon frequencies of bare armchair nanoribbon reveal the fourth acoustic branch and indicate the stability. Force constant and in-plane stiffness calculated in the harmonic elastic deformation range signify that the MoS 2 nanoribbons are stiff quasi one dimensional structures, but not as strong as graphene and BN nanoribbons. 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 are semiconductor for minority spins, but metallic for the majority spins. Their magnetic moments and spin-polarizations at the Fermi level are reduced as a result of the passivation of edge atoms by hydrogen. The functionalization of MoS 2 nanoribbons by adatom adsorption and vacancy defect creation are also studied. The nonmagnetic armchair nanoribbons attain net magnetic moment depending on where the foreign atoms are adsorbed and what kind of vacancy defect is created. The magnetization of zigzag nanoribbons due to the edge states is suppressed in the presence of vacancy defects.