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This concise book offers an essential introduction and reference guide for the many newcomers to the field of physics of elemental 2D materials. Silicene and related materials are currently among the most actively studied materials, especially following the first experimental synthesis on substrates in 2012. Accordingly, this primer introduces and reviews the most crucial developments regarding silicene from both theoretical and experimental perspectives. At the same time the reader is guided through the extensive body of relevant foundational literature. The text starts with a brief history of silicene, followed by a comparison of the bonding nature in silicon versus carbon atoms. Here, a simple but robust framework is established to help the reader follow the concepts presented throughout the book. The book then presents the atomic and electronic structure of free-standing silicene, followed by an account of the experimental realization of silicene on substrates. This topic is subsequently developed further to discuss various reconstructions that silicene acquires due to interactions with the substrate and how such effects are mirrored in the electronic properties. Next the book examines the dumbbell structure that is the key to understanding the growth mechanism and atomic structure of multilayer silicene. Last but not least, it addresses similar effects in other elemental 2D materials from group IV (germanene, stanane), group V (phosphorene) and group III (borophene), as well as transition metal dichalcogenides and other compositions, so as to provide a general comparative overview of their electronic properties.

Employing density functional theory-based methods, we investigate monolayer and bilayer structures of hexagonal SnS$_{2}$, which is recently synthesized monolayer metal dichalcogenide. Comparison of 1H and 1T phases of monolayer SnS$_{2}$ confirms the ground state to be the 1T phase. In its bilayer structure we examine different stacking configurations of the two layers. It is found that the interlayer coupling in bilayer SnS$_{2}$ is weaker than that of typical transition-metal dichalcogenides (TMDs) so that alternative stacking orders have similar structural parameters and they are separated with low energy barriers. Possible signature of the stacking order in SnS$_{2}$ bilayer has been sought in the calculated absorbance and reflectivity spectra. We also study the effects of the external electric field, charging, and loading pressure on the characteristic properties of bilayer SnS$_{2}$. It is found that (i) the electric field increases the coupling between the layers at its prefered stacking order, so the barrier height increases, (ii) the bang gap value can be tuned by the external E-field and under sufficient E-field, the bilayer SnS$_{2}$ can become semi-metal, (iii) the most favorable stacking order can be switched by charging and (iv) a loading pressure exceeding 3 GPa changes the stacking order. E-field tunable bandgap and easy-tunable stacking sequence of SnS$_{2}$ layers make this 2D crystal structure a good candidate for field effect transistor and nanoscale lubricant applications.

We determined frictional figures of merit for a pair of layered honeycomb nanostructures, such as graphane, fluorographene, MoS$_2$ and WO$_2$ moving over each other, by carrying out ab-initio calculations of interlayer interaction under constant loading force. Using Prandtl-Tomlinson model we derived critical stiffness required to avoid stick-slip behavior. We showed that these layered structures have low critical stiffness even under high loading forces due to their charged surfaces repelling each other. The intrinsic stiffness of these materials exceed critical stiffness and thereby avoid the stick-slip regime and attain nearly dissipationless continuous sliding. Remarkably, tungsten dioxide displays much better performance relative to others and heralds a potential superlubricant. The absence of mechanical instabilities leading to conservative lateral forces is also confirmed directly by the simulations of sliding layers.

Single layer core/shell structures consisting of graphene as core and hexagonal boron nitride as shell are studied using first-principles plane wave method within density functional theory. Electronic energy level structure is analysed as a function of the size of both core and shell. It is found that the confinement of electrons in two dimensional graphene quantum dot is reduced by the presence of boron nitride shell. The energy gap is determined by the graphene states. Comparison of round, hexagonal, rectangular and triangular core/shell structures reveals that their electronic and magnetic states are strongly affected by their geometrical shapes. The energy level structure, energy gap and magnetic states can be modified by external charging. The core part acts as a two-dimensional quantum dot for both electrons and holes. The capacity of extra electron intake of these quantum dots is shown to be limited by the Coulomb blockade in two-dimension.

Silica or SiO$_2$, the main constituent of earth's rocks has several 3D complex crystalline and amorphous phases, but it does not have a graphite like layered structure in 3D. Our theoretical analysis and numerical calculations from the first-principles predict a single-layer honeycomb like allotrope, h$\alpha$-silica, which can be viewed to be derived from the oxidation of silicene and it has intriguing atomic structure with re-entrant bond angles in hexagons. It is a wide band gap semiconductor, which attains remarkable electromechanical properties showing geometrical changes under external electric field. In particular, it is an auxetic metamaterial with negative Poisson's ratio and has a high piezoelectric coefficient. While it can form stable bilayer and multilayer structures, its nanoribbons can show metallic or semiconducting behavior depending on their chirality. Coverage of dangling Si orbitals by foreign adatoms can attribute new functionalities to h$\alpha$-silica. In particular, Si$_2$O$_5$, where Si atoms are saturated by oxygen atoms from top and bottom sides alternatingly can undergo a structural transformation to make silicatene, another stable, single layer structure of silica., Comment: Accepted for publication in Physical Review Letters

Using a gold (111) surface as a substrate we have grown in situ by molecular beam epitaxy an atom-thin, ordered, two-dimensional multi-phase film. Its growth bears strong similarity with the formation of silicene layers on silver (111) templates. One of the phases, forming large domains, as observed in Scanning Tunneling Microscopy, shows a clear, nearly flat, honeycomb structure. Thanks to thorough synchrotron radiation core-level spectroscopy measurements and advanced Density Functional Theory calculations we can identify it to a $\sqrt{3}$x$\sqrt{3}$R(30{\deg}) germanene layer in coincidence with a $\sqrt{7}$x$\sqrt{7}$R(19.1{\deg}) Au(111) supercell, thence, presenting the first compelling evidence of the birth of a novel synthetic germanium-based cousin of graphene., Comment: 16 pages, 4 figures, 1 table

The thermoelectric properties in one- and two-dimensional silicon and germanium structures have been investigated using first-principle density functional techniques and linear response for the thermal and electrical transport. We have considered here the two-dimensional silicene and germanene, together with nano-ribbons of different widths. For the nano-ribbons, we have also investigated the possibility of nano-structuring these systems by mixing silicon and germanium. We found that the figure of merit at room temperature of these systems is remarkably high, up to 2.5., Comment: 15 pages, 18 figures, revtex4-1

A single graphene layer placed between two parallel Ni(111) surfaces screens the strong attractive force and results in a significant reduction of adhesion and sliding friction. When two graphene layers are inserted, each graphene is attached to one of the metal surfaces with a significant binding and reduces the adhesion further. In the sliding motion of these surfaces the transition from stick-slip to continuous sliding is attained, whereby non-equilibrium phonon generation through sudden processes is suppressed. The adhesion and corrugation strength continues to decrease upon insertion of the third graphene layer and eventually saturates at a constant value with increasing number of graphene layers. In the absence of Ni surfaces, the corrugation strength of multilayered graphene is relatively higher and practically independent of the number of layers. Present first-principles calculations reveal the superlubricant feature of graphene layers placed between pseudomorphic Ni(111) surfaces, which is achieved through the coupling of Ni-3d and graphene-$\pi$ orbitals. The effect of graphene layers inserted between a pair of parallel Cu(111) and Al(111) surfaces are also discussed. The treatment of sliding friction under the constant loading force, by taking into account the deformations corresponding to any relative positions of sliding slabs, is the unique feature of our study., Comment: Accepted paper for Physical Review B

Motivated by recent experimental observations of Tongay et al. [Tongay et al., Nano Letters, 12(11), 5576 (2012)] we show how the electronic properties and Raman characteristics of single layer MoSe2 are affected by elastic biaxial strain. We found that with increasing strain: (1) the E' and E" Raman peaks (E1g and E2g in bulk) exhibit significant red shifts (up to 30 cm-1), (2) the position of the A1' peak remains at 180 cm-1 (A1g in bulk) and does not change considerably with further strain, (3) the dispersion of low energy flexural phonons crosses over from quadratic to linear and (4) the electronic band structure undergoes a direct to indirect bandgap crossover under 3% biaxial tensile strain. Thus the application of strain appears to be a promising approach for a rapid and reversible tuning of the electronic, vibrational and optical properties of single layer MoSe2 and similar MX2 dichalcogenides., Comment: http://link.aps.org/doi/10.1103/PhysRevB.87.125415

The growth process of single layer graphene with and without substrate is investigated using ab initio, finite temperature molecular dynamic calculations within density functional theory. An understanding of the epitaxial graphene growth mechanisms in the atomic level is provided by exploring the transient stages which occur at the growing edges of graphene. These stages are formation and collapse of large carbon rings together with the formation and healing of Stone-Wales like pentagon-heptagon defects. The activation barriers for the healing of these growth induced defects on various substrates are calculated using the climbing image nudge elastic band method and compared with that of the Stone-Wales defect. It is found that the healing of pentagon-heptagon defects occurring near the edge in the course of growth is much easier than that of Stone-Wales defect. The role of the substrate in the epitaxial growth and in the healing of defects are also investigated in detail, along with the effects of using carbon dimers as the building blocks of graphene growth., Comment: Published version

Based on first-principles calculations we revealed fundamental properties of infinite and finite size monatomic chains of carbon atoms in equilibrium and under an applied strain. Distributions of bond lengths and magnetic moments at atomic sites exhibit interesting even-odd disparity depending on the number of carbon atoms in the chain and on the type of saturation of carbon atoms at both ends. It was shown that, the $\pi$-bands of carbon atomic chains behave as a one dimensional free electron system. A local perturbation created by a small displacement of the single carbon atom at the center of a long chain induces oscillations of atomic forces and charge density, which are carried to long distances over the chain. These long ranged oscillations are identified as Friedel oscillations showing $1/r$ decay rate in one dimensional systems., Comment: Please find the published version in http://link.aps.org/doi/10.1103/PhysRevB.82.195444

We present a study of mechanical, electronic and magnetic properties of two dimensional (2D), monolayer of silicon carbide (SiC) in honeycomb structure and its quasi 1D armchair nanoribbons using first-principles plane wave method. In order to reveal dimensionality effects, a brief study of 3D bulk and 1D atomic chain of SiC are also included. Calculated bond-lengths, cohesive energies, charge transfers and band gaps display a clear dimensionality effect. The stability analysis based on the calculation of phonon frequencies indicates that 2D SiC monolayer is stable in planar geometry. We found that 2D SiC monolayer in honeycomb structure and its bare and hydrogen passivated nanoribbons are ionic, non-magnetic, wide band gap semiconductors. The band gap is further increased upon self-energy corrections. The mechanical properties are investigated using the strain energy calculations. The effect of various vacancy defects, adatoms and substitutional impurities on electronic and magnetic properties in 2D SiC monolayer and in its armchair nanoribbons are also investigated. Some of these vacancy defects and impurities, which are found to influence physical properties and attain magnetic moments, can be used to functionalize SiC honeycomb structures., Comment: please see published version. http://prb.aps.org/abstract/PRB/v81/i7/e075433

We present a first-principles study of bare and hydrogen passivated armchair nanoribbons of the puckered single layer honeycomb structures of silicon and germanium. Our study includes optimization of atomic structure, stability analysis based on the calculation of phonon dispersions, electronic structure and the variation of band gap with the width of the ribbon. The band gaps of silicon and germanium nanoribbons exhibit family behavior similar to those of graphene nanoribbons. The edges of bare nanoribbons are sharply reconstructed, which can be eliminated by the hydrogen termination of dangling bonds at the edges. Periodic modulation of the nanoribbon width results in a superlattice structure which can act as a multiple quantum wells. Specific electronic states are confined in these wells. Confinement trends are qualitatively explained by including the effects of the interface. In order to investigate wide and long superlattice structures we also performed empirical tight binding calculations with parameters determined from \textit{ab initio} calculations., Comment: please find the published version in http://link.aps.org/doi/10.1103/PhysRevB.81.195120

Based on first-principles calculations, we resent a method to reveal the elastic properties of recently synthesized monolayer hydrocarbon, graphane. The in-plane stiffness and Poisson's ratio values are found to be smaller than those of graphene, and its yielding strain decreases in the presence of various vacancy defects and also at high ambient temperature. We also found that the band gap can be strongly modified by applied strain in the elastic range., Comment: accepted version at: http://link.aip.org/link/?APL/96/091912

Using first-principles plane wave calculations, we investigate two dimensional 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 GW0 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 ..., Comment: 12 Pages, 7 Figures, 1 Table; http://link.aps.org/doi/10.1103/PhysRevB.80.155453

We present a first-principles study of the atomic, electronic, and magnetic properties of two-dimensional (2D), single and bilayer ZnO in honeycomb structure and its armchair and zigzag nanoribbons. In order to reveal the dimensionality effects, our study includes also bulk ZnO in wurtzite, zincblende, and hexagonal structures. The stability of 2D ZnO, its nanoribbons and flakes are analyzed by phonon frequency, as well as by finite temperature ab initio molecular-dynamics calculations. 2D ZnO in honeycomb structure and its armchair nanoribbons are nonmagnetic semiconductors but acquire net magnetic moment upon the creation of zinc-vacancy defect. Zigzag ZnO nanoribbons are ferromagnetic metals with spins localized at the oxygen atoms at the edges and have high spin polarization at the Fermi level. However, they change to nonmagnetic metal upon termination of their edges with hydrogen atoms. From the phonon calculations, the fourth acoustical mode specified as twisting mode is also revealed for armchair nanoribbon. Under tensile stress the nanoribbons are deformed elastically maintaining honeycomblike structure but yield at high strains. Beyond yielding point honeycomblike structure undergo a structural change and deform plastically by forming large polygons. The variation in the electronic and magnetic properties of these nanoribbons have been examined under strain. It appears that plastically deformed nanoribbons may offer a new class of materials with diverse properties., Comment: http://prb.aps.org/abstract/PRB/v80/i23/e235119

In this paper we present a detailed analysis of the atomic and electronic structure of GaAs nanowires using first-principles pseudopotential calculations. We consider six different types of nanowires with different diameters all grown along [111] direction and reveal interesting trends between cohesive energy and nanowire type with varying diameters. Generally, the average cohesive energy of nanowires with wurtzite stacking is higher than those with zinc blende stacking for small diameters. We found that most of the bare nanowires considered here are semiconducting and continue to be semiconducting upon the passivation of surface dangling bonds with hydrogen atom. However, the surface states associated with the surface atoms having two dangling bonds in zinc blende stacking occur in the band gap and can decrease the band gap to change the nanowire from semiconducting to metallic state. These nanowires become semiconducting upon hydrogen passivation. Even if the band gap of some nanowires decreases with increasing diameter and hence reveals the quantum confinement effect, generally the band gap variation is rather complex and depends on the type and geometry, diameter, type of relaxation and also whether the dangling bonds of surface atoms are saturated with hydrogen., Comment: Please find the published version in http://link.aps.org/doi/10.1103/PhysRevB.79.165118

In this paper we investigated structural, electronic and magnetic properties of 3d (light) transition metal (TM) atomic chains using first-principles pseudopotential plane wave calculations. Periodic linear, dimerized linear and planar zigzag chain structures and their short segments consisting of finite number of atoms have been considered. Like Cu, the periodic, linear chains of Mn, Co and Ni correspond to a local shallow minimum. However, for most of the infinite periodic chains, neither linear nor dimerized linear structures are favored; to lower their energy the chains undergo a structural transformation to form planar zigzag and dimerized zigzag geometry. Dimerization in both infinite and finite chains are much stronger than the usual Peierls distortion and appear to depend on the number of 3d-electrons. As a result of dimerization, a significant energy lowering occurs which, in turn, influences the stability and physical properties. Metallic linear chain of Vanadium becomes half-metallic upon dimerization. Infinite linear chain of Scandium also becomes half-metallic upon transformation to zigzag structure. An interplay between the magnetic ground state and atomic as well as electronic structure of the chain has been revealed. The end effects influence the geometry, energetics and magnetic ground state of the finite chains. Structure optimization performed using noncollinear approximation indicates significant differences from the collinear approximation. Variation of the cohesive energy of infinite and finite-size chains with respect to the number of 3d-electrons are found to mimic the bulk behavior pointed out by Friedel. The spin-orbit coupling of finite chains are found to be negligibly small., Comment: 13 pages, 9 figures