Based on first-principles phonon and finite temperature molecular dynamics calculations including spinorbit coupling, we showed that free-standing single-layer phases of bismuth, namely buckled honeycomb and asymmetric washboard structures named as bismuthene, are stable at high temperature. We studied the atomic structure, mechanical, and electronic properties of these single-layer bismuthene phases and their bilayers. The spin-orbit coupling is found to be crucial in determining lattice constants, phonon frequencies, band gaps, and cohesion. In particular, phonons of 3D hexagonal crystal, as well as those of single-layer bismuthene phases, are softened with spin orbit coupling. By going from 3D hexagonal crystal to free-standing single-layer structures, 2D hexagonal lattice is compressed and semimetal is transformed to semiconductor as a result of confinement effect. On the contrary, by going from single-layer to bilayer bismuthenes, the lattice is slightly expanded and fundamental band gaps are narrowed. Our results reveals that interlayer coupling in multilayer and 3D Bi crystal is crucial for topologically trivial to nontrivial and semimetal to semiconductor transitions.

The pseudolayered character of 3D bulk crystals of antimony has led us to predict its 2D single-layer crystalline phase named antimonene in a buckled honeycomb structure like silicene. Sb atoms also form an asymmetric washboard structure like black phospherene. Based on an extensive analysis comprising ab initio phonon and finite-temperature molecular dynamics calculations, we show that these two single-layer phases are robust and can remain stable at high temperatures. They are nonmagnetic semiconductors with band gaps ranging from 0.3 eV to 1.5 eV, and are suitable for 2D electronic applications. The washboard antimonene displays strongly directional mechanical properties, which may give rise to a strong influence of strain on the electronic properties. Single-layer antimonene phases form bilayer and trilayer structures with wide interlayer spacings. In multilayers, this spacing is reduced and eventually the structure changes to 3D pseudolayered bulk crystals. The zigzag and armchair nanoribbons of the antimonene phases have fundamental band gaps derived from reconstructed edge states and display a diversity of magnetic and electronic properties depending on their width and edge geometry. Their band gaps are tunable with the widths of the nanoribbons. When grown on substrates, such as germanene or Ge(111), the buckled antimonene attains a significant influence of substrates.

Based on first-principles density functional calculations, we predict that nitrogen atoms can form a single-layer, buckled honeycomb structure called nitrogene, which is rigid and stable even above room temperature. This 2D crystalline phase of nitrogen, which corresponds to a local minimum in the Born-Oppenheimer surface, is a nonmagnetic insulator with saturated π bonds. When grown on a substrate like Al(111) surface and graphene, nitrogene binds weakly to substrates and hence preserves its free-standing properties, but it can easily be pealed off. Zigzag and armchair nanoribbons of nitrogene have fundamental band gaps derived from reconstructed edge states. These band gaps are tunable with size and suitable for the emerging field of 2D electronics. Nitrogene forms not only bilayer, but also 3D graphitic multilayer structures. Single-layer nitrogene can nucleate and grow on the armchair edges of hexagonal boron nitride.

Soon after the synthesis of two-dimensional (2D) ultrathin black phosphorus and fabrication of field effect transistors thereof, theoretical studies have predicted that other group-VA elements (or pnictogens), N, As, Sb, and Bi can also form stable, single-layer (SL) structures. These were nitrogene in a buckled honeycomb structure, arsenene, antimonene, and bismuthene in a buckled honeycomb, as well as washboard and square-octagon structures with unusual mechanical, electronic, and optical properties. Subsequently, theoretical studies are followed by experimental efforts that aim at synthesizing these novel 2D materials. Currently, research on 2D pnictogens has been a rapidly growing field revealing exciting properties, which offers diverse applications in flexible electronics, spintronics, thermoelectrics, and sensors. This review presents an evaluation of the previous experimental and theoretical studies until 2019, in order to provide input for further research attempts in this field. To this end, we first reviewed 2D, SL structures of group-VA elements predicted by theoretical studies with an emphasis placed on their dynamical and thermal stabilities, which are crucial for their use in a device. The mechanical, electronic, magnetic, and optical properties of the stable structures and their nanoribbons are analyzed by examining the effect of external factors, such as strain, electric field, and substrates. The effect of vacancy defects and functionalization by chemical doping through adatom adsorption on the fundamental properties of pnictogens has been a critical subject. Interlayer interactions in bilayer and multilayer structures, their stability, and tuning their physical properties by vertical stacking geometries are also discussed. Finally, our review is concluded by highlighting new research directions and future perspectives on the challenges in this emerging field.

Recent experiments revealed that monolayer α-RuCl 3 can be obtain by chemical exfoliation method and exfoliation or restacking of nanosheets can manipulate the magnetic properties of the materials. In this present paper, the electronic and magnetic properties of α-RuCl 3 monolayer are investigated by combining first-principles calculations and Monte Carlo simulations. From first-principles calculations, we found that the spin configuration FM corresponds to the ground state for α-RuCl 3 , however, the other excited zigzag oriented spin configuration has energy of 5 meV/atom higher than the ground state. Energy band gap has been obtained as 3 meV using PBE functionals. When spin-orbit coupling effect is taken into account, corresponding energy gap is determined to be as 57 meV. We also investigate the effect of Hubbard U energy terms on the electronic band structure of α-RuCl 3 monolayer and revealed band gap increases approximately linear with increasing U value. Moreover, spin-spin coupling terms (J 1 , J 2 , J 3 ) have been obtained using first principles calculations. By benefiting from these terms, Monte Carlo simulations with single site update Metropolis algorithm have been implemented to elucidate magnetic properties of the considered system. Thermal variations of magnetization, susceptibility and also specific heat curves indicate that monolayer α-RuCl 3 exhibits a phase transition between ordered and disordered phases at the Curie temperature 14.21 K. We believe that this study can be utilized to improve two-dimensional magnet materials.

We investigated the effects of chemical/substitutional doping, hydrogenation, and anti-site and vacancy defects on the atomic, optoelectronic and magnetic properties of AlN and GaN monolayers. Upon doping of selected atoms, AlN and GaN monolayers can acquire magnetic properties, and their fundamental band gaps are modified by the localized gap states. Spin-polarized gap states broaden into bands at patterned coverage of adatoms, whereby half-metallic or magnetic semiconducting properties can be attained. Specific adatoms adsorbed to Ga atoms break the nearest vertical Ga-N bonds in the GaN bilayer in the heackelite structure and result in changes in the electronic and atomic structure. While adjacent and distant pairs of anion + cation vacancies induce spin polarization with filled and empty gap states, anti-site defects remain nonmagnetic; but both defects induce dramatic changes in the band gap. Fully hydrogenated monolayers are stable only for specific buckled geometries, where one geometry can also lead to an indirect to direct band gap transition. Also, optical activity shifts to the ultra-violet region upon hydrogenation of the monolayers. While H2 and O2 molecules are readily physisorbed on the surfaces of the monolayers with weak van der Waals attraction, they can be dissociated into constituent atoms at the vacancy site of the cation. Our study performed within density functional theory shows that the electronic, magnetic and optical properties of AlN and GaN monolayers can be tuned by doping and point defect formation in order to acquire diverse functionalities.

Theoretical and experimental studies present that metal halogens in MX3 forms can show very interesting electronic and magnetic properties in their bulk and monolayer phases. Many MX3 materials have layered structures in their bulk phases, while RuBr3 and RuI3 have one-dimensional chains in plane. In this paper, we show that these metal halogens can also form two-dimensional layered structures in the bulk phase similar to other metal halogens, and cleavage energy values confirm that the monolayers of RuX3 can be possible to be synthesised. We also find that monolayers of RuX3 prefer ferromagnetic spin orientation in the plane for Ru atoms. Their ferromagnetic ground state, however, changes to antiferromagnetic zigzag state after U is included. Calculations using PBE+U with SOC predict indirect band gap of 0.70 eV and 0.32 eV for the optimized structure of RuBr3 and RuI3, respectively. Calculation based on the Monte Carlo simulations reveal interesting magnetic properties of RuBr3, such as large Curie temperature against RuI3, both in bulk and monolayer cases. Moreover, as a result of varying exchange couplings between neighboring magnetic moments, magnetic properties of RuBr3 and RuI3 can undergo drastic changes from bulk to monolayer. We hope our findings can be useful to attempt to fabricate the bulk and monolayer of RuBr3 and RuI3.

This paper reveals how the electronic structure, magnetic structure, and topological phase of two-dimensional (2D), single-layer structures of bismuth are modified by point defects. We first showed that a free-standing, single-layer, hexagonal structure of bismuth, named h-bismuthene, exhibits nontrivial band topology. We then investigated interactions between single foreign adatoms and bismuthene structures, which comprise stability, bonding, electronic structure, and magnetic structures. Localized states in diverse locations of the band gap and resonant states in band continua of bismuthene are induced upon the adsorption of different adatoms, which modify electronic and magnetic properties. Specific adatoms result in reconstruction around the adsorption site. Single vacancies and divacancies can form readily in bismuthene structures and remain stable at high temperatures. Through rebondings, Stone-Whales-type defects are constructed by divacancies, which transform into a large hole at high temperature. Like adsorbed adatoms, vacancies induce also localized gap states, which can be eliminated through rebondings in divacancies. We also showed that not only the optical and magnetic properties, but also the topological features of pristine h-bismuthene can be modified by point defects. The modification of the topological features depends on the energies of localized states and also on the strength of coupling between point defects.