Three-dimensional (3D) GaN is a III-V compound semiconductor with potential optoelectronic applications. In this paper, starting from 3D GaN in wurtzite and zinc-blende structures, we investigated the mechanical, electronic, and optical properties of the 2D single-layer honeycomb structure of GaN ($g-\mathrm{GaN}$) and its bilayer, trilayer, and multilayer van der Waals solids using density-functional theory. Based on high-temperature ab initio molecular-dynamics calculations, we first showed that $g-\mathrm{GaN}$ can remain stable at high temperature. Then we performed a comparative study to reveal how the physical properties vary with dimensionality. While 3D GaN is a direct-band-gap semiconductor, $g-\mathrm{GaN}$ in two dimensions has a relatively wider indirect band gap. Moreover, 2D $g-\mathrm{GaN}$ displays a higher Poisson ratio and slightly less charge transfer from cation to anion. In two dimensions, the optical-absorption spectra of 3D crystalline phases are modified dramatically, and their absorption onset energy is blueshifted. We also showed that the physical properties predicted for freestanding $g-\mathrm{GaN}$ are preserved when $g-\mathrm{GaN}$ is grown on metallic as well as semiconducting substrates. In particular, 3D layered blue phosphorus, being nearly lattice-matched to $g-\mathrm{GaN}$, is found to be an excellent substrate for growing $g-\mathrm{GaN}$. Bilayer, trilayer, and van der Waals crystals can be constructed by a special stacking sequence of $g-\mathrm{GaN}$, and they can display electronic and optical properties that can be controlled by the number of $g-\mathrm{GaN}$ layers. In particular, their fundamental band gap decreases and changes from indirect to direct with an increasing number of $g-\mathrm{GaN}$ layers.

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.

Structural symmetry breaking in two-dimensional materials can lead to superior physical properties and introduce an additional degree of piezoelectricity. In the present paper, we propose three structural phases ($1H, 1T$, and $1T^{\prime }$) of Janus $\mathrm{W}X\mathrm{O}$ ($X=\mathrm{S}$, Se, and Te) monolayers and investigate their vibrational, thermal, elastic, piezoelectric, and electronic properties by using first-principles methods. Phonon spectra analysis reveals that while the $1H$ phase is dynamically stable, the $1T$ phase exhibits imaginary frequencies and transforms to the distorted $1T^{\prime }$ phase. Ab initio molecular dynamics simulations confirm that $1H$- and $1T^{\prime }\text{−}\mathrm{W}X\mathrm{O}$ monolayers are thermally stable even at high temperatures without any significant structural deformations. Different from binary systems, additional Raman active modes appear upon the formation of Janus monolayers. Although the mechanical properties of $1H\text{−}\mathrm{W}X\mathrm{O}$ are found to be isotropic, they are orientation dependent for $1T^{\prime }\text{−}\mathrm{W}X\mathrm{O}$. It is also shown that $1H\text{−}\mathrm{W}X\mathrm{O}$ monolayers are indirect band-gap semiconductors and the band gap narrows down the chalcogen group. Except $1T^{\prime }$-WSO, $1T^{\prime }\text{−}\mathrm{W}X\mathrm{O}$ monolayers have a narrow band gap correlated with the Peierls distortion. The effect of spin-orbit coupling on the band structure is also examined for both phases and the alteration in the band gap is estimated. The versatile mechanical and electronic properties of Janus $\mathrm{W}X\mathrm{O}$ monolayers together with their large piezoelectric response imply that these systems are interesting for several nanoelectronic applications.

Using first-principles spin-polarized density functional theory, we carried out an analysis on the atomic structure, stability, energetics, and mechanical and electronic properties of single-layer structures of arsenene. These are buckled honeycomb, symmetric, and asymmetric washboard arsenene structures. Our analysis is extended to include layered three-dimensional crystalline phase of arsenic, as well as bilayer and trilayer structures to reveal dimensionality effects. The buckled honeycomb and symmetric washboard structures are shown to maintain their stability at high temperatures even when they are freestanding. As a manifestation of the confinement effect, the large fundamental band gap of single-layer phases decreases with increasing number of layers and eventually is closed. Concomitantly, lattice constants partially increase, while interlayer distances decrease. The effects of hybrid functional or self-energy corrections together with the spin-orbit coupling on the electronic structure of arsenene are crucial. The responses of direct and indirect band gaps to biaxial or uniaxial strain are rather complex and directional; while the fundamental band gap decreases and changes from indirect to direct with the biaxial strain applied to buckled arsenene, these effects are strongly directional for washboard arsenene. The width and the indirect/direct character of the band gap can be tuned by the number of layers, as well as by applied uniaxial/biaxial strain.