Electronic Structure and Band Gap Engineering of Two-Dimensional Octagon-Nitrogene

A new phase of nitrogen with octagon structure has been predicted in our previous study, which we referred to as octagon-nitrogene (ON). In this work, we make further investigations of its stability and electronic structures. The phonon dispersion has no imaginary phonon modes, which indicates that ON is dynamically stable. Using ab initio molecular dynamic simulations, this structure is found to be stable up to room temperature and possibly higher, and ripples that are similar to that of graphene are formed on the ON sheet. Based on the density functional theory calculation, we find that single layer ON is a two-dimension wide gap semiconductor with an indirect band gap of 4.7 eV. This gap can be decreased by stacking due to the interlayer interactions. Biaxial tensile strain and perpendicular electric field can greatly influence the band structure of ON, in which the gap decreases and eventually closes as the biaxial tensile strain or the perpendicular electric field increases. In other words, both biaxial tensile strain and a perpendicular electric field can drive the insulator-to-metal transition, and thus can be used to engineer the band gap of ON. From our results, we see that ON has potential applications in many fields, including electronics, semiconductors, optics and spintronics.

(a) and the indirect band gap is 2.9 eV, which is the widest gap found in the octagon monolayer of group V elements 17,23 . Since pure functional tends to underestimate the band gap, we also calculated the  band structure using HSE functionals for comparison, as shown in Fig. 4(b). The band gap calculated using HSE functionals is 4.7 eV and the PBE result underestimates the gap by about 1.8 eV, even though these band structures near the Fermi level are similar. From the band of free ON, the conduction band minimum (CBM) is along the X-Γ line and the valence band maximum (VBM) is along the Γ-M line, which means that ON is an indirect gap semi-conductor.
To further investigate the orbital feature of band structures, the projected density of states (PDOS) and projected band are calculated, as shown in Fig. 5. From Fig. 5(a-c), it is clear that the band is mainly made up of s and p orbitals, but the contributions are different. Below the Fermi level, bands in the lower energy main have more s characters, while those bands near the Fermi level have more p z characters, which are responsible for the sharp peak near the Fermi energy in the density of states (DOS) as shown in Fig. 5(d). The lower band mainly consists of s orbitals, as shown in Fig. 5(a), while the contribution of p x+y orbitals becomes greater as the energy increases as shown in Fig. 5(b). p z orbitals play a dominant role near the Fermi level, as shown in Fig. 5(c). There is a flat band near the Fermi level, and the DOS is singular, which is mainly due to p z orbitals.
Our previous study 16 has shown that the stacking of nitrogene can change its electronic structure. The band gap decreases as the number of layers increases and some of the degeneracy of the bands is broken, especially at some high symmetry points, as shown in Fig. 6(a,b). The gap decreases rapidly as the number of layers increases. The general trend is similar for both the AA stacking and AB stacking, see Fig. 6(c,d), and the band gap is found to be linearly dependent on the reciprocal of the number of layers.

Effect of Biaxial Tensile Strain.
In addition to multilayer stacking, tensile strain is also a frequently used technique for manipulating the band gaps of 2D materials, because it is easier to realize experimentally. Tensile strain affects the kinetic energy of electrons, which changes the band structure directly. In the process of biaxial strain, the lattice constants have been enlarged synchronously and the atoms have been relaxed again. In Fig. 7(a), the band gap decreases with the strain, decreasing slowly in the range before 8%. Interestingly, there is a small maximum at a strain of 9%, then the gap decreases more rapidly and is almost linear as the strain exceeds 9%. The gap eventually closes at the strain of 13.2%, and the system becomes a metallic state, which is a second order phase transition. The relaxation results indicated that the ON structure was still stable at the strain of 13.2%. In the process of strain, some bands shift toward to the Fermi level. However, some bands shift up and away from it. Figure 7(b) shows the dependence of the energy gap on strain. In the beginning, the CBM is located at a point along the X-Γ line in the Brillouin zone. The CBM then shifts to the Γ point when the strain reaches 9% or above. Figure 7(c) shows the change of structural parameters with respect to tensile stain. Without strain, l a is longer than l b , and both l a and l b are monotonically increasing with respect to strain. As strain reaches 12% or more, l a becomes shorter than l b .
Effect of an External Electric Field. The application of an external electric field is also a useful technique to control the band structure of 2D materials. From Fig. 8(a) we can see that the band structure changes as the electric field strength increases. In the beginning, the CBM stays on the X-Γ line in the Brillouin zone but CBM shifts to Γ point when the electric field reaches 1.5 eV/Å or more. However, with the increases of the field strength, some bands shift down but some bands remain unchanged. For comparison, we plot the band structure in the absence of an external electric field and in the presence of an electric field of 1.95 V/Å, together, in the fourth panel of Fig. 8(a). The gap opens at 3 eV below Fermi level under the presence of the electric field. The band gap does not change untill the field strength reaches electric field of 1.5 eV/Å but the high energy bands move toward to the Fermi level. When the electric field reaches 1.5 eV/Å, the band gap decreases rapidly and closes at 2.0 eV/Å. The system then becomes metallic, as shown in Fig. 8(b). Some other materials 16,24,25 such as nitrogene also show similar phenomenon, due to the electron density redistributed under the electric field 26,27 . However, the critical field for transition is much higher than for nitrogene.

Discussion
In this study, the stability and electronic structure of ON have been studied by first-principle calculations. Phonon dispersion, as well as first-principle molecular dynamics (MD) suggest that ON is stable. The MD result shows the ON lattice is dynamically stable at 300 K without breaking the bonds, and that wraps and ripples are present at finite temperatures, which indicates the structure is stable at room temperature. Results based on the density functional theory calculation suggest that ON is a semiconductor with an indirect band gap of 2.9 eV/4.7 eV (PBE functional/HSE06 functional), which is the widest one in the octagon monolayer of group V elements. Analysis of the orbital character of the band structure is very helpful in constructing the tight-binding model, which would be beneficial for further study of its properties. In addition to monolayer ON, we also studied the electronic structure of multilayer ON. Both the AA stacking and AB stacking can decrease the band gap and have almost the same band gap for multilayer ON. Biaxial tensile strain can decrease the band gap as well, and a nearly linear dependence of gap on strain is found when the strain is between 9% and 13.2%, where the gap closes. Moreover, the perpendicular electric field can lower the energy of bands far above the Fermi level while keeping the ordinary bands intact. We therefore found that the gap remains the same at the range of from zero to 1.5 eV/Å but begins to decrease as the electric field strength reaches 1.5 eV/Å and closes at 2.0 eV/Å. Though the critical electric field is much high, this perhaps can be realized by the substrate. This study suggests that ON is a wide band gap semi-conductor and that its electronic structure can be tailored by several techniques. Our results suggest that further analysis using other methods, such as vacancy, doping and adsorption may demonstrate the existence of other interesting phenomena in the ON system, such as the existence of a Dirac cone or additional topological properties 29 . The transport properties of ON may exhibit some interesting phenomena, which could be seen by combining the density functional theory with the nonequilibrium Green's function formalism 30 . We expect that ON can be further stabilized when assembled on a substrate, because the rotational freedom will be quenched. The real ON can possibly be synthetized by comprising non-hexagonal rings with nitrogen molecules on Au(111) surfaces. This new novel material may be expected to be of use in many fields such as electronics, semiconductors, optics and spintronics.

Methods
The material and electronic structure of ON have been calculated using the VASP code 28 based on PAW with PBE of exchange-correlation. The system satisfied the periodic boundary conditions with the vacuum at least 15 Å thick between the interlayer. In order to obtain the stable structure, ions have relaxed by the conjugate-gradient method until the total force on each ion is less than 0.01 eV/Å, then it is further relaxed by a quasi-Newton algorithm until the total force on each ion is less than 0.0001 eV/Å. Phonon dispersions have been calculated by RESCU with a 2 × 2 × 1 supercell 31 . In the self-consistent calculation, an 8 × 8 × 1 k-point mesh with Monkhorst-Pack scheme was used for sampling the Brillouin zone under the perpendicular electric field and a 20 × 20 × 1 grid with Monkhorst-Pack scheme was used for other conditions. The MD simulations have been performed by using an NVT ensemble for a 4 × 4 × 1 supercell at 200 K and 300 K. We have not considered the spin-orbit coupling during the calculation because it is negligibly small in the ON.