Tuning magnetic properties of penta-graphene bilayers through doping with boron, nitrogen, and oxygen

Penta-graphene (PG) is a carbon allotrope that has recently attracted the attention of the materials science community due to its interesting properties for renewable energy applications. Although unstable in its pure form, it has been shown that functionalization may stabilize its structure. A question that arises is whether its outstanding electronic properties could also be further improved using such a procedure. As PG bilayers present both sp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}2 and sp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^3$$\end{document}3 carbon planes, it consists of a flexible candidate for functionalization tuning of electromagnetic properties. In this work, we perform density functional theory calculations to investigate how the electronic and structural properties of PG bilayers can be tuned as a result of substitutional doping. Specifically, we observed the emergence of different magnetic properties when boron and nitrogen were used as dopant species. On the other hand, in the case of doping with oxygen, the rupture of bonds in the sp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}2 planes has not induced a magnetic moment in the material.


Results
We begin our discussions by presenting the structural properties ( Fig. 1) and the charge localization (Fig. 2) profiles for the model doped PG bilayers studied here. In these figures, the radius of the spheres that represent the dopant atoms was increased for better visualization of the dopant sites. Figure 1a presents the optimized geometry of the two layers without defects, i.e. before the doping procedure took place.  www.nature.com/scientificreports/ between them by matching their rings to compose the bilayer complexes. Subsequently, these complexes were optimized to obtain their ground state solutions. The results presented in Fig. 1 (structural properties) do not show any relative displacement between the two layers upon doping. In the doping mechanism adopted here, the PG plane at the bottom is always pristine. The second PG layer on top receives the dopant in three distinct channels: (dopant-sp 2 -out) when the dopant is placed in the sp 2 plane above the interlayer region interacting with the vacuum, (dopant-sp 2 -in) when the dopant is placed in the sp 2 plane within the interlayer region interacting with the PG plane at the bottom, and (dopant-sp 3 ) for the doping in the sp 3 plane. For these nomenclatures, "dopant" stands for oxygen (O), boron (B), or nitrogen (N) atom. Importantly, some theoretical works have studied the structural stability of oxygen-, nitrogen-, and boron-doped PG layers 29,29,33,36,39,[39][40][41]41 . In a reactive molecular dynamics study, the results have revealed that oxygen-doped PG layers present remarkable enhancement in failure stress and strain when contrasted with pristine PG layers 40 . Moreover, it was recently demonstrated, by using DFT calculations, that boron-and nitrogen-doped PG layers are structurally stable when concentrated with pristine PG layers 29,36,39 . Figure 1b-d illustrate the cases B-sp 2 -in, B-sp 3 , and B-sp 2 -out, respectively. One can observe that the bond lengths between B-C slightly deviate from that of the bond length C-C in the pristine monolayer, which is 1.57 Å. These bond lengths (B-C) assume minimum and maximum values of 1.51-1.61 Å for all the cases of doping with B. As for the oxygen doping picture, represented by Fig. 1e-g, we observe a greater deformation around the doping site. Figure 1e,g show the result of doping the sp 2 planes. It is possible to note a tendency of carbonyl formation with the elevation of the oxygen atom by the distance of 1.18 and 1.19 Å from the carbon atom in the respective sp 3 plan. With the elevation of the oxygen from the sp 2 plane, the formation of a vacancy is observed with bond lengths in the edges whose sizes vary from 1.40 to 1.60 Å for the case O-sp2-in and O-sp2-out. In the case O-sp3 (Fig. 1f), a tendency of the oxygen to leave the plane is also observed, as the bond length of 1.40-1.72 www.nature.com/scientificreports/ Å is achieved between the first neighbors of the dopant. The nitrogen-doped PG lattices, Fig. 1h-j, present similar results to the ones for the boron-doped case. The bond lengths between N-C also slightly deviate from the C-C ones in the pristine case. These bond lengths (N-C) assume minimum and maximum values of 1.38-1.52 Å for all doping channels. The charge density wrapped around the dopant is depicted in Fig. 2. The yellowish cloud stands for the density due to up spin electrons, whereas the blueish on of the down spin electrons. The net charge observed is responsible for the magnetic moment, which characterizes a magnetization due to the presence of the dopant. The values of the magnetic moment for each structure are listed in Table 1, to be discussed later. It is observed that this charge concentration is more effective in the case of doping with boron ( Fig. 2a-c) and nitrogen ( Fig. 2g-i). On the other hand, no spontaneous magnetization was observed in the O-sp2-in and O-sp2-out cases ( Fig. 2d-f). This behavior suggests that magnetization in the case of doping with oxygen is not a direct consequence of doping, but rather of the deformation of the geometry that the dopant produces. The sp 3 plane has two dangling carbons with a distance of 2.80 and 2.72 Å from the oxygen atom. This distance makes the π-electrons of these two atoms to contribute to the effective magnetization of the bilayer, whose magnetic moment is 2.00 Bohr Magneton. In the O-sp2-in and O-sp2-out cases, the non-concentration of charge in the oxygen atom, which makes two connections in the plane, suggests a double bonding with the carbon, which characterizes a carboxyl. The resulting bond configuration for the carbon atoms in the edge keeps the symmetry of the vacancy.
The first row of Table 1 presents the formation energy, which is defined as: , where E b is the total energy for each doped bilayer, E mp the total energy of the monolayer without defect, and E md total energy of the doped bilayer. One can observe that the energy cost (average value) for the formation of the bilayer is approximately the same for boron and oxygen doping, i.e., − 9.49 to − 9.53 eV, respectively. For the nitrogen doping case, the average value of the formation energy is − 7.54 eV. In the second row of this table, we present the cohesion energy that is given by , where E C is the total energy of a carbon atom and N C is the number of carbon atoms of the bilayer. E x and N x are the total energies and number of doping atoms respectively, where X stands for B, N, or O. N total is the total number of atoms in the bilayers. The cohesion energy has values similar for all systems, suggesting the same level of cohesion for the three types of dopants. In the third row, we present the magnetic moment of each bilayer. One can realize that for the O-sp2 case, the value of the magnetic moment is zero, which is in agreement with what was already discussed of the net charge density. In the fourth row, the distances d 0 between the two layers are shown. After optimizing the geometry of the bilayers, these distances remained larger for the two both B-sp2-in and O-sp2-in doping cases, compared to the others that were between 2.50 and 2.61 Å, while for B-sp2-in and O-sp2-in is 3.12 and 2.70 Å, respectively. These results suggest that the dopant has a significant contribution to the interactions between the two layers. Figure 3 presents the band structure of the doped bilayer bands. For the pure bilayer (Fig. 3a), one can note that an indirect gap of 2.3 eV takes place, a value approximately equal to that found for the PG monolayer 9 . In the case of doping with boron ( Fig. 3b-d) and nitrogen (Fig. 3h-j), we observe a reduction of the bandgap to approximately 2.0 eV, which remained indirect. For the two cases of sp 2 doping (Fig. 3b,d,h,j), it occurs the emergence of states in the middle of the bandgap. In Fig. 3b,d, one can note a downstate above the Fermi level, one up and other down states, below the Fermi level. On the other hand, in Fig. 3h,j an upstate below the Fermi level. For the sp 3 doping cases (Fig. 3c,f,i), the two states are symmetrically positioned with respect to the Fermi level. In the case of oxygen doping, we also observed the appearance of the states in the middle of the bandgap: these states are symmetrical concerning the Fermi level and have no spin degeneration for the O-sp2-in and O-sp2-out cases (Fig. 3e,g). In these configurations, the bandgap was reduced to 2.2 and 2.1 eV, respectively. For the O-sp3 case (Fig. 3f), the bandgap is also 2.2 eV and with the two symmetrical states about the Fermi level, with spin up below and down above the Fermi Level.
Finally, Fig. 4 presents the projected density of states (PDOS) for all the complexes studied here. For the sake of comparison, Fig. 4a,e,i present the PDOS for the pristine case. For all the cases, the most significant contribution to the formation of the bands is for the p states of sp 2 carbon atoms. The Fermi level is closer to the valence bands, which characterizes a n-type semiconductor. In the B-sp 2 cases (Fig. 4b,d), a slight contribution of p orbitals of boron at the first peak in the middle of the bandgap (above the Fermi level) is observed. Still, for these two cases, we observed that the Fermi level is closer to the valence band, which characterizes a n-type semiconductor. The N-sp 2 cases (Fig. 4j,l) present a similar trend for PDOS when compared to the B-sp 2 cases. Regarding the B-sp 3 and N-sp 3 cases (Fig. 4c,k, respectively), there is no significant contribution of the dopants to the states near the Fermi level and the structure behaves as a n-type semiconductor, once the Fermi level is touching the top of the valence band. In the case of oxygen doping (Fig. 3f-h), we did not observe any significant contribution from O atoms. In the O-sp2-in case (Fig. 3f), the Fermi level is in the middle of the bandgap with peaks symmetrically localized regarding it for both spin channels, which characterizes the non-magnetization Table 1. Formation energy, cohesion energy, magnetic moment and distance between the two layers for all the cases studied here. B-sp2-in B-sp3  B-sp2-out O-sp2-in O-sp3 O-sp2-out N-sp2-in N-sp3 N- www.nature.com/scientificreports/ of this material. In the O-sp3 case (Fig. 3g), we have observed that the Fermi level is slightly displaced towards the conduction states, which characterizes a p-type semiconductor. It is also observed antisymmetric peaks concerning the spin, which stands for a significant magnetic moment of this structure. For the O-sp2-out case (Fig. 3h), a slight displacement of the Fermi level near the conduction band was also observed, characterizing a p-type semiconductor. It is observed that the peaks closest to the Fermi level are symmetrical concerning the spin states, proving the non-magnetic behavior of the material.

Methods
To investigate the electronic structure of doped PG bilayers, we used DFT calculations as implemented in the SIESTA software 42,43 . It makes use of a numerical base to expand the wave functions of the many atoms system. In the present work, it was used the DZP basis set 44,45 . As for the functional approximation, it was considered the generalized approximation of the gradient proposed by Perdew, Burke, and Ernzerhof (GGA/PBE) + vDW 46 , which is built from the expansion of the second-order density gradient. Pseudopotentials parameterized within the Troullier-Martins formalism are also considered 47 . This approximation is of fundamental importance for the description of the magnetic and electronic properties of materials composed of atoms with many electrons. All calculations were performed considering spin polarization. To calculate the bands and state densities, an MPK mesh of 15 × 15 × 1 is used 48 . A mesh cut of 200 Ry is chosen as a parameter for our calculations 49 . The forces converged until reaching a minimum value of 0.001 eV/Å. In order to ensure a good compromise between the accuracy of our results and the computational feasibility, the tolerance in the density of the matrix and the total energy was set at 0.0001 and 0.00001 eV, respectively. Importantly, this set of parameters were used recently to study other carbon-based lattices 29,50-52 .

conclusion
In summary, we carried out DFT calculations to investigate the influence of boron, nitrogen, and oxygen doping on the electronic properties of PG bilayers. Our findings showed that the difference between dopant on the sp 2 and sp 3 planes have a significant impact on the magnetic properties of boron and nitrogen doping. It was observed a spontaneous magnetization in the system when these doping species were considered. This is because boron and nitrogen contains one and three electrons, respectively, in the orbital valence 2p, whereas the substituted carbon has a pair of electrons in this same orbital. Therefore, the C-B and C-N bonds result in a magnetic polarization due to electronic covalence. This effect is characterized by the flat energy levels that appear in the middle of the bandgap for the cases of boron and nitrogen doping in the sp 2 planes. Such an effect is not observed in the case of doping with oxygen due to bond breaking. Regarding the effect on the pristine layer, there was no significant difference in its electronic properties. In the cases of boron and nitrogen doping, the resulting system characterizes a n-type semiconductor. On the other hand, for the oxygen doping in the sp 3 plane, we have observed that the Fermi level is slightly displaced towards the conduction states, which characterizes a p-type semiconductor. Since the electronic structure of PG bilayers present extra doping channels and can be easily tuned by doping its structure with just a single atom, they can represent an interesting alternative for replacing graphene in some optoelectronic applications.  www.nature.com/scientificreports/