Research Article  Open Access
Hari Krishna Neupane, Narayan Prasad Adhikari, "Tuning Structural, Electronic, and Magnetic Properties of C Sites Vacancy Defects in Graphene/MoS_{2} van der Waals Heterostructure Materials: A FirstPrinciples Study", Advances in Condensed Matter Physics, vol. 2020, Article ID 8850701, 11 pages, 2020. https://doi.org/10.1155/2020/8850701
Tuning Structural, Electronic, and Magnetic Properties of C Sites Vacancy Defects in Graphene/MoS_{2} van der Waals Heterostructure Materials: A FirstPrinciples Study
Abstract
In this work, we systematically studied the structure, and electronic and magnetic properties of van der Waals (vdWs) interface Graphene/MoS_{2} heterostructure (HSG/MoS_{2}) and C sites vacancy defects in HSG/MoS_{2} materials using firstprinciples calculations. By the structural analysis, we found that nondefects geometry is more compact than defects geometries. To investigate the electronic and magnetic properties of HSG/MoS_{2} and C sites vacancy defects in HSG/MoS_{2} materials, we have studied band structure, density of states (DOS), and partial density of states (PDOS). By analyzing the results, we found that HSG/MoS_{2} is metallic in nature but C sites vacancy defects in HSG/MoS_{2} materials have a certain energy bandgap. Also, from the band structure calculations, we found that Fermi energy level shifted towards the conduction band in vacancy defects geometries which reveals that the defected heterostructure is ntype Schottky contacts. From DOS and PDOS analysis, we obtained that the nonmagnetic HSG/MoS_{2} material changes to magnetic materials due to the presence of C sites vacancy defects. Right 1C atom vacancy defects (R1C), left 1C atom vacancy defects (L1C), centre 1C atom vacancy defects (C1C), and 2C (1C right and 1C centre) atom vacancy defects in HSG/MoS_{2} materials have magnetic moments of −0.75 µ_{B}/cell, −0.75 µ_{B}/cell, −0.12 µ_{B}/cell, and +0.39 µ_{B}/cell, respectively. Electrons from 2s and 2p orbitals of C atoms have main contributions for the magnetism in all these materials.
1. Introduction
Graphene has a honeycomb lattice of carbon atoms; each atom in a lattice contains four valence electrons and interacts with its three nearest neighbor carbon through σbond due to sp^{2} hybridization of 2s, 2p_{x}, and 2p_{y} orbitals of three valence electrons. The fourth electron occupies the 2p_{z} orbital which overlaps with the nearest 2p_{z} electrons and forms a πbond perpendicular to the Graphene plane. These electrons are loosely bound, and most of the electronic properties of the pure Graphene are dictated by these delocalized electrons [1, 2]. The band structure of the pure Graphene (two bands π and π) originating from p_{z}orbital meets at six points in kspace known as Dirac points. Dirac points of Graphene are formed at the Fermi energy level, so it is called zero bandgap semiconductors. The structure of Graphene containing Dirac points bears astonishing electronic, optical, mechanical, and magnetic properties, so electronic devices, transparent electrodes, and spintronics devices can be manufactured by using Graphene [1–3]. In nanoscience research, a keen interest is given by the researchers for the study of twodimensional hexagonal structural materials. Like Graphene, MoS_{2} monolayer is a 2D transition metal dichalcogenide (TMDC) honeycomb structure material with a direct bandgap of the value of 1.80 eV [4]. It also has winsome properties, because of which it can be applied in industry for producing signal amplifier, integrated logic circuits, flexible optoelectronic devices, transistors, photodetectors, photocatalysts, optoelectronic devices, solar cells, and lubricants. Fundamentally, also it is interesting as it is just a singlelayered material [5–10]. The Graphenebased research in 2D materials has made enormous success [11–13]. The metal/semiconductor interface such as G/MoS_{2} is a new contact type of the Graphenebased van der Waals (vdWs) interface, known as heterostructures (HS) material. The heterostructures can be used to wipe out the unwanted properties of the constituents and hence give rise to desired properties than the constituents [14]. The firstprinciples study of HSG/MoS_{2} can be done in periodically repeated supercells. The supercells contain two interfaces which are equivalent to the term of stoichiometry and geometry [15]. This G/MoS_{2} vdWs interface was studied by various research groups [15, 16]. The report presented that the structure contains some innovative properties which can create different components in the electronic devices [17]. Also, vdWs HSG/MoS_{2} has intriguing electronic properties, transport properties, optical transparency, mechanical flexibility, and photoconductivity. Thus, it can be highly recommended in the application of electronic, photovoltaic, and memory devices [18–21].
In our previous work, we studied structural, electronic, and magnetic properties of Mo sites vacancy defects in HSG/MoS_{2} materials by firstprinciples calculations using vdWs correction in the DFTD2 approach [22]. To the best of our knowledge, C sites vacancy defects in HSG/MoS_{2} materials have not been studied. Therefore, in the present work, we investigated the structural, electronic, and magnetic properties of vdWs interfaces, HSG/MoS_{2}, and C sites vacancy defects in HSG/MoS_{2} materials using firstprinciples calculations with the DFTD2 approach. The vacancy defects in solids cause deviation of atoms or ions from the periodicity, and they are used to find innovative properties. They can be used to design new materials [23]. Also, the magnetic materials can be applied in various fields such as biomedicine, molecular biology, biochemistry, diagnosis, catalysis, nanoelectronic devices, and various other industrial applications like magnetic seals in motors, magnetic sensors, magnetic inks, electrical power generator, transformers, magnetic recording media, and computers [24, 25].
The rest part of the paper is organized as follows. The computational details will be discussed in Section 2 whereas Section 3 contains results and discussion. We close the paper with the main conclusions and outlook of the present work in Section 4.
2. Computational Model and Methods
We have performed the firstprinciples calculations to investigate the structural, electronic, and magnetic properties of HSG/MoS_{2} and C atom vacancy defects in HSG/MoS_{2} materials within the framework of density functional theory (DFT) [26], with van der Waals (vdWs) corrections taken into account by DFTD2 [27] approach using Quantum ESPRESSO (QE) computational package [28]. To incorporate the electronic exchange and correlation effects in the density functional theory, Generalized Gradient Approximation (GGA) was used via PerdewBurkeErnzerhof (PBE) exchange correlations [29]. Grimme’s RappeRabeKaxirasJoannopoulos (RRJK) model of ultrasoft pseudopotentials is used to replace the complicated effects of the motion of the core (i.e., nonvalence) electrons of an atom and its nucleus with an effective potential for all atoms in a system. It helps to deal with only the chemically active valence electrons which are included explicitly in our calculations. The electronic configurations of valence electrons in C, Mo, and S atoms of our system are C:[He] 2s^{2}2p^{2}, Mo:[Kr] 4d^{5}5s^{1}, and S:[Ne] 3s^{2}3p^{4}, respectively. All the structures are optimized and relaxed by the BFGS scheme [30], using Quantum ESPRESSO code [28], until the total energy changes are less than 10^{−4} Ry and force acting between two consecutive selfconsistent fields is less than 10^{−3} Ry/Bohr. After the relax calculations, we have done selfconsistent total energy calculations, for this Brillouin zone of heterostructure is sampled in kspace using MonkhorstPack (MP) scheme [31], with an appropriate number of mesh (4 × 4 × 1) of kpoints, which is determined from the convergence test. The MarzariVanderbilt (MV) [32] smearing of the small width of 0.001 Ry is used. In addition, we have chosen the “David” diagonalization method with a “plain” mixing mode and mixing factor of 0.6 for selfconsistency. For band structure calculations, a mesh of (4 × 4 × 1) kpoints is used, and for the density of states (DOS) and partial density of states (PDOS) calculations, an automatic denser mesh of (8 × 8 × 1) kpoints is used, where, in both the cases, 100 kpoints are chosen along the high symmetric points connecting the reciprocal space.
In this work, we have prepared the HSG/MoS_{2} by using (4 × 4) supercell structure of Graphene and (3 × 3) supercell structure of monolayer MoS_{2} with lattice mismatch about 4.13%, where we maintained vacuum distance greater than 20 Å to avoid the interactions between two adjacent layers as shown in Figure 1(c). For the construction of these supercell structures, at first, we have created a unit cell of Graphene and MoS_{2} by using structural analysis tool XCrySDen and computational tool Quantum ESPRESSO. To construct the unit cell, we used the Bravais lattice index, cell dimension parameters, and lattice constant in the input file. For the Graphene unit cell, we have taken the experimentally reported value of the distance between two carbon atoms that is 1.42 Å [31]. After the construction of the Graphene unit cell, we calculated the kinetic energy cutoff value, kpoints, and lattice parameters from the convergence test and found the constant kinetic energy cutoff value 35 Ry. The charge density cutoff value for ultrasoft pseudopotential is calculated by using the relation 10 × kinetic energy cutoff, which is 350 Ry. These obtained parameters (kinetic energy cutoff, charge density cutoff, kpoints, and lattice parameters) are used in the input file to relax our system. We found the distance between two carbon atoms of the relaxed Graphene unit cell to be 1.42 Å, which is very close to the starting value for relaxation [31]. The unit cell of MoS_{2} is prepared by using the experimental value of 3.19 Å [6, 33]. Its unit cell contains a single layer of two S and one Mo atoms. The Mo atom bounds with the S atom in a trigonal prismatic arrangement, where each Mo atom is surrounded by six first neighboring S atoms. After the construction of a unit cell, we have calculated its optimized values of kinetic energy cutoff, kpoints, lattice parameters, and charge density cutoff values as in Graphene, and then these parameters are used in the input file to relax the system. We found that the value of the lattice constant to be 3.18 Å, which is also close to the experimentally reported value of 3.19 Å [6, 33]. We then developed (4 × 4) supercell structure of Graphene and (3 × 3) supercell of monolayer MoS_{2} from these prepared unit cells, by extending along x and y direction as shown in Figures 1(a) and 1(b), respectively. After that, we have constructed the stable and relaxed structures of right 1C atom vacancy defects (R1C), left 1C atom vacancy defects (L1C), centre 1C atom vacancy defects (C1C), and 2C (1C right and 1C centre) atom vacancy defects in HSG/MoS_{2} as shown in Figure 2. These prepared structures are used for further investigations.
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3. Results and Discussion
In the present work, we have carried out a firstprinciples study of C sites vacancy defects in HSG/MoS2 heterostructures. In this section, we present the main findings and their interpretations from the investigation of the heterostructures.
3.1. Structural Analysis
The Graphenebased stable heterostructure materials in G/MoS_{2} is prepared by using (4 × 4) supercell structure of Graphene and (3 × 3) supercell structure of monolayer MoS_{2} with considerable (4.13%) lattice mismatch as shown in Figures 1(a)–1(c). The stability of the structure is determined by binding energy calculations. The higher the value of binding energy is, the more stable the system is. Thus, the greater value of binding energy material is more favorable for the calculations of its physical properties. The binding energy (E_{b}) of HSG/MoS_{2} is calculated by using the following relation: E_{b} = E_{Graphene} + E_{MoS2} – E_{HSG/MoS2}, where E_{Graphene}, E_{MoS2}, and E_{HSG/MoS2} represent the ground state energy of a fully relaxed (4 × 4) supercell of Graphene, (3 × 3) supercell of MoS_{2}, and heterostructure of G/MoS_{2}, respectively. The heterostructures of carbon atom vacancy defects are prepared by using optimized and relaxed HSG/MoS_{2} material as shown in Figure 2, where out of 32C atoms, the concentrations of the vacancy defects of R1C, L1C, C1C, and 2C in HSG/MoS_{2} materials are found to be 3.13%, 3.13%, 3.13%, and 6.25%, respectively. These are also stable structures. The order of binding energy of the structures is found to be as HSG/MoS_{2} > 1C atoms HSG/MoS_{2} > 2C atoms HSG/MoS_{2} as given in Table 1. So, the stability of the structure is decreased with an increase in its defects concentrations. Among the various carbon atom vacancy defects in HSG/MoS_{2} configurations, we have used the most stable R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials. R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} have defects formation energies of 0.20 eV, 0.20 eV, 0.20 eV, and 0.41 eV, respectively. These energy values are less than the defects formation of energy values of other vacancy defects configurations. The defects formation energies in our systems are calculated based on the standard formalism [34]; E_{f} = E_{T} (defect) + n_{C}µ_{C} − E_{T}(perfect), where E_{T}(defect) is the total energy of a supercell with the defects, n_{C}is the numbers of C atoms removed from the perfect supercell to introduce a vacancy, µ_{C} is chemical potentials of C atoms, and E_{T}(perfect) is the total energy of the neutral perfect supercell, respectively. Figures 1(d)–1(f) are interlayer and interatomic distances measurement geometries of HSG/MoS_{2}, 1C, and 2C atom vacancy defects in HSG/MoS_{2} geometries, respectively.

We have analyzed the structural properties of HSG/MoS_{2} and C sites vacancy defects in HSG/MoS_{2} materials and then obtained the data of interlayer distances which are given in Table 2. Also, interatomic distances of HSG/MoS_{2} and its C sites vacancy defects in HSG/MoS_{2} materials are given in SI (Table S1).
 
Here, (CMo), (CUS), and (CDS) represent distance from C atom in Graphene to Mo atom in MoS_{2}, distance from C atom in Graphene to upper S atom in MoS_{2}, and distance from C atom in Graphene to down S atom in MoS_{2}, respectively. 
From Table 2, we found that HSG/MoS_{2} geometry is more compressed than C sites vacancy defects in HSG/MoS_{2} geometries, and compactness of material increases with a decrease in its defects concentrations. Also, we found that the C1C vacancy defects structure is slightly compact than other R1C and L1C vacancy defects structures.
3.2. Electronic and Magnetic Properties
To know the electronic and magnetic properties of HSG/MoS_{2} and C sites vacancy defects in HSG/MoS_{2} materials, we first consider the key characteristics of freestanding Graphene supercell, monolayer MoS_{2} supercell, and G/MoS_{2} heterostructure. From band structure calculations, Graphene has zero bandgap energy because the states below the Fermi level characterized by π bonds and states above the Fermi level characterized by π antibonding states and corresponding bands meet at Fermi level that is Dirac cone. The monolayer MoS_{2} is an intrinsic semiconductor with a direct band of value 1.65 eV; this value is close to the experimentally reported value of 1.80 eV [10, 33]. The zerobandgap energy material (Graphene) and widebandgap energy material (MoS_{2}) are joined together to form vdWs HSG/MoS_{2} material with 4.13% of the lattice mismatch as shown in Figure 1(c). In HSG/MoS_{2}, ntype Schottky contact is formed with a Schottky barrier height of 0.56 eV as shown in Figure 3(a). Figure 3(a) represents the band structure plot of HSG/MoS_{2}, where the xaxis represents high symmetric points in the first Brillouin zone and the yaxis represents the corresponding energy values. We have taken 100 kpoints along the specific direction of the irreducible Brillouin zone to get a fine band structure by choosing ΓMKΓ high symmetric points. We found that the Dirac point shifted 0.56 eV above the Fermi level in HSG/MoS_{2}, which shows that HSG/MoS_{2} is metallic in nature. The shift in the Dirac point is in good agreement with the previously reported value of 0.49 eV [10, 35]. The Dirac point is formed at 0.56 eV height from the Fermi level in HSG/MoS_{2}, because higher values of potential barrier existed between the positions of C and S atoms in Graphene and monolayer MoS_{2} surfaces separately. The work function value of HSG/MoS_{2} is greater than MoS_{2}; as a result, electrons are moved from Graphene to MoS_{2} surface making ntype Schottky contact [5, 36]. Figures 3(b) and 3(c) represent the density of states (DOS) and partial density of states (PDOS) plots of HSG/MoS_{2,} where the yaxis represents spinup and spindown electrons states of DOS/PDOS and the xaxis represents the corresponding energy values.
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In addition, to tune the electronic properties at C sites vacancy defects in HSG/MoS_{2} materials, we used band structure calculations of R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials as shown in Figure 4, where the xaxis represents high symmetric points in the first Brillouin zone and the yaxis represents the corresponding energy values. We have also taken 100 kpoints along the specific direction of the irreducible Brillouin zone by choosing ΓMKΓ high symmetric points.
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We found that the Dirac point is not formed in electronic band structures and a small energy gap formed between the lower energy level of the conduction band and upper energy level of the valence band in R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials. These R1C, L1C, C1C, and 2C vacancy defects materials have opened narrow bandgap of values 0.15 eV, 0.13 eV, 0.14 eV, and 0.37 eV, respectively. Thus, the strength of metallic nature decreased with an increase in the concentration of defects. It is obvious that electronic configurations of valence electrons in C, Mo, and S atoms are [He] 2s^{2} 2p^{2}, [Kr] 4 d^{5} 5s^{1}, and [Ne] 3s^{2} 3p^{4}, respectively. Each C atom has a single spinup in 2p_{x} and 2p_{y} and vacancy in 2p_{z} suborbital; Mo atom has one unpaired spinup in suborbital 5s and 4d_{xy}, 4d_{xz}, 4d_{yz}, 4d_{x}^{2}_{y}^{2}, and 4d_{z}^{2}; S atom has paired spins (up and down) in 3p_{x} suborbital and one unpaired spinup in 3p_{y} and 3p_{z} suborbital. We have prepared a stable structure of 2C atom vacancy defects in HSG/MoS_{2} materials by removing two C atoms together from HSG/MoS_{2} material containing 59 atoms, as shown in Figure 2(d). Similarly, R1C, L1C, and C1C atom vacancy defects in HSG/MoS_{2} stable materials are prepared by pulling out right 1C, left 1C, and centre 1C positions of carbon atoms from HSG/MoS_{2} structure having 59 atoms, respectively, as shown in Figures 2(a)–2(c). These vacancy positions of carbon atoms developed unpaired spin electrons in suborbital of atoms of 2C defects in HSG/MoS_{2} structure. Similarly, carbon atom vacancy in R1C, L1C, and C1C defects in HSG/MoS_{2} materials produced unpaired spin electrons in the suborbital of atoms. Due to the unpaired total spinup and total spindown electrons in the orbitals of atoms in the system, unequal Fermi energy values are obtained in HSG/MoS_{2} and its C sites vacancy defect materials. Therefore, we found that the Fermi energy of HSG/MoS_{2} material has value 0.32 eV and R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials have values 0.52 eV, 0.53 eV, 0.54 eV, and 0.56 eV, respectively. It means that the Fermi level shifted upwards (towards conduction band) by 0.20 eV, 0.21 eV, 0.22 eV, and 0.24 eV values, respectively, which means Schottky barrier transition from ptype to ntype Schottky contact by the movement of interfacial charges [35]. The formation of ntype Schottky contact can provide important information for enhancing the power given by high efficiency Schottky nanoelectronic devices [37]. The parameters of Fermi level shift and energy gap look to be associated with each other. Also, they are increased with an increase in its vacancy defects concentrations in materials as shown in Table 1.
To get well competency of electronic and magnetic properties of materials, we have carried out DOS and PDOS calculations [23]. Figures 5(a)–5(d) represent DOS plots of R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials, respectively, and Figures 6(a)–6(d) represent PDOS plots of R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials, respectively, where the vertical dotted line represents Fermi energy level and the horizontal line separates states of spinup and spindown electrons in the orbitals of C, Mo, and S atoms; i.e., the states above the horizontal line represent spinup electrons and a state below the horizontal line represents spindown electrons.
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The magnetic properties of materials can be investigated by the analysis of spins of electrons distributed in DOS and PDOS plots. The asymmetrically distributed spinup and spindown of atoms in DOS and PDOS plots mean that materials have magnetic properties. Similarly, symmetrically distributed spinup and spindown of atoms in DOS and PDOS plots mean that materials carry nonmagnetic properties. We observed the spinup and spindown states of electrons, which are symmetrically distributed in the DOS and PDOS plot of HSG/MoS_{2} material as shown in Figures 3(b) and 3(c). Hence, HSG/MoS_{2} is a nonmagnetic material.
In addition, we have done the DOS and PDOS analysis of R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials. The data of magnetic moment calculations of these materials are given in SI (Table S2). The PDOS plots of 2s and 2p orbital of C atoms, 4p, 4d, and 5s orbital of Mo atoms, and 3s and 3p orbitals of S atoms in R1C atom vacancy defects in HSG/MoS_{2} material are shown in Figure 6(a). PDOS value near the Fermi level of 2s and 2p orbitals of C atoms reflects that spinup and spindown states are asymmetrical. We found that the total magnetic moment of R1C in HSG/MoS_{2} has a value −0.75 µ_{B}/cell; this is due to 2s and 2p spins electrons in the orbitals of C atoms. Also, the magnetic moment given by spins of electrons in 2s and 2p orbitals of C atoms is separately calculated, which have −0.24 µ_{B/}cell and −0.51 µ_{B/}cell values, respectively. These values are obtained by calculating the net magnetic moment given by spinup and spindown electrons of carbon atoms in the structure. The negative values of magnetic moment reveal that spindown electrons of atoms have a principal role compared to spinup electrons of atoms for magnetism in the system. This means that other atoms do not play a role in the magnetism of R1C atom vacancy defects in HSG/MoS_{2}. In Figure 6(b), the unoccupied spinup electron states in the 2p orbital of C atoms and spindown electron states in the 2s and 2p orbital of C atoms are asymmetrically distributed near the Fermi level. Magnetic moment values given by 2s and 2p orbital of C atoms are −0.23µ_{B}/cell and −0.52µ_{B}/cell, respectively. Therefore, the total value of the magnetic moment of L1C vacancy defects in HSG/MoS_{2} material is −0.75µ_{B}/cell, due to dominant contributions of spin electrons in 2s and 2p orbital of C atoms in the system. Similarly, in Figure 6(c), the only unoccupied spindown electron states are seen near the Fermi level, which reflects that spin states are asymmetrical. We have evaluated PDOS of C1C defects in HSG/MoS_{2} material and found that the values of the magnetic moment due to spin electrons in 2s and 2p orbital of C atoms are −0.07µ_{B}/cell & −0.05µ_{B}/cell, respectively. Therefore, the total value of the magnetic moment given by spin electrons in the orbital of C atoms in the system is −0.12µ_{B}/cell. In Figure 6(d), we saw that the asymmetrically distributed spinup and spindown electron states are presented beyond −0.0025 eV energy in the valence band and above 0.0024 eV energy in the conduction band. The magnetic moment given by 2s and 2p orbital of C atoms in the system has values 0.7µ_{B}/cell and 0.31µ_{B}/cell, respectively. These values are obtained by calculating net magnetism given by spinup and spinown electrons of atoms existing in the system. Therefore, the total value of the magnetic moment of 2C atom vacancy defects in HSG/MoS_{2} material is +0.39µ_{B}/cell. The positive value of magnetic moment means that spinup electrons of atoms have a preeminent role compared to spindown electrons of atoms in the magnetism. In all these cases, 2s and 2p orbitals of C atoms have major contributions of magnetic moments in C sites vacancy defects in HSG/MoS_{2} materials, which are also shown in SI (Figure S1).
4. Conclusions
We have constructed HSG/MoS_{2} and C sites vacancy defects in HSG/MoS_{2} structures and investigated their structural, electronic, and magnetic properties by firstprinciple calculations with van der Waals corrections in the DFTD2 levels of approximation. We studied structures of HSG/MoS_{2} and C sites vacancy defects in HSG/MoS_{2} materials and found that the nondefects structure is more compressed than defects structures. The binding energy of these materials is decreased with an increase in its defects concentrations. Then, we investigated the electronic and magnetic properties of these materials from the band structure calculations and DOS/PDOS analysis. From band structure calculations of HSG/MoS_{2}, we found that it is metallic in nature. R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials have small energy gap of values 0.15 eV, 0.13 eV, 0.14 eV, and 0.37 eV, respectively. Thus, the strength of metallic nature decreased with an increase in the concentration of vacancy in structures. Also, we have calculated the Fermi energy level of pure and vacancy defects geometries, which shows that ntype Schottky barrier contact is formed due to the interfacial charge transfer. For better comprehension of the electronic and magnetic properties of materials, we have performed the DOS and PDOS calculations. We found that DOS and PDOS states of spinup and spindown electrons are symmetrically distributed in HSG/MoS_{2} and asymmetrically distributed in C sites vacancy defects in HSG/MoS_{2} materials. Therefore, HSG/MoS_{2} is a nonmagnetic material but C sites vacancy defects in HSG/MoS_{2} materials carry magnetic properties. The total magnetic moment in R1C, L1C, C1C, and 2C atom vacancy defects in HSG/MoS_{2} materials is found to be −0.75µ_{B}/cell, −0.75µ_{B}/cell, −0.12µ_{B}/cell, and +0.39µ_{B}/cell, respectively. The spins of electrons in 2s and 2p orbitals of C atoms have the main role to bring a magnetic moment in all these materials. The strength of magnetic properties is developed in C sites vacancy defects in HSG/MoS_{2} materials due to the convenient arrangement of spin electrons in the structures.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
HKN acknowledges the UGC Nepal Award no. PhD75/76S&T09 and network project NT14 of ICTP/OEA. NPA acknowledges UGC Nepal (Grant CRG 073/74 S&T 01).
Supplementary Materials
Table S_{1}: the interatomic distances measurement of HSG/MoS_{2} and C sites vacancy defects in HSG/MoS_{2} geometries, where (SS), (MoMo), and (CC), respectively, represent the interatomic distance between two sulpher atoms in MoS_{2}, two molybdenum atoms, and two carbon atoms in Graphene. Table S_{2}: magnetic values generated by total and individual spinup and spindown electron orbital of C, Mo, and S atoms in pure and C sites vacancy defects (HS) in G/MoS_{2} geometries from PDOS analysis. Figure S_{1}: (a) PDOS plot of total spinup and spindown electron orbital of all atoms in R1C atom vacancy defects in HSG/MoS_{2}. (b) PDOS plot of total spinup and spindown electron orbital of all atoms in L1C atom vacancy defects in HSG/MoS_{2}. (c) PDOS plot of total spinup and spindown electron orbital of all atoms in C1C atom vacancy defects in HSG/MoS_{2}. (d) PDOS plot of total spinup and spindown electron orbital of all atoms in 2C atom vacancy defects in HSG/MoS_{2}, where the states above the horizontal line represent spinup electrons and a state below the horizontal line represents spindown electrons. (Supplementary Materials)
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Copyright © 2020 Hari Krishna Neupane and Narayan Prasad Adhikari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.