Tuning Structural, Electronic, and Magnetic Properties of C Sites Vacancy Defects in Graphene/MoS2 van der Waals Heterostructure Materials: A First-Principles Study

In this work, we systematically studied the structure, and electronic and magnetic properties of van der Waals (vdWs) interface Graphene/MoS2 heterostructure (HS-G/MoS2) and C sites vacancy defects in HS-G/MoS2 materials using first-principles calculations. By the structural analysis, we found that nondefects geometry is more compact than defects geometries. To investigate the electronic and magnetic properties of HS-G/MoS2 and C sites vacancy defects in HS-G/MoS2 materials, we have studied band structure, density of states (DOS), and partial density of states (PDOS). By analyzing the results, we found that HS-G/MoS2 is metallic in nature but C sites vacancy defects in HS-G/MoS2 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 n-type Schottky contacts. From DOS and PDOS analysis, we obtained that the nonmagnetic HS-G/MoS2 material changes to magnetic materials due to the presence of C sites vacancy defects. Right 1C atom vacancy defects (R-1C), left 1C atom vacancy defects (L-1C), centre 1C atom vacancy defects (C-1C), and 2C (1C right and 1C centre) atom vacancy defects in HS-G/MoS2 materials have magnetic moments of −0.75 µB/cell, −0.75 µB/cell, −0.12 µB/cell, and +0.39 µB/cell, respectively. Electrons from 2s and 2p orbitals of C atoms have main contributions for the magnetism in all these materials.


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 σ-bond due to sp 2 hybridization of 2s, 2p x , and 2p y orbitals of three valence electrons. e fourth electron occupies the 2p z orbital which overlaps with the nearest 2p z electrons and forms a π-bond perpendicular to the Graphene plane. ese electrons are loosely bound, and most of the electronic properties of the pure Graphene are dictated by these delocalized electrons [1,2]. e band structure of the pure Graphene (two bands π and π * ) originating from p z -orbital meets at six points in k-space known as Dirac points. Dirac points of Graphene are formed at the Fermi energy level, so it is called zero bandgap semiconductors. e 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][2][3]. In nanoscience research, a keen interest is given by the researchers for the study of two-dimensional 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 single-layered material [5][6][7][8][9][10]. e Graphene-based research in 2D materials has made enormous success [11][12][13]. e metal/semiconductor interface such as G/MoS 2 is a new contact type of the Graphene-based van der Waals (vdWs) interface, known as heterostructures (HS) material. e heterostructures can be used to wipe out the unwanted properties of the constituents and hence give rise to desired properties than the constituents [14]. e first-principles study of HS-G/MoS 2 can be done in periodically repeated supercells. e supercells contain two interfaces which are equivalent to the term of stoichiometry and geometry [15]. is G/MoS 2 vdWs interface was studied by various research groups [15,16]. e report presented that the structure contains some innovative properties which can create different components in the electronic devices [17]. Also, vdWs HS-G/MoS 2 has intriguing electronic properties, transport properties, optical transparency, mechanical flexibility, and photoconductivity. us, it can be highly recommended in the application of electronic, photovoltaic, and memory devices [18][19][20][21].
In our previous work, we studied structural, electronic, and magnetic properties of Mo sites vacancy defects in HS-G/MoS 2 materials by first-principles calculations using vdWs correction in the DFT-D2 approach [22]. To the best of our knowledge, C sites vacancy defects in HS-G/MoS 2 materials have not been studied. erefore, in the present work, we investigated the structural, electronic, and magnetic properties of vdWs interfaces, HS-G/MoS 2 , and C sites vacancy defects in HS-G/MoS 2 materials using first-principles calculations with the DFT-D2 approach. e vacancy defects in solids cause deviation of atoms or ions from the periodicity, and they are used to find innovative properties. ey 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]. e rest part of the paper is organized as follows. e 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.

Computational Model and Methods
We have performed the first-principles calculations to investigate the structural, electronic, and magnetic properties of HS-G/MoS 2 and C atom vacancy defects in HS-G/MoS 2 materials within the framework of density functional theory (DFT) [26], with van der Waals (vdWs) corrections taken into account by DFT-D2 [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 Perdew-Burke-Ernzerhof (PBE) exchange correlations [29]. Grimme's Rappe-Rabe-Kaxiras-Joannopoulos (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. e 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 self-consistent total energy calculations, for this Brillouin zone of heterostructure is sampled in k-space using Monkhorst-Pack (MP) scheme [31], with an appropriate number of mesh (4 × 4 × 1) of k-points, which is determined from the convergence test. e Marzari-Vanderbilt (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 self-consistency. For band structure calculations, a mesh of (4 × 4 × 1) k-points is used, and for the density of states (DOS) and partial density of states (PDOS) calculations, an automatic denser mesh of (8 × 8 × 1) k-points is used, where, in both the cases, 100 k-points are chosen along the high symmetric points connecting the reciprocal space.
In this work, we have prepared the HS-G/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 20Å 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 1.42Å [31]. After the construction of the Graphene unit cell, we calculated the kinetic energy cut-off value, k-points, and lattice parameters from the convergence test and found the constant kinetic energy cut-off value 35 Ry. e charge density cut-off value for ultrasoft pseudopotential is calculated by using the relation 10 × kinetic energy cut-off, which is 350 Ry. ese obtained parameters (kinetic energy cut-off, charge density cut-off, k-points, 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 1.42Å, which is very close to the starting value for relaxation [31]. e unit cell of MoS 2 is prepared by using the experimental value of 3.19Å [6,33]. Its unit cell contains a single layer of two S and one Mo atoms. e 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 cut-off, k-points, lattice parameters, and charge density cut-off 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 3.18Å, which is also close to the experimentally reported value of 3.19Å [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 (R-1C), left 1C atom vacancy defects (L-1C), centre 1C atom vacancy defects (C-1C), and 2C (1C right and 1C centre) atom vacancy defects in HS-G/ MoS 2 as shown in Figure 2. ese prepared structures are used for further investigations.

Results and Discussion
In the present work, we have carried out a first-principles study of C sites vacancy defects in HS-G/MoS2 heterostructures. In this section, we present the main findings and their interpretations from the investigation of the heterostructures.

Structural Analysis.
e Graphene-based 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). e stability of the structure is determined by binding energy calculations. e higher the value of binding energy is, the more stable the system is. us, the greater value of binding energy material is more favorable for the calculations of its physical properties. e binding energy (E b ) of HS-G/MoS 2 is calculated by using the following relation: E b � E Graphene + E MoS2 -E HS-G/MoS2 , where E Graphene , E MoS2 , and E HS-G/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. e heterostructures of carbon atom vacancy defects are prepared by using optimized and relaxed HS-G/MoS 2 material as shown in Figure 2, where out of 32C atoms, the concentrations of the vacancy defects of R-1C, L-1C, C-1C, and 2C in HS-G/MoS 2 materials are found to be 3.13%, 3.13%, 3.13%, and 6.25%, respectively. ese are also stable structures. e order of binding energy of the structures is found to be as HS-G/ MoS 2 > 1C atoms HS-G/MoS 2 > 2C atoms HS-G/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 HS-G/MoS 2 configurations, we have used the most stable R-1C, L-1C, C-1C, and 2C atom vacancy defects in HS-G/MoS 2 materials. R-1C, L-1C, C-1C, and 2C atom vacancy defects in HS-G/MoS 2 have defects formation energies of 0.20 eV, 0.20 eV, 0.20 eV, and 0.41 eV, respectively.
ese energy values are less than the defects formation of energy values of other vacancy defects configurations.
e defects formation energies in our systems are calculated based on the standard formalism [34]; 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. We have analyzed the structural properties of HS-G/MoS 2 and C sites vacancy defects in HS-G/MoS 2 materials and then obtained the data of interlayer distances which are given in Table 2. Also, interatomic distances of HS-G/MoS 2 and its C sites vacancy defects in HS-G/MoS 2 materials are given in SI (Table S1).
From Table 2, we found that HS-G/MoS 2 geometry is more compressed than C sites vacancy defects in HS-G/MoS 2 geometries, and compactness of material increases with a decrease in its defects concentrations. Also, we found that the C-1C vacancy defects structure is slightly compact than other R-1C and L-1C vacancy defects structures.

Electronic and Magnetic Properties.
To know the electronic and magnetic properties of HS-G/MoS 2 and C sites vacancy defects in HS-G/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. e 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]. e zero-bandgap energy material (Graphene) and wide-bandgap energy material (MoS 2 ) are joined together to form vdWs HS-G/MoS 2 material with 4.13% of the lattice mismatch as shown in Figure 1(c). In HS-G/MoS 2 , n-type 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 HS-G/MoS 2 , where the x-axis represents high symmetric points in the first Brillouin zone and the y-axis represents the corresponding energy values. We have taken 100 k-points along the specific direction of the irreducible Brillouin zone to get a fine band structure by choosing Γ-M-K-Γ high  In addition, to tune the electronic properties at C sites vacancy defects in HS-G/MoS 2 materials, we used band structure calculations of R-1C, L-1C, C-1C, and 2C atom vacancy defects in HS-G/MoS 2 materials as shown in Figure 4, where the x-axis represents high symmetric points in the first Brillouin zone and the y-axis represents the corresponding energy values. We have also taken 100 k-points along the specific direction of the irreducible Brillouin zone by choosing Γ-M-K-Γ high symmetric points.
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 R-1C, L-1C, C-1C, and 2C atom vacancy defects in HS-G/MoS 2 materials. ese R-1C, L-1C, C-1C, 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. us, 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 spin-up in 2p x and 2p y and vacancy in 2p z suborbital; Mo atom has one unpaired spin-up 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 spin-up in 3p y and 3p z suborbital. We have prepared a stable structure of 2C atom vacancy defects in HS-G/MoS 2 materials by removing two C atoms Table 2: e interlayer distances of (i) HS-G/MoS 2 and (ii) C sites vacancy defects in HS-G/MoS 2 materials.

Interlayer distances of HS-G/MoS 2 along x-, y-, and z-axis
Interlayer distances of C sites vacancy defects in HS-G/MoS 2 materials along x-, y-, and z-axis Here, (C-Mo), (C-US), and (C-DS) 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. 24 eV values, respectively, which means Schottky barrier transition from p-type to n-type Schottky contact by the movement of interfacial charges [35]. e formation of n-type Schottky contact can provide important information for enhancing the power given by high efficiency Schottky nanoelectronic devices [37]. e 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].   Advances in Condensed Matter Physics  (Table S2). e 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 R-1C atom vacancy defects in HS-G/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 spin-up and spin-down states are asymmetrical. We found that the total magnetic moment of R-1C in HS-G/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. ese values are obtained by calculating the net magnetic moment given by spin-up and spin-down electrons of carbon atoms in the structure. e negative values of magnetic moment reveal that spin-down electrons of atoms have a principal role compared to spin-up electrons of atoms for magnetism in the system. is means that other atoms do not play a role in the magnetism of R-1C atom vacancy defects in HS-G/MoS 2 . In Figure 6(b), the unoccupied spinup electron states in the 2p orbital of C atoms and spin-down 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. erefore, the total value of the magnetic moment of L-1C vacancy defects in HS-G/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 spin-down electron states are seen near the Fermi level, which reflects that spin states are asymmetrical. We have evaluated PDOS of C-1C defects in HS-G/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. erefore, 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 spin-down electron states are presented beyond −0.0025 eV energy in the valence band and above 0.0024 eV energy in the conduction band. e 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. ese values are obtained by calculating net magnetism given by spin-up and spin-own electrons of atoms existing in the system. erefore, the total value of the magnetic moment of 2C atom vacancy defects in HS-G/MoS 2 material is +0.39µ B /cell. e positive value of magnetic moment means that spin-up 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 HS-G/MoS 2 materials, which are also shown in SI ( Figure S1).

Conclusions
We have constructed HS-G/MoS 2 and C sites vacancy defects in HS-G/MoS 2 structures and investigated their structural, electronic, and magnetic properties by firstprinciple calculations with van der Waals corrections in the DFT-D2 levels of approximation. We studied structures of HS-G/MoS 2 and C sites vacancy defects in HS-G/MoS 2 materials and found that the nondefects structure is more compressed than defects structures. e binding energy of these materials is decreased with an increase in its defects concentrations.
en, we investigated the electronic and magnetic properties of these materials from the band structure calculations and DOS/PDOS analysis. From band structure calculations of HS-G/MoS 2 , we found that it is metallic in nature. R-1C, L-1C, C-1C, and 2C atom vacancy defects in HS-G/MoS 2 materials have small energy gap of values 0.15 eV, 0.13 eV, 0.14 eV, and 0.37 eV, respectively. us, 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 n-type 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 spin-up and spin-down electrons are symmetrically distributed in HS-G/MoS 2 and asymmetrically distributed in C sites vacancy defects in HS-G/MoS 2 materials. erefore, HS-G/MoS 2 is a nonmagnetic material but C sites vacancy defects in HS-G/MoS 2 materials carry magnetic properties. e total magnetic moment in R-1C, L-1C, C-1C, and 2C atom vacancy defects in HS-G/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. e spins of electrons in 2s and 2p orbitals of C atoms have the main role to bring a magnetic moment in all these materials. e strength of magnetic properties is developed in C sites vacancy defects in HS-G/MoS 2 materials due to the convenient arrangement of spin electrons in the structures.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.