Hydrogenated-Graphene-Encapsulated Graphene: A Versatile Material for Device Applications.

Graphene and its heterostructures exhibit interesting electronic properties and are explored for quantum spin Hall effect (QSHE) and magnetism-based device applications. In present work, we propose a heterostructure of graphene encapsulated by hydrogenated-graphene, which could be a promising candidate for a variety of device applications. We have carried out DFT calculations on this system to check its feasibility to be a versatile material. We found that electronic states of multilayer pristine graphene, especially the Dirac cone, an important feature to host QSHE, can be preserved by sandwiching it by fully hydrogenated graphene. The interference of electronic states of hydrogenated graphene was insignificant with those of graphene. States of graphene were also found to be stable upon application of an electric field up to ±2.5 V/nm. For device applications, multilayer graphene or its heterostructures are required to be deposited on a substrate, which interacts with the system opening up a gap at the Dirac cone making it less suitable for QSHE applications, and hydrogenated graphene can prevent it. Magnetization in these hydrogenated-graphene-sandwiched graphene systems may be induced by creating vacancies or distortions in hydrogenated graphene, which was found to have a minimal effect on graphene's electronic states, thus providing an additional degree of manipulation. We also performed a set of calculations to explore its applicability for detecting some molecules. Our results on trilayer graphene encapsulated by hydrogenated graphene indicate that all these observations can be generalized for systems with a larger number of graphene layers, indicating that multilayer graphene sandwiched between two hydrogenated graphene is a versatile material that can be used in QSHE and sensor devices.

Introduction

The honeycomb lattice structure of graphene (GR) is the nearest analogy to Haldane’s model[1] in condensed matter physics. However, due to the weak spin–orbit coupling (SOC) of carbon atoms, it is not an ideal quantum spin Hall insulator (QSHI) or 2D topological insulator.[2] The quantum spin Hall effect (QSHE) is realized in GR, but the band gap of GR is zero, limiting its application. For this reason, a lot of work has been devoted to finding an alternative QSHI with high SOC and high bulk band gap. A non-Haldane model system HgTe quantum well has been found to be a good alternative. However, it requires low operating temperature, which hinders its applications.[3] Further, 2D allotropes of group VI(A) and V(A) have also been predicted to be QSHIs.[4] Out of these, stanene (a 2D allotrope of tin) has been reported to meet most of the requirements and has been studied both theoretically and experimentally.[5−8]

Even after all these developments, GR, both in pristine and heterostructures forms, is still being investigated for QSHE.[9,10] To preserve the QSHI nature, GR is generally coupled with 2D boron-nitrate (2D BN) as a heterostructure, fabricated by alternating layers of GR and 2D BN.[11] Apart from 2D BN, other 2D materials, like WS2[12] and MoS2[13] (inducing spin–orbit coupling), yttrium iron garnet[14,15] and EuS[16] (inducing ferromagnetism), and MoSe2[17] (fabrication of Schottky devices), have been studied for various applications. One of the biggest drawbacks of these heterostructures is that they strain GR, opening up a band gap in place of the Dirac cone, and fabrication of these abovementioned structures is not a trivial process, as explained further in the text. In the present work, we propose an alternative to this system by replacing the 2D BN with hydrogenated GR (HG). This substitution preserves the essential Dirac cone of the GR layer enabling the composite multilayer system to host QSHE. However, there are certain benefits to this approach over the GR–BN heterostructures as discussed below.

The mismatch in the lattices between the graphene and other layers may have profound effects on its structural and electronic properties. For instance, a moiré pattern is seen in the crystal structure of the GR–BN heterostructures as a consequence of a slight mismatch of their lattice vectors.[18] However, these are reported to form inside the GR, and their effects on the QSHI states are required to be studied in detail. Such an effect breaks the inversion symmetry of the GR opening up a band gap. Further, the QSHI states in GR are reported to be quite fragile due to which a high-quality and defect-free sample is required. The preferred method has been to mechanically exfoliate the sheets of GR via a Scotch tape process.[19,20] This process is also repeated for the fabrication of 2D BN sheets, and then these sheets are stacked on each other in the required orientation. Though this yields a high-purity and defect-free sample, it requires a high level of skill and is time-consuming. While a method like chemical vapor deposition is used, it creates nanoflakes of GR rather than a continuous film.[21] Other than that, strain matching GR and 2D BN is again a complex process.[22,23] Hence, the large-scale extension of this process is challenging.

On the other hand, to fabricate the proposed systems, one needs to exfoliate multilayer graphene and only hydrogenate the outermost layer. A similar technique has been implemented for the fabrication of a heterostructure of GR and monolayer transition-metal dichalcogenides,[24] or the recent developments in the fabrication of high-quality graphene can be used for the same.[25] In addition, the magnetization in HG can be modulated via photolithographic processes.[26] Such modulations in the proposed GR–HG heterostructures can be used to tune its properties for desired magnetic applications. We demonstrate this tunability for GR and HG trilayer nanoribbons. Hence, the present work is divided into two parts: In the first part, we discuss the stability of the proposed systems and the role of HG in preserving the essential electronic states of the GR layer. As the dimensions of the gate in nanodevices are being reduced, it can be described as 1D structures. Hence, in the second part, we construct nanoribbons of up to 20 unit cellsa to study magnetization in it. We also explore the ability of the HG–GR trilayer to adsorb simple molecules such as H2, O2, CO2, and ethanol.

Computational Details

We have performed the first-principles density functional theory (DFT) calculations as implemented in the Quantum ESPRESSO (QE)[28] package. We have used the Perdew–Burke–Ernzerhof (PBE)[29] exchange-correlation function and included the DFT-D2 van der Waals corrections[30,31] for representing the electron dispersion effect induced due to the multilayer nature of the systems. A Γ-centered Monkhorst–Pack k-point grid of 15 × 15 × 1 was sufficient to sample the irreducible Brillouin zone. A kinetic energy cutoff of 40 Ry for the wave functions gave the required convergence in the total energy. This energy cutoff has been used in all the calculations presented in this work. The pseudopotentials used in this work were obtained from the PSlibrary version 1.0.[32,33] Further, to limit the interaction between the periodic images of the unit cell, a vacuum of ≈10 Å is added to the unit cell above and below the trilayer system. The geometry optimization was performed until the forces per atom were reduced to less than 10–6 Ha/au. The phonon spectra calculations of the systems were performed by the density-functional perturbation method, as implemented in QE.

To compute the edge states, nanoribbons were constructed having a width of up to 20 unit cells along the Y direction and a single unit cell in the X direction. To minimize the interactions from neighboring images, a vacuum of ≈10 Å was added on both sides along the Y and Z directions. A k-point mesh of 6 × 1 × 1 was used. A small and arbitrary initial value of the magnetic moment was set for each atom for the spin-polarized calculations, and a full geometry optimization was carried out to obtain the final magnetic state. For computing the band structures, high-symmetry k-points of the Brillouin zone were selected along the path M → Γ → K → M. The k-points were generated by the XCrysDens package.[34] It may be noted that we have not considered spin–orbit coupling since it is quite weak in both carbon and hydrogen atoms.

We studied two types of trilayer systems: (1) single GR layer sandwiched between two HG layers denoted as system A and (2) single HG layer sandwiched between two GR layers denoted as system B as illustrated in Figure c,d, respectively. As these are multilayer systems, the stacking angle is also an important feature. The two selected different stacking angles are 0° generally denoted as the AB configuration and 60° generally denoted as the AA configuration, as shown in Figure a,b, respectively. The selection of the stacking angle was done in accordance with the Bernal stacking method. For convenience, the systems have been named using the following nomenclature: a prefix is used to denote trilayer configuration, and a postfix is used to indicate the stacking angle.

Figure 1

Configurations of trilayer HG–GR systems. (a,b) Top views of the two different stacking angles (0 and 60° , respectively). The axis of rotation is the z axis that is perpendicular to the plane of the paper. (c,d) Different stacking orders (HG–GR–HG and GR–HG–GR, respectively). These structures are before geometry optimization.

As an example, the system of GR encapsulated by HG with stacking angle of 0° is named A0, while the system where HG is encapsulated by GR with a stacking angle of 60° is named B60. Hence, the structures have been named A0, A60, B0, and B60. Similar configurations for the bilayer systems were also studied. However, from the phonon dispersion calculations, they were found to be very unstable and hence were not considered for the presented work. The crystal and band structure details regarding these additional systems can be found in Figure S6. The systems described in the text were generated using ATK Virtual Nano Lab.[35]

Results and Discussion

QSHE in Graphene–HG Heterostructures

We first discuss the structures of the GR–HG heterosystems and their stability. We then describe their band structures followed by the effect of the electric field on the electronic structure properties of these heterostructures.

Structure and Stability of Proposed Systems

In Figure , we display the optimized structures as well as phonons dispersion for A0, A60, B0, and B60 systems. The carbon atoms present in the plane of the HG layers are buckled due to the bonding with hydrogen atoms. A slight lateral displacement of the outer layers is also seen with respect to the central layer for A0 and B0 systems. The layers however approximately retain their stacking angles with respect to the central plane. Such a behavior has been reported in the 3R-type MoS2 system[36] where one of the layers, when laterally moved in the plane, showed a second energy minimum. The optimized lattice constants of A-type and B0 and B60 were found to be 2.50, 2.50, 2.48, and 2.48 Å, respectively. Note that the lattice constant for graphene is 2.46 Å. Thus, the lattice mismatch between our proposed systems and pristine graphene is less than 1.5%; it is an important merit for the proposed systems.

Figure 2

(color online) (a) Top and (b) side views of A0 system, (c) top and (d) side views of A60 system, and (i,j) phonon dispersion of the systems A0 and A60, respectively, plotted along the high-symmetry k path. (e) Top and (f) side views of B0 system, (g) top and (h) side views of B60 system, and (i,j) phonon dispersion of the systems B0 and B60, respectively, plotted along the high-symmetry k path.

To understand the stability of the systems, phonon dispersion was calculated (Figure ). Most of the phonon frequencies are positive with a few exceptions primarily in the vicinity of the Γ-point for most of the systems. The spread along the k-axis of these negative frequencies is also small and likely to be due to numerical errors rather than the instability in structure.[37] The stability of these systems can further be checked based on their cohesive and formation energies. The energy of formation of the trilayer from monolayers and the binding energy per atom can be calculated as

Negative values of these energies suggest that the system is thermodynamically stable; that is, the processes that can decompose and (or) transform these systems are forbidden and (or) very gradual. In Table , we show the energy of formation of the trilayer from monolayers and the binding/cohesive energy per atom. Taking into account the magnitude of the values from the last column of the table, it may be concluded that the systems are energetically and thermodynamically favorable.

Table 1

Formation and Binding Energies of the Trilayer Systems

name	total energy (Ry)	energy of trilayer formation (Ry)	binding/cohesive energy per atom (Ry)
graphene	–36.8942		–0.6805
hydrogenated graphene	–39.2646		–0.4737
A0	–115.4449	–0.0214	–0.5172
A60	–115.4429	–0.0194	–0.5170
B0	–113.0683	–0.0153	–0.5790
B60	–113.0694	–0.0163	–0.5792
energy of isolated carbon atom		–17.7666 Ry
energy of isolated hydrogen atom		–0.9183 Ry

The negative frequencies near the Γ point do not necessarily mean that the system is unstable as in this case the energetics are favorable. This has been demonstrated in the work of Mounet et al.,[38] where a screening of 2D materials from 3D bulk was performed with the help of a high-throughput methodology. This leads to the creation of a database of 2D materials that includes their crystal structures, electronic band structures, and phonon dispersion. They have classified the materials with negative frequencies near the Γ-point as stable as their energetics were favorable. Further, as the hydrogenated graphene layer is under strain, it will give rise to negative frequencies, and as mentioned above, it does not imply that the system is unstable. With these arguments, we may conclude that the systems under consideration are stable.

Electronic Band Structures of Proposed Systems

The band structures for all the systems were calculated to assert the feasibility of proposed systems to host QSHE. In Figure , we show the band structures for all the configurations. Clearly, from the plot, we can note that, for the different configurations of the proposed systems, the stacking order or stacking angles seem to have little to no effect on the band structure of the sandwiched layer. The band structures of all systems were found to be quite similar, as they consist of the same components arranged in different configurations. From the initial observation, it may be noted that, at the K-point, there is a Dirac point similar to that of pristine GR. However, there is an extremely small and negligible gap, which is less than the error of DFT calculations; hence, it can be considered as gapless. There are also some additional bands flanking the Dirac point. These bands touch the Fermi level, effectively interacting with the Dirac point providing an indirect conduction path, indicating these systems to be semimetallic in nature. If the proposed systems are semimetallic, then the possibility of them hosting QSHE is reduced. However, detailed analyses of the band structures show that they still hold a possibility of hosting QSHE.

Figure 3

(color online) Band structures of (a) pristine graphene and (b) hydrogenated graphene. Band structures of the systems (c) A0, (d) A60, (e) B0, and (f) B60. Note that the Dirac point is present for the systems A0, A60, B0, and B60 (see insets) and the band structure of the trilayer systems is basically an addition of the band structures of graphene and HG.

For understanding these features further, we plot the k-resolved projected density of states (PDOS) given in Figure S5. From these plots, one can observe that the Dirac cone at the K-point is formed out of the carbon atoms of the GR sheet, with negligible contribution from the HG atoms. Further, the band structures of the individual pristine GR and HG do not interfere with each other indicating a weak chemical coupling between GR and HG. Hydrogen bonding is observed when the distance of the hydrogen with the heavier and high-electronegative elements such as O and N is of the order of 1.5–2.5 Å. However, the distance of the hydrogen atoms nearest to any of the carbon atoms from the GR layer is about 2.8 Å indicating negligible interaction between the HG and GR layers. In addition, the electron density overlap between these layers is also not present (see Figure S6). Thus, we may conclude that the presence of the additional band does not affect or alter the presence of the Dirac cone and the origin of the Dirac cone in the system can be attributed to the central GR plane, providing a possibility of hosting QSHI states.

In order to examine whether if the HG layer shields multilayer graphene, we studied trilayer graphene encapsulated by HG. Note that, even in pristine trilayer graphene, the Dirac cone is preserved and has a possibility of hosting QSHI states.[39] We compute the band structure of this system and found that the characteristics of trilayer graphene have been preserved (Figure S2) supporting the abovementioned claim. Thus, the electronic properties of the graphene layers seem to be protected by the HG layer. Recall that, for device applications, the multilayer graphene, which holds QSHE, is generally required to be deposited on a substrate. The substrate states then interact with the graphene system opening up a gap at the Dirac cone making it less suitable for QSHE-related applications. One way to protect the graphene states would be to add an HG monolayer between the graphene and the substrate. However, we found that the HG–graphene bilayer itself is very unstable. Hence, it could be difficult to synthesize and then deposit on a substrate. On the other hand, our calculations on the HG-encapsulated monolayer, as well as trilayer graphene, indicate that, upon deposition on a substrate, the graphene states are likely to be protected by the HG layers, thus retaining the property of graphene layers to host QSHE.

Effect of the Electric Field on Band Structures of Proposed Systems

It is well known that the electronic structure of graphene is not affected by the applied electric field. Hence, an application of an electric field to the HG–GR–HG trilayer should not affect the Dirac cone. In the buckled structure of the 2D system such as silicene in the presence of the electric field, the potential felt by the sublattice is different, which leads to an opening up of a band gap. Hence, in the presence of the electric field, if the HG layers due to their buckled nature interact with the graphene layer in the presence of an electric field, the Dirac cone may get altered. In order to probe the stability of the Dirac cone in the presence of the electric field, the HG–GR–HG trilayer systems in the A0 and A60 configurations were subjected to electric fields in the range from −2.5 to +2.5 V/nm in steps of 0.5 V/nm (see Figure ). The electric field is modeled by a saw-tooth potential, which is purely a mathematical technique. Hence, care must be taken to set the boundary conditions so that the electric field drops to zero in the vacuum region away from the HG layers.

Figure 4

(color online) Band structures of systems A0 (a–j) and A60 (k–t) under electric fields of ±0.5, ±1.0, ±1.5, ±2.0, and ±2.5 V/nm. The energy range in the inset is from 0.75 to −0.75 eV.

Upon switching the electric field, we noted that the Dirac point present at the K-point is not affected at any given value of the electric field. A few bands in the vicinity of the Γ-point above and below the Fermi level do split. The projected density of states (PDOS) analysis shows that these bands are from the HG layer indicating that the HG states in A0 and A60 configurations do not interfere with the those of GR even in the presence of an electric field. Rather, it acts as a shield for the central GR layer. A similar conclusion can be made for the systems B0 and B60 (see Figure ). Unlike the A0 and A60 systems, here, the Dirac point observed due to the GR sheets is split albeit at high electric fields of about 4.0 V/nm and higher. Further, from Figure , it can be observed that the range of negative phonon dispersion is higher than those of A0 and A60. Thus, one may conclude that, in the A0 and A60 systems, the Dirac point is quite stable. Hence, only these systems were considered for further investigation. From the above observations of the systems A0 and A60 and the derived conclusion, it is clear that the effect on the electronic states of GR is not unfavorably affected. Thus, the HG-encapsulated GR holds a possibility of hosting QSHE.

Figure 5

(color online) Band structures of systems B0 (a–j) and B60 (k–t) under electric fields of ±0.5, ±1.0, ±1.5, ±2.0, and ±2.5 V/nm. The energy range in the inset is from 0.75 to −0.75 eV.

A direct method of testing this claim would be calculating the Z2 topological invariant where Z2 = 1 means that the system is QSHI and Z2 = 0 means that the system is not QSHI. However, as these systems are constructed via stacking of multiple layers and the system as a whole is conducting, the current methods for determining the Z2 invariant cannot be reliably used here.[2,40] An indirect method of determining if a system can host QSHE is to compute the edge state and to count the number of band crossings, which should be odd-numbered.[41] Even this method is difficult to implement since the systems A0 and A60 as a whole have an indirect band closing between the bands of GR (at the K-point above the Fermi level) and HG (near the Γ-point below the Fermi level), which will give the systems conducting edges. Thus, the only possible ab initio method of determining whether the systems A0 and A60 can host the QSHE is to verify that the electronic states of GR are not affected. This has been performed and is concluded that electronic states are indeed not affected. Hence, the proposed systems A0 and A60 do have a possibility of hosting QSHE.

Magnetization in GR–HG Heterostructures

Magnetization in graphene and related materials has been typically studied by adding adatoms, which can be done using the scanning tunneling microscopy method in a controlled manner.[42,43] Magnetization may be induced by creating vacancies or distortions in graphene.[44] However, such modulation may significantly affect the Dirac cone making graphene lose its QSHI states. Such limitations may be overcome with the proposed HG–graphene system by introducing distortions in the HG layer or by forming nanoribbons. As we shall see below, by both methods, the graphene edge states are observed in addition to significantly induced magnetic moments in the heterostructure.

First, we discuss the results of magnetization in nanoribbons. For this purpose, we constructed nanoribbons with widths up to 20 unit cells by the procedure discussed in Computational Details, in the zigzag and arm-chair conformations of the A0 and A60 systems and performed DFT calculations. The systems are further named R0 and R60 for nanoribbons of systems A0 and A60, respectively, to distinguish them from their parent systems.

We also added a prefix Z to denote the zigzag nanoribbon and A to denote the arm-chair nanoribbon. For example, a zigzag nanoribbon of A0 is denoted as ZR0, while an arm-chair nanoribbon of A60 is denoted as AR60. See Table for detailed nomenclatures.

Table 2

Labeling Schemes for Nanoribbons

conformation	system A0	system A60
arm chair	AR0	AR60
zigzag	ZR0	ZR60

Before we discuss the electronic structure, we make note the following characteristics of the nanoribbons: (1) The structures have unique atomic arrangements; that is, even if zigzag nanoribbons are created, one of the edges is in an arm-chair configuration (see Figure c). (2) To observe the distinction between the electronic states of zigzag and arm-chair nanoribbons, their dimensions should be as large as possible.[27] The 20 unit cell width nanoribbon was the largest system that we could compute without reducing the accuracy of the calculations. For each system, three sets of distinct DFT calculations were performed. The first set of calculations was performed on systems without any modification where the nanoribbons were constructed using the parameters described in Computational Details. In the second set of calculations, 2 unit cells from the center of the top HG layer were removed to introduce a defect to increase the number of edges of the HG (see Figure a). The third set of calculations was performed after saturating all the dangling bonds with hydrogen for both systems described above. Finally, band structures for all the above systems were computed.

Figure 8

(color online) (a) Side view of the nanoribbon with 2 unit cells removed form the top HG layer, (b) top view of the top HG layer of the system A0 showing the cavity, and (c) the edges of the system AR60. The hydrogen atoms of the system have been removed. The top HG is represented by a pinkish/brownish color, while the bottom HG is represented using the red color. The graphene layer is colored gray. Note that the edge of the graphene layer is arm chair, whereas that of HG is zigzag.

The band structure of the system ZR0 is given in Figure a. As anticipated due to the metallic nature of the systems, there is the presence of metallic states at edges. The number of edge states is even. However, the edge states are due to contributions from both conduction and valence bands. For topologically protected states, there should be a pair of bands that connects the conduction and valence bands while creating an odd number of Dirac crossing/points.[41,45] Thus, one can conclude that these states are not topologically protected (as explained herea). Interestingly, the presence of absolute magnetization of about 7.18 μB/cell is observed, causing a considerable spin split in the electronic structure of the system. This is marked in Figure by black arrows. This marked band originates from the edges of both HG and encapsulated GR layers. Such behavior is seen in the band structures of all of the systems (AR0, ZR60, and AR60, see Figure ), which are not hydrogenated, asserting the importance of passivation of the dangling bonds. The most remarkable observation is that the electronic structures of the systems are independent of the direction of the construction of the nanoribbon or the stacking angles between the layers; that is, the nanoribbons A0 (A60) and R0 (R60) have similar band structures even after selecting 20 unit cells.

Figure 6

(color online) Band structures of (a) ZR0, (b) AR0, (c) ZR60, and (d) AR60. The red lines represent up electron bands, and the blue lines represent down electron bands. Some of the important features of the band structure are highlighted by yellow circles. The black arrows mark the edge states emerging from the edges of the HG layer.

We see that feature characteristics of the 0° and 60° stacking angles are present such as in the band structure of the ZR0 system (Figure a), in the sense that the band crossing occurs at the integer value of the k point while for the ZR60 system (Figure c) the band crossing is observed near the half-integer k-points. This has been marked by the translucent yellow circle in Figure . The majority of these features arise from the dangling edge bonds, which have a very poor experimental realization. Upon hydrogenation, all the ribbons display a significant change in the band structure as well as magnetization. In Figure , we show the band structures of the passivated ZR0 and ZR60, respectively. A substantial change is observed. The absolute magnetizations for both the systems are reduced drastically to about 0.47 (0.71) and 0.56 (0.69), respectively, due to saturation of the dangling bonds, which is reflected well in the reduced spin splitting as compared to that of the non-hydrogenated systems. The interference from HG layers is reduced so significantly that the electronic states near the Fermi level are from graphene only.

Figure 7

(color online) Band structures of (a) diss-ZR0, (b) hydrogenated ZR0, (c) hydrogenated dis-ZR0, (d) ZR60, (e) hydrogenated ZR60, and (f) hydrogenated dis-ZR60. The red lines represent up electron bands, and the blue lines represent down electron bands. The green arrows point to the edge states emerging from the edge atoms of graphene alone. The splitting of bands due to passivation of the HG edges is marked by yellow ovals.

It is only logical from this discussion that further calculations can be carried out either on zigzag or arm-chair ribbons. We carried out the calculations on zigzag ribbons ZR0 and ZR60. Further, in order to modulate magnetization, we introduce distortions in these systems by removing 2 unit cells from one of the HG layers. We label these distorted nanoribbons as diss-ZR0 and diss-ZR60, respectively. In Figure a,c, we show the band structures of the diss-ZR0 (non-hydrogenated and passivated), and in Figure , we show the band structures for diss-ZR60 (non-hydrogenated and passivated), respectively. Due to the presence of an additional HG edge, an increase in the absolute magnetization is observed. It has now increased to 7.49 μB/cell for diss-ZR0, further increasing the split in the band structure. As mentioned earlier, the major contribution to this split is from the edges of the HG. However, for diss-ZR60, the magnetization has decreased by a small value to 7.14 μB/cell. This also explains the decrease in the number of degenerate bands. Thus, by just increasing the number of edges of HG, the magnetization of the proposed system can be altered, an additional parameter for customization of the proposed system.

Interestingly, after hydrogenation, the band structures of distorted ribbons seem to resemble those of the undistorted ribbons (compare Figure b for the band structure of ZR0 with that of diss-ZR0 in Figure c). However, this observation seems to be misleading as on closer analysis we found that there are some noticeable and important differences. First, there is a small increase in the spin split due to the increase in edges. These spin-split states are primarily in the vicinities of k = 0 and 2π/a, marked by yellow translucent ovals. This may imply that, by fine-tuning the number of edges of HG, one can increase the magnetization of the ribbon without significantly interfering the GR states at the Fermi level. However, in order to retain most of the features of the graphene states, especially the Dirac crossing, one may have to increase the width of the nanoribbon up to 50 unit cells or more.[27]

Adsorption of Molecules on GR–HG Heterostructures

Graphene with substitutional nonmetal dopants or adatoms has been widely studied for applications in sensing molecules and electrocatalysis.[46] In this section, we test the applicability of the proposed system for adsorption of molecules such as H2, O2, CO2, and ethanol. As it has been proposed that QSHI like stanene can also be utilized for gas sensing applications,[47] a brief investigation was performed on the proposed system. Concluded from the above, either by nonpassivation of the edges or by increasing the distortions in one of the HG layers, magnetization can be fine-tuned. The magnetization in these systems can certainly be affected by the presence of additional factors like adsorbed molecules. For this purpose, a base system consisting of an 8 × 8 × 1 number of unit cells of the system A0 was created. In order to induce magnetization, an asymmetric cavity was created on the top HG, which was hydrogenated, since such a vacancy or impurities are required as these molecules generally do not get adsorbed on defect-free surfaces. In Figure , we show the image of the top HG with the cavity along with the optimized structures of adsorbed H2, O2, CO2, and ethanol molecules on the system A0. The adsorbed H2 molecule is shown in the yellow translucent circle in Figure a.

Figure 9

(color online) Structures of molecules adsorbed on the HG–graphene–HG trilayer system with cavity in the top HG layer. Only the top HG layer is shown. (a) H2 molecule (in yellow region); (b) O2 molecule; (c) CO2 molecule; (d) ethanol molecule.

Geometry optimization of the distorted A0 system with the molecules adsorbed was carried out. These molecules are likely to change the magnetization upon adsorption on the A0 surface. However, the total number of the atoms exceeds 600 making the geometry optimization within the DFT framework difficult. Hence, we performed the geometry optimization using the Brenner force field for the substrate distorted A0 system and RelaxFF force field for the adsorbed molecules as implemented in the ATK VNL package[35] until the maximum absolute forces on the atoms were less than 10–4 eV/Å. Then the optimized geometry was used to calculate magnetization using DFT. The DFT parameters are kept the same as described in Computational Details, except that the calculations were performed for the Γ-point only due to a large number of atoms. We observed a distinct and significant change in the magnetization of the system for each molecule as summarized in Table . These changes can be easily detected in the experiments. Hence, we may conclude that the proposed system can be used to detect these molecules.

Table 3

Magnetization Induced due to the Presence of Cavity and upon Adsorption of Molecules on to the System A0

name	absolute magnetization (μB/cell)
system A0	0.1
A0:H2	2.35
A0:O2	7.23
A0:CO2	7.28
A0:ethanol	7.29

Conclusions

We performed DFT calculations on hydrogenated graphene–graphene trilayer systems with PBE exchange-correlation potential including the DFT-D2 van der Waals correction for representing accurately the phonon dispersion effects. We found that the heterostructure of graphene encapsulated by hydrogenated graphene could be a promising candidate for a variety of device applications. A detailed investigation shows that this system does have a possibility of preserving and protecting the edge states of GR. The presence of the HG layer makes the system magnetic, which can further be tuned by controlling the vacancies in HG layers. These defects or vacancies in the outermost HG layer can also be used to detect molecules such as H2, O2, CO2, and ethanol since upon adsorption a significant change in magnetic moments is observed, which can be detected experimentally. An additional important feature that was noted was the system independence on the direction of nanoribbons providing an additional simplicity for experimental realization of the proposed system. Our results on trilayer graphene encapsulated by HG indicate that the above observations can be extended to these systems with a larger number of central graphene layers. Interestingly, such systems are relatively simpler to fabricate by first exfoliating or synthesizing multilayer graphene and then hydrogenating the outermost layers. This work brings out the versatility of the multilayer GR sandwiched between two HG layers and thus has the merit of being experimentally investigated.