Doped defective graphene nanoribbons: a new class of materials with novel spin filtering properties

Abstract

We present the results of our spin polarized density functional study of the electronic and transport properties of defective graphene nanoribbons doped with boron or nitrogen atoms. We have analysed the formation energy, electronic band structure, magnetic charge density and quantum conductance of the doped defective graphene nanoribbon systems. We have demonstrated the half metallic behaviour of the doped defective graphene nanoribbons. The primary cause of the half metallic behaviour of this particular system is the charge transfer from carbon to dopant atoms. We have also shown that the band gap of the doped defective graphene nanoribbons decreases with the intensity of a transverse electrical field and reaches the state of a spin gapless semiconductor. The current–voltage characteristics of the doped defective graphene nanoribbons show the polarization of the spin current and have high spin filtering efficiencies.

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1 Introduction

One of the primary objectives in the field of materials research is the invention of new materials with new and interesting properties. In this context, single layer graphite, i.e. 2D graphene, has received serious attention because of its potential applications in diverse fields. Many reports discuss the possibility of tailoring the properties of graphene nanoribbons (GNR) thereby making them suitable for use in nanosensors and spin filter devices. Among the different proposals is the use of dopant atoms that inject electrons or holes into the nanoribbons, altering the electronic properties and sometimes affecting the polarized transport degeneracy, which makes them useful as spin filtering devices. Research in spintronic materials has gained tremendous momentum because of their potential use in different applications such as memory storage, high speed computing devices and magnetic sensors. A spintronic device uses spin instead of charge as the carrier. So, a key challenge in this area is the generation of 100% spin polarized currents at the Fermi level. Among the different materials discovered, the most important are half-metals,¹ in which one spin state is metallic and the other is semiconducting so that only one spin state can conduct. Other interesting systems are spin semiconductors² and spin gapless semiconductors, which come from the concept of gapless semiconductors. In a spin semiconductor, both spin states have a gap but these are relatively shifted in energy, while for a spin gapless semiconductor,³ at least one of the spin channels in the valence band just touches only one of the spin channels in the conduction band at the Fermi level or vice versa. In this work we have predicted the half-metallic and spin semiconducting behaviour of doped defective graphene nanoribbons.

The honeycomb structure of graphene⁴ is the most favorable arrangement for sp² hybridized carbon atoms, but still, the presence of defects⁵ is ubiquitous in graphene. Recent progress in experimental techniques focuses on the extended line defect. Two of them are very important; one is the mass-scale production of graphene that leads to a polycrystalline material, with 1-D tilt grain boundaries,^6–9 and the other is controlled deposition on a metallic substrate that results in a translational grain boundary^10–13 in graphene. The synthesis of graphene nanoribbons with translational grain boundaries by Lahiri et al.¹⁰ indicates that one can design an experiment to produce defective graphene nanoribbons.

It is very well known that doping alters the electronic structure of GNRs and thus provides a way to tune the band gap as well as the nature of spin polarization.^14–22 In this context it is to be noted that the doping position also regulates the electronic properties of GNRs. There are many proposals by which one can control the electronic properties of GNRs and make them half metal. Thus, Cruz-Silva et al.²³ have studied the electronic structures of boron, nitrogen and phosphorus doped zigzag and armchair graphene nanoribbons and highlighted their interesting spin-dependent properties. By using first-principles density functional calculations, Botello-Mendez et al.²⁴ have studied the electronic and transport properties of intramolecular graphene hetero-junctions. These hybrid nanoribbons are found to exhibit width-dependent magnetic behaviour and act as spin polarized conductors. The spin transport properties of GNRs with embedded boron nitride dots and substitutional Mn impurities were studied by Nemnes et al.²⁵ By analyzing the spin resolved current calculated by a non-equilibrium Green's function based approach, these authors suggested that the systems studied are suitable for spin filter applications or for spin current switching devices. Chauhan et al.²⁶ have studied the effects of boron and nitrogen doping on the electronic and transport properties of zigzag GNRs (ZGNRs) using spin-unpolarized density-functional theory. These authors have shown that the doping of boron and nitrogen in ZGNRs changes the material from metallic to half-metallic or semiconducting. Based on a non-equilibrium Green's function and density-functional theory, Liu et al.²⁷ have investigated the magneto transport properties of ZGNRs with non-magnetic doping on the double ribbon edges. These authors have shown that boron–nitrogen double edge doping in GNRs induces perfect spin-filter properties with 100% negative spin polarization at the Fermi level.

Defective graphene is relatively new and may be a good candidate for the exploration of new and interesting properties. In a very recent article, Botello-Mendez et al.²⁸ reported a general overview of the electronic and quantum transport properties of both doped and defective graphene. Though a lot of work has been done on defective graphene, studies on the effect of doping on the electronic properties of defective graphene are still limited in the literature. In this work, we have considered a defective graphene nanoribbon, which resembles the line defect embedded in perfect graphene recently synthesized by Lahiri et al.¹⁰ We doped the ribbon using boron and nitrogen atoms separately and looked for any interesting properties such as half metallicity or spin gapless semiconducting behaviour, etc. The detailed electronic structure of the defective graphene nanoribbon, which is also one of the derivatives of HOPG,²⁹ is studied elsewhere; in this study we found that the ribbon is a non-magnetic metal.

2 Computational modelling and methodology

The ribbons that we have considered for this study consist of one octagon and a pair of pentagons periodically repeated along the z-direction, as shown in Fig. 1, and have four distinct doping positions, namely A, B, C and D. We replaced the carbon atoms at these sites with boron and nitrogen atoms separately and have investigated the electronic structures of the doped ribbons. All of the first-principles calculations were performed using density functional theory (DFT) as implemented in the SIESTA³⁰ code, and used a double-ζ plus polarization (DZP) basis set and norm-conservative Troullier–Martins pseudo-potentials (PP)³¹ to represent the valence and core electrons, respectively. The exchange–correlation functional of the generalized gradient approximation is represented by the Perdew–Burke–Ernzerhof approximation.³² A real space mesh cutoff of 300 Ry is used throughout the entire calculation and the electronic temperature is set to 300 K. The convergence criterion for the density matrix is taken as 10⁻⁴. The conjugate gradient method is used to relax all the atoms until the maximum force becomes less than 0.001 eV Å⁻¹. The k-point sampling for the ribbon was performed with a 1 × 1 × 8 Monkhorst-Pack k-grid. The spin transport properties are simulated using the TranSIESTA module within the SIESTA package, which is based on a combination of density functional theory and the non-equilibrium Green's function (NEGF).³³ The generalized gradient approximation in the PBE form is employed for the exchange–correlation functional. We have used similar basis and convergence criteria in our first-principles calculations. In the NEGF self-consistent loop, the charge density was integrated over 400 energy points along the semicircle in the complex plane. The spin polarized current is calculated with the help of the Landauer–Buttiker formula, which can be expressed as:where T_↑(↓) is the spin-resolved transmission function, f_L(R) is the Fermi–Dirac distribution function for the left (or right) electrode with an electrochemical potential μ_L(R) so that eV_b = μ_L − μ_R.

Fig. 1 The ribbon (which we have considered for this study) with different doping positions, namely A, B, C, etc. and 1, 2, 3, etc., which characterize different carbon atoms. The gray and white balls represent carbon and hydrogen atoms, respectively.

3 Results and discussion

We have relaxed the doped ribbon with ferromagnetic (FM) and antiferromagnetic (AFM) spin orientations, and also with a non-magnetic (NM) ground state, at different lattice constants in order to get an optimized geometry at an optimum lattice constant. The ribbon doped at the A and B sites preferred AFM spin alignment, while for the remaining sites the NM ground state is more favorable except for the ribbon containing boron at the D site (B@D), for which the FM spin configuration is energetically the most stable. At this instance it should be mentioned that the energy difference between the AFM and FM states is very small (in the order of meV). However, in the subsequent section we have only discussed the electronic structures of the magnetic nanoribbons. As can be seen from Table 1, the magnetic moments of the magnetic ribbons are very close to unity, except for the N@B configuration, whose magnetic moment is 0.1532 μ_b. The possibility of formation of the doped defective nanoribbons can be understood from the values of the formation energy (E_f), which is defined as:

E_f = E_doped + μ_C − E_pure − μ_D (2)

where E_doped and E_pure stand for the total energies of the doped and pure ribbons, respectively, while μ_C and μ_D are the chemical potentials of the carbon and dopant (B/N) atoms, respectively. The formation energies of the doped ribbons are tabulated in Table 1, which shows that boron doping is endothermic while nitrogen doping is an exothermic process, indicating the feasibility of the synthesis of nitrogen doped ribbons. The formation energies of the boron doped ribbons are much less than those of transition metal doped ribbons,³⁴ which are very recently synthesized in the laboratory and are doped at the edges. So, the formation of boron doped defective ribbons is also plausible.

Table 1 The ground states, formation energies E_f, and magnetic moments at different doping configurations of the defective graphene nanoribbons

Doping configuration	Ground state	Ef (eV per dopant)	Magnetic moment (μb per unit cell)
B@A	AFM	3.8797	1.0000
B@B	AFM	3.9989	0.9879
B@C	NM	3.8037	0.0000
B@D	FM	3.8865	1.0000
N@A	AFM	−1.0489	0.9989
N@B	AFM	−0.5079	0.1532
N@C	NM	−1.5109	0.0000
N@D	NM	−0.8576	0.0000

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After studying the magnetic ground state and energetics, we would like to go through the detailed electronic structure of all the magnetic nanoribbons. The electronic band structures of pristine and defective graphene reveal the metallic behaviour of this defective graphene and have been discussed in detail elsewhere.²⁹ Because of the lack of hexagonal symmetry, the π and π* pseudo-gaps at the Fermi level, present in graphene, disappear in defective graphene. To understand the effect of doping on the electronic band structures we show spin-resolved band structures in Fig. 2. From Fig. 2, it is clear that the ribbons with doping configurations B@A and N@A possess band gaps for one spin state (α for B@A with a gap of 0.25 eV, and β for N@A with a gap of 0.75 eV) while the other spin state is metallic as it crosses the Fermi level, i.e. these two doped ribbons show the half-metallic behaviour as the charge transport is dominated by one spin channel. In this context, it is worthwhile to mention that Lin et al.¹² have shown the half metallicity of graphene nanoribbons with a line defect close to the edges. The ribbon containing nitrogen at the B site is metallic as two bands of each spin channel cross the Fermi energy. In the case of the B@B ribbon, the band gap is 0.18 eV, which is in between the bands with opposite spins, while for the B@D ribbon, the valance band top (VBT) and conduction band minimum (CBM) belong to the same spin channel (β) with a band gap of 0.24 eV. We refer to these ribbons as spin semiconductors.

Fig. 2 Spin polarized band structures and magnetic charge density (Δρ = ρ_α − ρ_β) distributions of the different ribbons, designated by D@S, where D stands for the dopant atom (B or N) and S for the different sites, A, B, C, etc. The blue and red dotted lines denote the α and β spin states, respectively, while the reverse colours are valid for the charge density distribution. The Fermi level is set to zero. An isovalue of 0.0025 is used for the charge density plots.

Top views of the 3D isosurfaces of the magnetic charge density, which is defined as the electronic charge density difference between the α and β spins, are shown in the right panels of Fig. 2. The figure shows that in almost all cases, the edge states are ferromagnetically coupled with each other at each edge and also with opposite edges, except in the B@B ribbon, in which ferromagnetic coupling is observed between the edge states of one edge and antiferromagnetic coupling is noticed with other edges. The boron atom at the B site is responsible for the antiferromagnetic coupling as it attracts a net α spin density from one edge carbon atom due to its Lewis acid character, which results in the generation of a net (though very small) β spin density on another edge carbon atom. In this context it is to be noted that in pure zigzag graphene nanoribbons, the edge states are ferromagnetically coupled with each other at each edge, but these are antiferromagnetically coupled with opposite edges.¹ In addition to the ferromagnetic coupling between two opposite edges, the C₂ unit at the middle of the ribbon is also ferromagnetically coupled with two edges. As we have stated earlier, the boron atom pulls electron density from the adjacent carbon, giving rise to a charge transfer from carbon to boron and creating a potential gradient in the B@A and B@B ribbons. A close observation of the figure reveals that unlike boron, the nitrogen at the A site repels the electron density of the same spin on the adjacent carbon atom.

In order to investigate the cause of the half-metallicity of the D@A (D stands for dopant) systems, we have gone through the detailed contributions of each and every atom to the total density of states and the result is shown in Fig. 3. From the figure it is clear that the maximum contribution comes from boron and the horizontal carbon atom (C5) directly attached to the boron, and that the contribution of other atoms decreases with the increase in separation from the boron atom. This observation indicates that the half-metallic behavior of the B@A system is mainly due to a charge transfer (distinct from the magnetic charge density) from the carbon to the boron atom. In the case of the N@A system, the maximum contribution is from the horizontal carbon atom (C5). This may be due to a large coulombic repulsion on the nitrogen atom, which repels the charge density on the horizontal carbon atom, as is evident from the magnetic charge density plot. In this context it is very important to note that the contributions and locations of the PDOS of symmetric carbon atoms (with respect to the vertical mirror plane) are identical. This again confirms that the dopant equally affects the equidistant carbon atoms.

Fig. 3 Spin polarized PDOS of the B@A and N@A ribbons including contributions from the different carbon atoms, designated by 1, 2, 3, etc. The blue (or red) colour arrow is for the α (or β) spin state.

Another interesting observation we made in the B@B and B@D ribbons is the spatial separation of charge carriers. This feature is shown for both the B@B and B@D ribbons in Fig. 4. The figure shows a clear spatial separation of the charge carriers at two opposite edges of the B@B ribbons while for the B@D ribbons the charge is partially separated. This spatial separation of the charge carriers is a characteristic of type-II super-lattices and can be of potential use in solar cells. Our study demonstrates an effective way of separating electrons and holes by doping defective graphene with B atoms. Wang et al.¹⁴ have found a similar kind of spatial separation of the charge carriers in graphene nanoribbons with sawtooth edges but this separation occurs only in the presence of an applied electric field.

Fig. 4 The spatial distribution of the VBT (red) and CBM (blue) of the B@B and B@D ribbons. An isovalue of 0.1 is used for plotting. The cyan, white and brown balls are carbon, hydrogen and boron atoms, respectively.

Next, we focus on the effect of a transverse electric field on the B@B and B@D ribbons. On the application of the electric field across the width of the ribbon, the electronic structure around the Fermi level changes significantly for both ribbons. Under a transverse electric field, a pair of opposite spin states (of the AFM B@B ribbon) around the Fermi level are converging and another pair are separating apart, as is evident from Fig. 5. The situation is a little bit different for the FM B@D ribbon. In the case of the B@D ribbon, the band gap between the α spin channels decreases with an external electric field, due to the shift of two α spin states to the Fermi level, while the gap between opposite spin channels rises because of a higher downward movement of the occupied state relative to the unoccupied state. However, the overall result is a decrease in the spin band gap with the application of an electric field across the width of both ribbons. The spin band gaps for the B@B and B@D ribbons reduce to 0.0054 (at 0.252 V Å⁻¹) and 0.06 eV, (at 0.5 V Å⁻¹), respectively. As defined by Wang et al.¹⁴ the term gapless is valid when the band gap is close to or less than 0.1 eV. Hence, the B@B and B@D ribbons are spin gapless semiconductors under a transverse electric field. For spin gapless semiconductors the charge carriers are fully spin polarized and can be very useful in designing qubits for quantum computing or in magnetic data storage.

Fig. 5 Spin-resolved electronic band structures of the B@B and B@D ribbons under an external transverse electric field, and variations of the band gaps with the electric field. The electronic structures are plotted with 0.252 and 0.5 V Å⁻¹ electric fields for the B@B and B@D ribbons, respectively.

In order to explore the applications of these ribbons, we have studied the transport properties of these ribbons with the help of non-equilibrium Green's function (NEGF) analysis coupled with DFT. The systems considered for the transport calculations consist of two parts, a central scattering region (SR) which is confined between the semi-infinite left and right electrodes (LE and RE). For the transport calculations we have chosen only the B@A, B@D and N@A nanoribbons. From the electronic band structures we found that the B@A and N@A nanoribbons (Fig. 2) show half metallic behaviour, and that the B@D nanoribbon is a semiconductor with a very small gap for the β spin. So we expect higher spin filtering efficiencies for these systems. Spin-resolved zero-bias transmission functions for the B@A, B@D and N@A nanoribbons are presented in Fig. 6. The transmission functions are very much consistent with the electronic structures, as shown in Fig. 2. The half-metallicity of the B@A and N@A ribbons observed in the electronic structure calculations is also evident from the transmission functions. The transmission channels close to the Fermi energy take part in electron conduction under an applied bias. In the case of the B@A ribbon, the α spin channels show a finite transmission function, while there is no transmission for the β spin channels at the Fermi level. The situation is reversed for the N@A ribbon compared to the B@A ribbon. There is no transmission function at the Fermi level for both spin channels of the B@D ribbon, but the transmission gap is different, which results in different I–V_b curves. As all electronic devices work at a finite bias, we have calculated I–V characteristics for the B@A, B@D and N@A systems, which are shown in Fig. 7. In the inset of the figure we have given a schematic representation of a two-probe system. The figure reveals that in the case of the B@D system, the current for both spins is negligible up to V_b = 0.2 V, but after that the β spin-current rises with an applied bias up to 1.8 V, and beyond that it starts to fall and continues up to 2.2 V, showing negative differential resistance (NDR). The α spin-current does not show any significant change up to 1.8 V, but begins to rise after that. For the B@A system, the α current starts to increase from zero bias, whereas the β current rises only after 0.7 V. The situation is reversed for the N@A ribbon, compared to the B@A ribbon. For the N@A ribbon, the β spin-current rises from zero bias, while the opposite spin-current rises after 0.8 V. In this context it is to be noted that apparently the I–V curve of the B@A ribbon is inconsistent with its electronic structure as the band gap of the α spin state is around 0.25 eV whereas the gap revealed from the I–V curve is about 0.7 eV. This is due to a rapid shift (with respect to other states) of the VBT of the α spin channel to a lower energy with an applied bias while at the same time the CBM becomes diffuse. The overall result is an increase in the gap at the Fermi level, which is reflected in the I–V characteristics. However, the I–V curves certainly establish the spin filtering ability of these ribbons: the B@D and N@A ribbons filter β-current and the B@A ribbon filters α-current. In recent times there has been lots of interest in the search for spin filtering materials, and the spin filtering action has been reported for a number of graphene based systems.^{1,24,25,27,35} In order to quantify the extent of the spin-resolved current, we have defined the spin filter efficiency (SFE) as:

where I_α and I_β are the α and β spin currents, respectively.

Fig. 6 Spin polarized zero bias transmission functions of the B@A, B@D and N@A ribbons. The blue (or red) shaded region represent the α (or β) spin channels.

Fig. 7 Spin-dependent I–V characteristics and spin filtering efficiencies (as a function of bias) of three ribbons (B@D, B@A and N@A). For the I–V plots, the blue (or red) symbols represent the α (or β) spins. In the case of the I–V plots of the B@A and N@A ribbons, circular and triangular symbols (regardless of colour) are used for the B@A and N@A ribbons, respectively. A schematic representation of the two-probe system is given in the inset.

The variation of the SFE as a function of the bias voltage is shown at the bottom of Fig. 7 for the three different systems, viz. B@D, B@A and N@A. The variation of the SFE is symmetric about the zero bias and almost 100% spin filtering efficiency has been achieved. The transmission spectra shown in Fig. 6 can explain the spin filtering efficiencies of the different systems well. Thus, for example, Fig. 6 clearly shows a strong transmission around the Fermi level for the B@A and N@A systems. The B@A system shows the metallic feature of the α spin while this is completely lost in the β spin channel near the Fermi level. For the N@A system while the β spin channel shows the metallic behaviour near the Fermi level, this is completely lost in the α spin channel.

4 Conclusion

In summary, here we propose a multifunctional material based on doped defective graphene. We demonstrate that defective graphene nanoribbons, when doped with either B or N atoms at suitable positions, give rise to half metallicity. For the B@B nanoribbons, there is a clear spatial separation of the charge carriers at two different edges indicating the possibility of using them in solar cells. The band gaps of the spin gap semiconductor systems, B@B and B@D nanoribbons, decrease under a transverse applied electric field and reach the state of a spin gapless semiconductor. Our study also suggests that suitable doping on the defective graphene breaks the symmetry of the transmission channel and thus shows an excellent spin filtering capacity. We strongly believe that the proposed doped defective graphene nanoribbons with different interesting properties will motivate experimental studies for the exploration of these materials for real world applications.

Acknowledgements

Financial support from CSIR, New Delhi [01(2744)/13/EMR-II] and UGC, New Delhi (UGC SAP) through research grants is gratefully acknowledged. The authors (B. M.) and (S. S.) are grateful to CSIR, New Delhi, for the award of Senior Research Fellowship and Research Associateship respectively. The author A. P. would like to thank UGC for awarding him the D S Kothari Postdoctoral Fellowship.

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