The Effect of Boron and Nitrogen Doping in Electronic, Magnetic, and

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The Effect of Boron and Nitrogen Doping in Electronic, Magnetic and Optical Properties of Graphyne Barnali Bhattacharya, and Utpal Sarkar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07478 • Publication Date (Web): 27 Oct 2016 Downloaded from http://pubs.acs.org on October 28, 2016

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The Journal of Physical Chemistry

The Effect of Boron and Nitrogen Doping in Electronic, Magnetic and Optical Properties of Graphyne Barnali Bhattacharya1 and Utpal Sarkar 1* 1

Department of Physics, Assam University, Silchar-788011, INDIA

*

To whom correspondence should be addressed. E-mail [email protected] (Utpal

Sarkar)

1

ACS Paragon Plus Environment


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ABSTRACT

The electronic, magnetic and optical properties of boron and nitrogen doped graphyne have been investigated with various doping positions and concentrations of boron and nitrogen atoms. We have explored how the presence of single dopant atom changes the conductivity of doped graphyne from the semiconducting to metallic one. The boron atom at chain site introduces spin polarization which is in ferromagnetic (FM) ground state for minimal boron concentration and in the antiferromagnetic (AFM) ground state for increasing number of the boron atom in the unit cell. We have examined the origin of spin polarization which increases with increasing dopant concentration. Our optical spectra show that the interband transition takes place in the low energy regime. Due to the presence of dopant atom, the absorption spectra extended from the infrared region to the UV region and exhibits strong peak. The reflectivity and energy loss spectra derived the plasmon energy for these systems where the reflectivity displays a sharp decline.

INTRODUCTION Low dimensional structures of carbon allotropes have become the principal focus of the modern research community, due to their novel intriguing properties like field emission,12

quantum

conductance,3-4

superconductivity, 5-8

half-metalicity,9-10

high

thermal

conductivity,11-14 high capacitance15-21 and transport.22-23 In this regard, graphene is the archetype of two-dimensional (2D) network of carbon having sp2 hybridized carbon atom and it has been projected as the promising candidate for future nanoscale electronic devices.24-25 The pristine graphene is a semi-metal and has some limitation for its use in the logic gate and other electronic circuits. Consequently, doped graphene offers an alternative pathway over their parent counterpart and also offers a significant potential as electrocatalysis.26-30 2


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Baughman et al.31 predicted a new type of carbon allotrope called graphyne having the same symmetry as graphene but is structurally different from graphene. Graphyne is a direct-bandgap semiconductor,

32-37

which enhances its application in the future nanoelectronics. It is

encouraging that, the graphdiyne tube and film, 38-42 flakes and substructures of graphyne43-45 are synthesized successfully using various chemical methods. However, it is in the initial stage towards the preparation of extended structures of graphyne. Additionally, the first principle calculations also established the stability of graphynes and its related derivatives.3637,46

The chemical doping is a well-adopted and effective method for tailoring the electronic and optical properties of nanostructure.47-67 The doping helps to tune the work function and carrier concentration of nanostructure which broadens the range of electronic and optical application. Now, doping of graphene by adding external atom or substitution has effectively tuned the electronic and optical properties of graphene resulting an application. Recent studies on N-doped graphene shows excellent electrocatalytic activity, 48-50 whereas Al and Si doping enhances the sensing activity51-53 of graphene by increasing the molecule graphene interaction. Nitrogen or silicon doping led to the appearance of band gap in graphene electronic spectrum.54-55 Current studies also indicate that nitrogen and boron-doped graphene,56-61 nitrogen and boron-doped carbon nanotubes,62-63 and carbon nitride64 could offer numerous optoelectronic properties61 including non-linear optical properties59 as well as catalytic behavior over their traditional counterpart. Recently many experiments have been performed to modify the properties of graphene with foreign atoms including nitrogen, boron, fluorine, and hydrogen.48,65-66 The successful preparation and characterization of B and Ndoped graphene by Panchakarla et al.48 confirms that doped graphene is highly possible to synthesize and can be used to fabricate the electronic device as the B and N-doped graphene 3



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exhibit p and n-type semiconducting properties respectively, that can be tuned by varying the concentration of dopant atom. The advances on doped graphene gradually grow interest among the research community for the modification of mechanical and optical properties of graphyne with dopant atom. The previous study of BN-doped graphyne,67 graphyne nanoribbons68 and graphyne nanotube69 exhibit an increase in band gap and shift the optical absorption spectra toward the UV region depending on doping site and concentration. The possibility of using Ca-decorated graphyne70-71 and graphyne nanotube72 as promising hydrogen storage materials open a new prospect for the study of doped graphyne. The applicability of Li-intercalated multilayer graphyne, as lithium ion battery anode, is reported by Hwang et al.73 The Na decorated graphyne sheet 37 has also been studied. Unlike B or Ndoped graphene, a little information is available in the literature about the effect of boron and nitrogen doping with different concentration on the electronic properties of graphyne. Although the electronic and optical properties of BN co-doped graphyne has been explored, but only boron and nitrogen doped graphyne74-76 with different concentration has been less explored. Very recently, the B and N-doped graphyne have been studied by a few researchers to explore their electrocatalytic activity,75,77 oxygen reduction activity,78 and their possible application as Lithium-Ion79 and hydrogen storage material.80 But, basic questions about the dopant distribution, and how their electronic, optical and magnetic properties change remains an open issue. To address these fundamental questions and to explore the possibility to use graphyne more widely into the field of electronics, optoelectronics and spinotronics; modification in electronic structure, and in optical property is necessary as a consequence of which a detailed investigation by doping is essential. Our study is complete in this sense and can serve the purpose suitably. In addition, to the best of our knowledge, optical properties study of only boron or nitrogen doped graphyne has yet to be reported.

4


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Being motivated by the above, in the present study, we have explored systematically the electronic, magnetic and optical properties of boron and nitrogen-doped graphyne. Tailoring the above-mentioned properties with increasing dopant concentration is also discussed. COMPUTATIONAL DETAILS Spin polarized density functional theory (DFT) calculations were performed using siesta package81 within the generalized gradient approximation (GGA) and Perdew-BurkeErnzerhof (PBE) is employed to treat the exchange-correlation part of density functional. The DZP basis set has been applied and the norm-conserving Troullier-Martins pseudopotential82 is utilized to describe the core-valence interactions. Structural relaxations were performed using conjugate-gradient method until the maximum forces on each atom are less or equal to 0.010 eV/Å is achieved and the energy difference between the consecutive self-consistent field steps is less than 10-4 eV. The 11×11×1 Monkhorst-Pack set of k points are used for sampling the Brillouin zone and the kinetic energy cutoff value was set at 300 Rydberg. To avoid the interaction between two neighboring images, periodic boundary condition along the z-axis is employed with a lateral vacuum region equal to 15 Å. The stability is determined through cohesive energy (Ecoh), which is calculated as

where

,

, and

represent the total energies of the doped graphyne,

isolated carbon, and isolated dopant (boron or nitrogen) atom, respectively. Here n and m denote the number of carbon, and dopant atoms present in the doped configuration, respectively. 5



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The optical properties of a system can be deduced from the frequency dependent complex dielectric function ℇ(ω)=ℇ ( )

ℇ ( ).61,83-84The imaginary part of dielectric function,

due to direct interband transition can be described as

ℇ ( )

Here

ℇ

,

,

and

ℇ

(1)

represent the unit cell volume, dipole transition matrix, energy of

occupied valance states and unoccupied conduction states, respectively. When the metallic intraband transition is added, the imaginary part of the dielectric function85-86 can be obtained using the relation

ℇ ( )

in which ω,

(

)

ℇ ( )

(2)

and Г stand for the photon energy, plasma frequency and relaxation time in

Drude model respectively. The relaxation time is taken as same as alpha graphyne, 87 as our considered doped graphyne structures are also metallic like alpha graphyne. The real part of dielectric function depends on the imaginary part and is related to each other by Kramer Kronig relation,88-89 using which the real part of the dielectric function for interband transition can be obtained as,

ℇ ( )

(3)

Here P is the principal value of integral. For metallic system, the real part of dielectric function involves the contribution of intra-band and inter-band transitions and ℇ ( ) be expressed as

ℇ ( )

(

(4)

)

6


can

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From the real and imaginary part of the dielectric function, the optical properties such as absorption coefficient (α),61,84,67 reflectivity (R),61,84,67 real part of optical conductivity (σ)89,90and energy loss spectrum (L) 61,83,84,67can be obtained. RESULTS AND DISCUSSION In the present study, we explore the influence of dopant atom, doping site and concentration on electronic and optical properties of graphyne. Our previous reports, 36,67,69 established the tunability of the electronic and optical properties of graphyne family due to co-doping with BN and motivated the present study. For substitution purpose, we have chosen two high symmetric sites of carbon atom having sp or sp2 hybridization (chain or ring). In addition, we have gradually increased the doping concentration step by step. The optimized 2D layered structures (Figure 1) of B or N-doped graphyne corresponding to the favorable doping site ensure that, substitutional doping of B or N brings a small distortion in local area only.

Figure 1. Optimized structure of doped graphyne with most favorable doping site: (a) graphyne with 1B at ring; (b) graphyne with 2B at ring; (c) graphyne with 3B at ring; (d) graphyne with 1N at chain; (e) graphyne with 2N at chain; (f) graphyne with 3N at chain. The boron

or

nitrogen

atoms

are

substituted 7


in

the

unit

cell.


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A. Detailed structures Depending on dopant type and doping site, the bond length and lattice constant of B or N- doped graphyne gets changed (Table S1). Due to doping, the deformation potential energy is developed by the lattice deformation and the hybrid orbitals are formed between dopant and carbon atom. Hence the energy involved in substitution process contains two parts; one part breaks the original C-C bond, and the other part is the deformation potential energy. We see that boron doping elongated the lattice vectors (both a and b) compare to pristine graphyne but nitrogen doping shortened the lattice vectors except for ‘graphyne with 1N at chain’ and ‘graphyne with 2N at chain’. The elongation/shortening of lattice vector is due to the larger/shorter atomic radius of B (85 pm)/N (65 pm) than that of the C (70 pm) atom. When sp hybridized C atom is substituted by B atom, two types of C-C bonds have been broken; one is strong triple bond and the other has a double bond characteristic which is comparatively stronger than C-C bond at hexagon of graphyne. As a result, the ‘graphyne with 1B at chain’ contains two types of B-C bonds with bond lengths of 1.361 and 1.498 Å, respectively. The former bond length is slightly less than the reported B-C double bond (1.440 A0),91 but greater than the B-C triple bond (1.230 A0) found in B-doped α-graphyne92 and hence this bond is expected to have mainly double bond character along with B-C triple bond character. In contrast, the B-C bond between chain and ring is shorter than the B-C single bond (1.522 A0),91 but larger than the B-C double bond thus contains some

character

which matches well with other findings. 91 Now the B-C bond length at chain site is slightly elongated compared to the pristine graphyne. To compensate this elongation, rearrangement of all bond lengths of graphyne unit cell take place. The nearest C-C bond length connecting 8


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ring and chain gets squeezed but the nearest C=C bond at hexagon gets expanded [Table S2]. When C atom is substituted by N atom, the entire situation gets changed. The substitution of the sp-hybridized carbon by nitrogen gives rise to two types of N-C bonds having bond lengths 1.186 A0 and 1.341 A0 respectively and consequently the chain lengths get shortened compare to graphyne. The N-C bond length in the chain is slightly shorter than the estimated N-C triple bond length92 and consider to exhibits a triple bond character. The N-C bond length connecting chain and ring is slightly greater than pure N-C double bond [1.270 A0] found in dimethylglyoxime,93 and smaller than the N-C single bond found in methylamine,94 thus behaves as an N-C double bond. To balance the contraction of chain length due to N substitution, the nearest C-C bond at ring gets expanded. The gradual increase of boron (nitrogen) concentration at chain site results same type of bond elongation (contraction) but the triple bond character in B-C (N-C) bond is reduced. For ‘graphyne with 3B at chain’, the B-C (N-C) bond connecting ring and chain gets contracted compare to ‘graphyne with 1B (N) at chain’ and ‘graphyne with 2B (N) at chain’. The elongation of bond length is also noticed when sp2 hybridized carbon atom is substituted by boron atom as found in ‘B-doped graphene’ reported by Panchakarla et al. 48 where they observed that the B-C bond is about 0.5% longer than the C-C bond. The B-C bond in the hexagon is same as reported for the B-C single bond92 but slightly larger than that observed in ‘B-doped graphene’,95 and the B-C bond connecting ring and chain is also nearly equal to the B-C single bond. The result gets changed when the sp2 hybridized C atom is substituted by N atom. Same as ‘N-doped graphene’,48,95 the N-C bond length (1.406 A0) in hexagon is nearly same as C-C bond length which is much greater than the N-C double bond length (1.270 A0)93 but smaller than the reported N-C single bond length (1.474 A0).94 Hence this bond has partial double bond character. Unlike B-C bond connecting ring and chain, the 9



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N-C bond connecting N atom and sp hybridized C atom at the chain is found to have strong character as the bond length (1.330 A0) is close to the reported N-C double bond [1.270 A0]. Upon analyzing the optimized structure and bond length from Table S2, we can infer that boron doping expands the bond length, whereas the nitrogen doping reduces the bond length. Due to substitutional doping, lattice deformation arises and simultaneously a residual stress is generated. To release the generated residual stress, the B-C (N-C) bonds get stretched (squeezed). The calculated cohesive energies (Table S1) indicate the stability of our substituted graphyne systems and are comparable with the experimental cohesive energy of graphite (7.37 eV).96,97 The cohesive energy trend makes it clear that with same doping concentration and doping site substitutional B doping is comparatively more favorable than N doping. Similar results were reported by Jafari et al.68 for B-doped graphyne nanoribbons (GNRs) where lowest formation energy is assigned to B-doped GNR inferring their stability. Lowest formation energy concludes greater stability of ‘B-doped graphene’ than ‘N-doped graphene’ and is reported by Ren et al.98 The most favorable site for B doping is the sp2 bonded C atom site instead of sp hybridized C atom site as the former offers higher coordination number for bonding and thus facilitates better stability. However, for N doping, the most preferred site for substitution is sp hybridized C atom at the chain. Generally, the breaking of two partially double bonds requires more energy than the breaking of one triple bond, therefore, the substitution of sp-hybridized C atom by dopant atom is energetically favorable which is observed for nitrogen doping too. But boron doping breaks three partially double bonds to generate three single bonds. Actually, when the sp2-hybridized C atom is substituted by B atom, a slight movement is sufficient to stretch the C-B bond and it needs a small energy to

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break C=C bond at the ring. Interestingly, the cohesive energy of B (N) doped graphyne decreases with increasing doping concentration. B. Electronic properties The previous study of pristine graphyne and BN co-doped graphyne36,67 established their non-magnetic nature. It is clear from Table S1 that, only boron substituted at chain position introduces spin polarization in graphyne. Thus, our ‘graphyne with B at chain’ systems are magnetic with a noticeable magnetic moment which increases with increasing doping concentration. In contrast, ‘graphyne with B atom at ring’ structures are nonmagnetic same as ‘B-doped graphene’.99 The difference of the total energy between ferromagnetic (FM) and antiferromagnetic (AFM) states indicates that ‘graphyne with 1B at chain’ is in the FM ground state, but ‘graphyne with 2B at chain’ and ‘graphyne with 3B at chain’ are in the AFM ground state. For systems with B substituted at chain site, the spin density difference as depicted in Figure 2, is mainly located around the B≡C bonds at the chain and a very small contribution from the carbon atoms in the ring and chain, which indicates that total magnetic moment of the system is essentially contributed by the B≡C bonds at the chain with a small contribution from the C atoms of the hexagon and chain. For N-substitution, similar to ‘Ndoped graphene’99 the total magnetic moment is zero irrespective of the substitutional site. Thus, only by varying the concentration of boron atom at chain site, the magnetism of doped graphyne can be tuned.

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Figure 2. Top view of spin density difference ρ = ρ↑ − ρ↓ for B-doped graphyne: (a) graphyne with 1B at chain; (b) graphyne with 2B at chain; (c) graphyne with 3B at chain configurations. C. Band structures The spin-resolved band diagrams of graphyne with one dopant atom and multiple dopant atoms are depicted in Figure 3 and S1 respectively. The bands around the Fermi energy are significantly affected due to the presence of B (N) atom because the doping by B (N) is similar as hole (electron) doping which results a gradual shift of bands in order to accommodate extra hole (electron). A similar type of downward/upward shift of bands due to the presence of B and N are also visible in B or N-doped graphenes,48 where some bands cross the Fermi level. Doping with boron or nitrogen, switched the conducting nature of pristine graphyne36 from semiconducting to metallic even when the concentration of dopant atom is minimum. No splitting of the band for up and down spin channels has been observed for nitrogen doping [Figures S1 (c), (d), (g), (h)] irrespective of the substitution site which indicates that spin degeneracy does not break for N-doped graphyne and remains same as pristine graphyne. Similar spin degeneracy has been observed in the case of ‘graphyne with B at ring’. For ‘graphyne with B at chain’ the bands correspond to up and down spins are asymmetrical, which implies that the spin degeneracy has been broken. When sp hybridized C atom is substituted by B atom the symmetry of the

bond between the substituted C atom

and its adjacent sp hybridized C atom is broken. Hence, B doping at chain breaks the

bond

and leave unpaired pz electron of the C atom at chain close to doped B atom. The local strain100 along with quantum entrapment gives rise to strong localization and densification of charge. In addition, the difference in radius between B and C generates local strain74,100 in Bdoped graphyne, which also produces strong localization and densification of charge. Thus 12


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localization of charge occurs around B-C bond. Moreover, the asymmetrical п bonds (due to asymmetric dumbbell-like orbitals) between B and C also create localized state near the Fermi level and break the spin degeneracy. The spin splitting takes place in the vicinity of Fermi level. Substitutional doping with boron gives rise to impurity states in both spin-up and spin-down bands and the impurity bands which cross the Fermi level, are well dispersed. The well-dispersed nature of the B-induced impurity bands increases the electrical conductivity of ‘B-doped graphyne’. When sp2 hybridized carbon atom is replaced by boron atom,

bonds

break and the boron atom form three sigma bonds with three neighboring carbon atoms. Surprisingly, this type of

bond breaking in ‘graphyne with B at ring’ does not break the

spin degeneracy and no spin splitting has been observed near the Fermi level. But the creation of holes due to boron doping shifts the Fermi level downward and the impurity states cross the Fermi level. As a result ‘graphyne with B at ring’ makes contribution on electrical activity. Substitutional N doping increases the number of electrons irrespective of the doping site and creates impurity state above the Fermi level except ‘graphyne with 3N at chain’ [Figure S2(g)]. Thus, the impurity states generated by nitrogen in N-doped graphyne make a contribution to electrical conductivity and this contribution increases with increasing N concentration. Spin splitting of the band has not been observed for N-doped graphyne since the difference in atomic radius between N and C is less compared to B and C, a small amount of local strain is generated, which cannot break the spin degeneracy. To get detailed information of a particular band fat band101 studies [Figure S3-S6] has been done. For 'graphyne with 1B at chain' the fat band plot shows [Figure S3] that, both C and B atom contributes to the energy band around the Fermi level. The dispersion less band at the edge of Fermi level is basically contributed by px-py bonding orbital of B as well as C atom (whose hybridization is in between sp and sp2 as discussed earlier) at chain and can be considered as px-pyπ band (as depicted in -COHP plot Figure S7 and S8). Similar to pristine graphyne, the 13



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bonding pz π band is mostly contributed by the carbon atom and ranging from -5.620 eV to Fermi energy in the VB. Besides, we found notable bands with px and py characters between -2.620 and -1.600 eV. These px and py states mainly originated from C chain-Cchain bond (as depicted in -COHP plot Figure S8) and can be considered as bonding px-py π bands, because sp C atom has ‘one

and two п’ character. The bands below -7.000 eV are the bonding σ

band arises from px and py orbital contribution. In CB the antibonding pz π* and px -py π* bands expanded from 0.000 to 11.780 eV and 2.280 to 6.780 eV, respectively. Above 12.000 eV, the bands are basically σ* bands contributed by px and py orbitals. For “graphyne with 1N at chain', [Figure S4] the bonding pz π bands are ranging from -7.820 eV to Fermi energy while the bonding px-py π bands arise from Cchain-Cchain bond lies between -3.320 to -1.000 eV, and -8.000 to -4.000 eV (as depicted in -COHP plot Figure S9 and S10). Below -8.500 eV, the bands exhibit bonding σ character. In CB, the antibonding pz π* bands are ranging from Fermi energy to 10.680 eV and the antibonding px-py π* bands appear in between 1.670 and 3.300 eV due to the contribution of sp hybridized C and N atom. Just above 11.100 eV, antibonding σ* band originated from px and py orbital are observed. When B (N) is substituted at ring, [Figure S5 and S6] in VB, the bonding pz π and px-py π bands are appeared in between -6.180 eV to Fermi energy (-7.200 eV to Fermi energy) and -2.180 to – 1.170 eV (-3.300 to -2.090 eV) respectively. Below -7.000 eV (-8.000 eV) the bands are bonding σ bands. In CB, antibonding pz π* and px-py π* bands are appeared in between Fermi energy to ~11.820 eV (Fermi energy to ~10.900 eV) and 3.820 to 6.500 eV (1.900 to 6.800 eV) respectively. Moreover, the px-py π and px-py π* bands in ‘graphyne with B or N at ring' are attributed by C-C bond at chain only, no contribution of dopant is visible in the px-py π and px-py π* bands, because now the dopant B atom is almost sp3 hybridized which mainly contribute to σ and σ* bands whereas N is sp2 hybridized which has σ + π character and

14


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contribute to pz π, pz π* and σ, σ* bands. Increasing dopant concentration moves px-py π and px-py π* bands closer to Fermi level.

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Figure 3. Bandstructure, projected density of states (PDOS) and –COHP plot of (a) graphyne with 1B at chain; (b) graphyne with 1N at chain; (c) graphyne with 1B at ring; (d) graphyne with 1N at ring. D. Density of states

In pristine graphyne, 36 the energy states near the Fermi level are arises from pz orbital of the C atom, and at Fermi level, no energy states is observed which confirm its semiconducting nature. But, for N or B-doped graphyne, a significant amount of energy states are present at Fermi level (Figure 3 and S2) confirming their metallic character which is also supported by our fat band study [Figure S3-S6]. The electronic density of states near the valence band is getting increased with increasing dopant atom concentration. This is due to the fact that, B tends to act as an electron donor in the vicinity of C-B bond and N tends to act as an acceptor in the vicinity of C-N bond. Substitution of single C atom by B atom shifts the 16


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Fermi level downwards due to electron deficient character of B atom and this type of shift is also observed in B-doped graphene.102-103 The shift is a little bit more for ‘graphyne with B at ring’ than ‘graphyne with B at chain’. Opposite effect has been observed for N doping where N atom shifts the Fermi level towards high energy and the shift is higher for ‘graphyne with N at chain’ than ‘graphyne with N at ring’. A similar shift of Fermi level towards CB is also reported for N-doped graphene102-103 to accommodate the extra electron. The downward (upward) shift of Fermi level for ‘B (N) doped graphyne’ increases with increasing concentration irrespective of doping site. It should be mentioned that the shift is more in case of N doping compare to B doping for same doping site and concentration [See Table S3]. The PDOS of doped graphyne not only shed insights on the contribution of orbitals of constituting atoms but also focus on the origin of spin polarization. Notably, except ‘graphyne with B at chain’, PDOS graphs indicate the non magnetic nature by exhibiting symmetrical DOS for up and down spin. For ‘graphyne with B at chain’ [Figure 3a II] the asymmetric nature of TDOS is only visible around the Fermi level, which implies the breaking of spin degeneracy around the Fermi level. From the PDOS of ‘graphyne with 1B at chain’ (Figure 3a II (ii) and (iii)), it is clear that the spin degeneracy originates from the px and py orbitals of B atom and the sp hybridized C atom in the chain nearest to it. The contribution of pz orbital of C and B atoms are symmetric for up and down spin, and hence, spin splitting is attributed by the px and py orbitals at and near the Fermi level [see Figure 3a (II) (ii) and (iii)]. At the Fermi level, PDOS of C atom [Figure 3a (II) (ii)] shows that the contribution of pz (px) orbital is highest for majority (minority) spin channel. But PDOS curve of B atom indicates that the contribution of px is highest for both spin channels at the Fermi level which further implies the presence of various degrees of orbital hybridization between p orbitals of B and nearest C atom. It is evident from –COHP calculation that, the orbital 17



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hybridization takes place between px-px, py-py and px-py orbital of B and nearest C atom and is comparatively stronger than px-pz, px-pz and py-pz orbital hybridization [Figure S7]. When B concentration increases in the chain [Figure S2 (a) and (e)], the contribution of pz orbital of C and B atom is no longer symmetric for both spins; a little bit asymmetry is observed. In addition, the asymmetric contribution of px and py orbitals of B and C to DOS also increased. Hence, the spin polarization increases with increasing B concentration. The TDOS and PDOS plots indicate that substitution of sp2 hybridized C atom by B atom (Figure 3b II and Figures S2 (b), (d)) make ‘graphyne with B at ring’ completely nonmagnetic as the contribution of both spins are symmetric and this nature is also observed in ‘B-doped graphene’.104 Similar to ‘B-doped graphene’,102-103 for ‘graphyne with B at ring’ the contribution of pz is highest for both C and B atoms around the Fermi level than px and py orbital, which indicates stronger hybridization between pz orbitals of B and C than px-px, py-py and px-py hybridizations. The contribution of px and py orbital gradually come closer to the Fermi level with increasing number of B atoms in the ring site as the hybridization between px-px, py-py and px-py increases with increasing concentration. The N-doped graphyne acts as an n-type material same as ‘N-doped graphene’102-103 due to electron rich character of N which results an increase of electrons in the system and causes an impurity state. In case of ‘graphyne with N at ring’, the impurity state lies at the Fermi level and spread over the valence and conduction band. However, for ‘graphyne with N at chain’ this impurity state is located in the conduction band away from the Fermi level [Figure 3c II and Figures S2 (c), (g)] except ‘graphyne with 3N at chain’. Increasing N concentration activates the contribution of px, py orbitals of N and C atoms near the Fermi level in the CB indicating various degrees of orbital hybridization between the p orbitals. The comparison of PDOS of both types of dopant shows that the B and N atom creates impurity states in the vicinity of the Fermi level 18


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and enhances the carrier density by creating additional charge carrier independent of the doping position. Additionally, the comparison of doping position shows that the substitution of sp-hybridized C atom by dopant activates the contribution of px, py and s orbitals near the Fermi level more significantly than when sp2 hybridized C atom is replaced by the dopant. It further implies that the substitution of a sp-hybridized C atom by dopant changed the hybridization more. Thus, the change of impurity position has a considerable effect on the electronic properties of doped graphyne. To complete the study of B and N-doped graphyne with different dopant concentration, it is important to analyze their nature of chemical bonding for further realization of the electronic structure. The bonding nature is characterized by crystal orbital Hamilton population (-COHP) analysis which present a clear-cut view of orbital-pair interactions [Figure 3 and Figure S11]. This technique partitions the band structure energy into bonding, nonbonding and antibonding energy regions within a specified energy range, based on which it is possible to interpret the bonding situation in doped graphyne and the nature of energy states at Fermi level. Positive value of –COHP stands for bonding state, whereas negative value represents anti-bonding state. The -COHP diagram of ‘graphyne with B at chain’ [Figure 3a III and Figure S11 (a) and (e)] shows that the energy states at Fermi level are basically bonding states. At Fermi level, it appears that C ring-Bchain and Cring-Cchain interactions are antibonding states, while Cchain-Bchain, Cchain-Cchain and CringCing interactions are bonding states, indicating that the interactions between C chain and Bchain in the unit cell are stronger than those of Cring and Bchain since the Cring-Bchain bond length is larger than Cchain-Bchain bond length, as shown by the structural parameter analysis. In contrary, for ‘graphyne with N at chain’, Cring-Cring contributes antibonding states and CchainCring contributes bonding states at and near the Fermi level. The C ring-Nchain bond contributes bonding states at and near the Fermi level, whereas the Cchain-Nchain bond contributes small antibonding state at Fermi level and strong antibonding states at CB in the energy range 19



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1.200– 2.000 eV . The bonding character gets entirely changed when the sp2 hybridized carbon atom is substituted by B or N atom. For ‘graphyne with B at ring’ the energy state at Fermi level is bonding in nature, contributed by Cchain-Bring , Cring-Bring, Cchain-Cchain and CringCring bonds. Only the Cring-Cchain interaction appears as antibonding state at Fermi level. With increasing concentration of B atom in the unit cell, above and below the Fermi level, the COHP analysis of Cring-Cchain bond shows that the antibonding contribution increases. In case of ‘graphyne with N at ring’ the Cring-Nring and Cring-Cring appear as antibonding states at the Fermi level and whole specified energy range in CB. But C chain-Cchain, Nring-Cchain and CringCchain interactions contribute bonding states at the Fermi level. With increasing N concentration, antibonding contribution of Cring-Nring and Cring-Cring is expanding below the Fermi level. In addition, Nring-Cchain interaction also appears as antibonding state at and near the Fermi level indicating the instability of N-C bond due to increasing concentration. The change in electronic properties originates from the electron redistribution due to doping. The substitution of C atom by B or N atom introduces unpaired electron in graphyne, which breaks the original electron distribution. Accordingly, the localized electron distribution is modified and will enhance its chemical reactivity as well as electrical conductivity. In pristine graphyne, most of the electron density is located around the carbon triple bond, whereas the charge density around C-C bond at ring shows the existence of covalent bond between the carbon atoms. In B (N) doped graphyne, the electron density is reduced (enhance) around the doping site because of the electronegativity difference of B (N) and C.

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Figure 4. Electron density plot of (a) graphyne with 3B at chain; (b) graphyne with 3N at chain; (c) graphyne with 3B at ring; (b) graphyne with 3N at ring. Because of the electronegativity (χ) difference between boron (χ = 2.04), carbon (χ = 2.55) and nitrogen (χ =3. 04) B-C and N-C bonds get polarized and the bond electron shift towards C and N for B-C and N-C bond respectively, which interprets the considerable ionicity of the B–C and N-C bond. The charge density plot [Figure 4] of ‘B-doped graphyne’ show that the asymmetricity of the electron cloud along the B-C bond is larger in the case of ‘substitution at ring site’ than ‘substitution at chain site’. Hence B-C bond at ring is more ionic than B-C bond at chain. The strong bonding between B and C atoms at ring, due to mixed ionic and covalent interactions, clarifies the B atom’s affinity towards sp2 bonded C atom over sp bonded C atom. Similarly, in case of nitrogen doping, asymmetric charge accumulation is also observed between sp bonded N atom and sp2 bonded N atom. Comparison between ‘N at chain’ and ‘N at ring’ shows that the charge accumulation is higher around ‘N at chain’ than around ‘N at ring’, which reflects N atom’s affinity towards sp bonded C site.

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E. Optical properties The real and imaginary parts of the dielectric function for B or N-substituted graphyne are calculated by considering the interband transition as well as intraband transition dominated by the free-carrier response which confirms that, the systems are optically metallic. Figure 5 shows the variation of real and imaginary parts of dielectric function with energy for ‘graphyne with 1B at chain’ considering an average electric field in which polarization is in all the directions. The magnitude of the static dielectric tensor (Figure 5(a)) is many times larger for intraband transition than interband transition. Near zero energy (upto 0.400 eV), only intraband transition dominates. The imaginary part of dielectric function [Figure 5(b)] also confirms the contribution of intraband transition near zero energy. When we compare the static dielectric tensor for interband transition of B or N-doped graphyne and BN co-doped graphyne, we see that ℇ ( ) of ‘B or N-doped graphyne’ is much greater than BN co-doped graphyne and it’s BN analogues [Table S4], which indicates that B or N-doped graphyne may have higher conductivity and carrier mobility than BN doped graphyne and it’s BN analogues. The inclusion of intraband transition shows that ℇ ( ) of B or N-doped graphyne is much greater than pristine graphyne [Figure S12]. Hence, ‘B or N-doped graphyne’ has a significant future in optoelectronic device application.

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Figure 5. Comparison of the dielectric function between interband and intraband transition of ‘graphyne with 1B at chain’ for average electric field: (a) real part of dielectric function; (b) imaginary part of dielectric function. Figure 6 and Figure 7 demonstrate the frequency-dependent absorption spectra and the real part of optical conductivity of doped graphyne respectively, considering the average electric field. Similar to graphene, the absorption spectra of ‘B or N-doped graphyne’ exhibits a wide spectral range, extended from the infrared to the ultraviolet region of electromagnetic spectrum. There are two types of contributions [Figure S13], namely intraband and interband optical transitions, in the absorption process. In the infrared region (up to 0.400 eV), the optical response is due to intraband transition and it is arising from the free carrier. However, the interband absorption occurs from the direct optical transition between the valence and conduction bands and governs the spectra in the UV region.

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Figure 6. Comparison of absorption spectra with increasing dopant concentration: (a) graphyne with B at chain (b) graphyne with B at ring (c) graphyne with N at chain (d) graphyne with N at ring. ‘GY’ stands for graphyne. It is evident from Figure 6 (a) and (b) that for boron doped structures, the strong absorption peak is shifted towards lower energy with increasing dopant concentration i.e. a red shift of strong peak is observed with increasing dopant concentration. In contrast, for nitrogen doped structures, the strong peak exhibits a more or less blue shift towards high energy with increasing nitrogen concentration irrespective of chain or ring position except for ‘graphyne with 2N at chain’. For ‘graphyne with 2N at chain’, two nearly equal strong peaks are observed in the energy range 19.000-22.000 eV, the first peak is red-shifted while the second peak is blue-shifted with respect to ‘graphyne with 1N at chain’. The absorption coefficient is pronounced in wide UV region and these peaks are originating from interband transitions. Similar to absorption spectra, with increasing B concentration, the strong peak of optical conductivity [Figure 7] shows a red shift. But in the case of N doping, ‘graphyne with 2N’ shows red shift whereas ‘graphyne with 3N’ shows blue shift with respect to ‘graphyne with 1N’. The optical conductivity also displays prominent peaks in the UV region. The interband transitions are liable for the well-defined peaks of conductivity spectra in the UV region [Figure S14]. At very low energy (upto 0.400 eV) only the intraband transition takes place.

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Figure 7. Comparison of real part of optical conductivity with increasing dopant concentration: (a) graphyne with B at chain (b) graphyne with B at ring (c) graphyne with N at chain (d) graphyne with N at ring. ‘GY’ stands for graphyne. Another important optical quantity, the reflectance of ‘B or N-doped graphyne’ is presented in Figure 8 and Figure S15, considering average electric field to explain the reflectivity from the surface of ‘B or N-doped graphyne’. Main peaks of reflectivity are arising below 5 eV (where the absorption is comparatively low) and for high energy, the reflectivity vanishes and the system becomes transparent. Moreover, the free carriers have pronounced effect on reflectance only at low frequencies make the reflectance value high. At 0.000-0.380 eV energy, the reflectivity for all ‘B or N-doped graphyne’ is equal to unity, irrespective of the doping site and concentration, attributed by the free carrier (intraband transition). That means in this energy range the reflectivity is 100%, so electromagnetic wave can’t pass through it. Energy loss function (ELF) spectrum arises from interband and intraband transitions, is contributed by plasmon excitations, thus by analyzing ELF in connection with dielectric function, all excitations can be recognized. The energy loss spectra of ‘B or N-doped graphyne’ are presented in Figure 9, where the peaks may correspond to 25



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plasmons and are arising due to the collective oscillations of free electrons or may be due to interband transitions from VB to CB.

Figure 8. Comparison of reflectivity between interband and intraband transition: (a) graphyne with 1B at chain; (b) graphyne with 2B at chain; (c) graphyne with 3B at chain; (d) graphyne with 1N at chain; (e) graphyne with 2N at chain; (f) graphyne with 3N at chain. ‘GY’ stands for graphyne. Table S5 presents the plasmon energy at which the ELF curve exhibits the highest peak. In the case of ‘graphyne with B at chain’, except ‘graphyne with 3B at chain’, [Figure 9(c)] the sharp resonance peak is situated in the infrared region which corresponds to plasmon that contributed by free carriers. The highest peak of ‘graphyne with 3B at chain’ is located in the visible region (1.851 eV) and is mainly contributed by interband transition with a small contribution of free carriers. It is obvious from Table S5 that with increasing boron concentration at chain site, the plasmon frequency increases. That means there is a blue shift in plasmonic frequencies with the increasing dopant concentration. In contrast, the ‘graphyne 26


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with N at chain’ exhibits a red shift of plasma frequency (from UV to infrared) with increasing dopant concentration. For ‘graphyne with 3N at chain’ the highest peak corresponds to the energy of volume plasmons and is located in the infrared region, contributed by the free carrier while for ‘graphyne with 1N at chain’ the major peak corresponds to inter-band transitions and is located in the UV region (7.471 eV). The strong peak of ELF spectra of ‘graphyne with 2N at chain’ is also situated in the UV region (7.441 eV).

Figure 9. Comparison of the energy loss function due to interband and intraband transitions: (a) graphyne with 1B at chain; (b) graphyne with 2B at chain; (c) graphyne with 3B at chain; (d) graphyne with 1N at chain; (e) graphyne with 2N at chain; (f) graphyne with 3N at chain. ‘GY’ stands for graphyne. Similar to ‘graphyne B at ring’ the plasmon frequency of ‘graphyne with N at ring’ are located at infrared and visible region respectively. Here also the major peak can be tuned from infrared to visible region with increasing dopant concentration. The strong peak of ELF 27



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spectrum, which are located in the infrared region, and originate from the collective oscillations of free electrons, correspond to the same energies at which reflectance (Figure 8) exhibits sharp reductions and the real part of the dielectric function passes from negative to positive values. The highest peak contributed by interband transition also corresponds to energy where reflectance falls, and the real part of the dielectric function also falls but does not pass from negative to positive values except ‘graphyne with 3B at chain or ring’. To tune the opto-metallic properties of our B or N-doped graphyne we have considered three types of electric field such as (a) average electric field (b) parallel electric field and (c) perpendicular electric field. As intraband transition due to free carrier dominates only in the low energy region, it does not affect the optical response for the perpendicular field. Comparison of dielectric functions for interband transition only, with three types of electric field, is presented in Figure 10. We have found same strong anisotropic nature in dielectric function in the low-energy region for our B or N-doped graphyne as we observed in pristine graphyne.67 For example in ‘graphyne with 1B at chain’ with the parallel electric field, the intensity of dielectric function appears high in the energy range of 0.020–10.000 eV which ultimately decreases with increasing photon energy. Whereas for the perpendicular electric field, the dielectric function is notable above 12.900 eV and below this value the absorption is negligible. At low energy, parallel electric field dominates while at high energy perpendicular electric field dominates. Furthermore, the direction of the electric field changes the value of static dielectric tensor as listed in Table S4. The static dielectric tensor (ℇ ( )) has a larger value for the parallel electric field than the perpendicular electric field, same as B or N-doped graphene and greater than pristine graphene.61 Moreover, same as ‘B or N-doped graphene’ the ℇ ( ) does not change appreciably with increasing concentration for perpendicular polarization and significantly changes for parallel polarization. Unlike ‘B28


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doped graphene’ ℇ ( ) increases with increasing concentration for ‘graphyne with B at chain’. For the perpendicular electric field, the optical response starts with a gap and optical responses show the optical semiconductor properties for these structures.

Figure 10. Variation of the imaginary part of dielectric function with respect to photon energy for average, parallel and perpendicular electric field: (a) graphyne with 1B at chain; (b) graphyne with 1B at ring; (c) graphyne with 1N at chain; (d) graphyne with 1N at ring. ‘GY’ stands for graphyne. The average, parallel and perpendicular electric fields are represented by black, red and green lines respectively. The position of the highest peak of ℇ for parallel field and the possible interband transition105 of ‘B or N-doped graphyne’ are tabulated in Table S6. Since the substitutional doping in graphyne with B or N does not hamper its hexagonal symmetry, we can identify the dominant interband transition in different energy range on the basis of symmetry arguments and projected band diagram [in Figures S3-S6]. Same as pristine graphyne,32 σ, σ*, px-py π and px-py π* states have even parity, whereas pz π and pz π* states have odd parity. For inplane polarization, the allowed transitions are taking place between the states with the same parity but for out-of-plane polarization, transitions take place between the states with 29



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different parity. In parallel polarization, for all systems except 'graphyne with B at chain', the strong interband absorption from ~0.500 to ~8.000 eV comes due to pzπ →pz π* transition since the bands around the Fermi level are pz π (in VB) and pz π* (in CB). Whereas in the energy range 8.000-10.000 eV, px-py π → px-py π* transition dominates and between 10.000 and 14.000 eV, the absorption is arising due to the px-py π → σ* and σ → px-py π* transitions. In the case of perpendicular polarization, the weak absorption below 9.000 eV is arising from px-py → pzπ* and pzπ → px-py π* transitions, whereas over 9.000 eV the absorption mainly originates from σ →pzπ* and pz π → σ* transitions. For 'graphyne with B at chain’ the strong interband absorption from ~0.500 to ~8.300 eV arises due to both pzπ →pzπ* and px-py → pxpy π* transitions. The absorption spectra depend on the polarization of electric field vector. In the case of a parallel field, the inclusions of intraband contribution significantly change the optical spectra of ‘B or N-doped graphyne’. On the other hand, the optical spectra of ‘B or N-doped graphyne’ remain unaltered for the perpendicular field since absorption starts at high energy in this case. The modification of conducting nature due to the different types of electric field is clearly visible from optical conductivity plot presented in Figure S16. The optical conductivity starts at nearly zero for the parallel electric field but starts with a gap for the perpendicular electric field, which confirms that all these structures are optically semiconductor for the perpendicular electric field. It is noticed [Figure S17] that the reflectivity spectra of all doped graphynes are characterized by strong peaks under parallel polarization in low energy region however for perpendicular polarization, strong peaks are located in the UV region. In comparison with pristine graphyne,32,62 ‘B or N-doped graphyne’ is more sensitive in the low-frequency region but less sensitive in the high-frequency region. In case of ‘N-doped graphyne’ with parallel polarization [Figure S18], the reflectance shows strong peak (Rmax) within infrared to visible region which increases with increasing 30


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concentration but ‘graphyne with 3N at chain’. A similar observation has been made on ‘Ndoped graphene’.61 The only difference is that for ‘N-doped graphyne’ Rmax is more extended towards visible region (even extended upto UV region for ‘graphyne with N at chain’) than ‘N-doped graphene’ which in turn indicates the illumination possibility of ‘N-doped graphyne’ with visible light of wide energy range. This feature is expected as N-doping increases electron in the system. On the other hand, unlike ‘B-doped graphene’,61 Rmax value of ‘B-doped graphyne’ also increases with increasing concentration and lies within infrared to visible

region.

CONCLUSIONS We have studied the structural, electronic, magnetic and optical properties of ‘B or N-doped graphyne’ using density functional theory. The cohesive energies of these doped graphynes are comparable with the experimental cohesive energy of graphite establishing their stability. Our study reveals that the B atom prefers to substitute the sp2-hybridized C atom in the hexagon while the favorable substitution site for N atom is sp-hybridized C atom in the chain. Both types of dopants produce a very small local structural deformation around the doping site. The presence of dopant atom in the unit cell induced energy levels at or close to Fermi level and convert the semiconductor graphyne into metallic in nature. All ‘N-doped graphyne’ and ‘B-doped graphyne’ are nonmagnetic, but in the case of ‘graphyne with B at chain’, a highly localized impurity state is created in the Fermi level which enhances the electrical activity and introduced the magnetism in ‘graphyne with B at chain’. The inclusion of single boron atom at the chain site of graphyne introduces ferromagnetism, while the presence of two or three boron atoms at chain site gives rise to antiferromagnetism. The spin density difference explores that the magnetism is basically attributed by C-B bond at the chain. The PDOS gives the evidence that spin degeneracy is broken only at and near the 31



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Fermi level, not far away from the Fermi level and the spin splitting is attributed by the px and py orbital at and near the Fermi level for single boron atom. Moreover, spin polarization increases with increasing boron concentration. Similar to graphyne, ‘B or N-doped graphyne’ shows same type of optical anisotropy for parallel and perpendicular electric field. It is found that, below 0.400 eV, the optical response is dominated by the intraband transition which arises from free carriers. The comparison of static dielectric tensor predicts the high conductivity and carrier mobility of B or N-doped graphyne than pristine graphyne and it’s BN analogues which in turn enhance the possibility of their use in optoelectronic devices. As like graphene, ‘B or N-doped graphyne’ shows strong absorption in UV region and also exhibits absorption in a wide spectral range, extended from the infrared to the ultraviolet region. The optical conductivity for perpendicular polarization exhibits the optically semiconducting nature of these structures. From ELF curves and corresponding reflectance, we have derived plasmon energies for all B or N-doped structures. The reflectivity for all structures is 100% at extremely low energy (below 0.380 eV) irrespective of the doping site and concentration showing their capability of reflecting electromagnetic waves in this range. In addition, for electric field polarized perpendicular to the plane, reflectivity starts with a gap and order of magnitude less than the parallel field, inferring to the capability of transmitting electromagnetic waves. ASSOCIATED CONTENT Supporting Information The Supporting Information includes details information of electronic and optical properties of B or N-doped graphyne. It also contains the list of bond length, magnetic moment, lattice vector, and possible interband transition of B or N-doped graphyne,. This material is available free of charge via the Internet at http://pubs.acs.org. 32


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AUTHOR INFORMATION Corresponding Author Dr. Utpal Sarkar 1, E-mail address: [email protected] (Utpal Sarkar), Tel. +919401542687 Notes: The authors declare no competing financial interest. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT Dr U Sarkar wishes to acknowledge the assistance of computational resources from Sharcnet and Compute Canada. This research is supported by Assam University, Silchar, India. REFERENCES 1) Rinzler, A. G.; Hafner, J. H.; Nikolaev, P.; Lou, L.; Kim, S. G.; Tomanek, D.; Nordlander, P.; Colbert, D. T.; Smalley, R.E. Unraveling Nanotubes: Field Emission from an Atomic Wire. Science 1995, 269, 1550-1553. 2) Li, G.; Li, Y.; Qian, X.; Liu, H.; Lin, H.; Chen, N.; Li, Y. Construction of Tubular Molecule Aggregations of Graphdiyne for Highly Efficient Field Emission. J. Phys. Chem. C 2012, 115, 2611-2615. 3) Li, T. C.; Lu, S. P. Quantum Conductance of Graphene Nanoribbons with Edge Defects. Phys. Rev. B 2008, 77, 085408 (1-8). 4) Williams, J. R.; Abanin, D. A.; DiCarlo, L.; Levitov, L. S.; Marcus, C. M. Quantum Hall Conductance of Two-terminal Graphene Devices. Phys. Rev. B 2009, 80, 045408 (1-7). 33



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5) Zhou, J.; Sun, Q.; Wang, Q.; Jena, P. High-temperature Superconductivity in Heavily N- or B-doped Graphene. Phys. Rev. B 2015, 92, 064505 (1-8). 6) Faye, J. P. L.; Sahebsara, P.; Sénéchal, D. Chiral Triplet Superconductivity on the Graphene Lattice. Phys. Rev. B 2015, 92, 085121 (1-10). 7) Nandkishore, R.; Chubukov, A. V. Interplay of Superconductivity and Spin-densitywave Order in Doped Graphene. Phys. Rev. B 2012, 86, 115426 (1-7). 8) Ludbrook, B. M.; Levy, G.; Nigge, P.; Zonno, M.; Schneider, M.; Dvorak, D. J.; Veenstra, C. N.; Zhdanovich, S.; Wong, D.; Dosanjh, P.; Straßer, C.; Stohr, A.; Forti, S.; Ast, C. R.; Starke, U.; Damascelli, A. Evidence for Superconductivity in Lidecorated Monolayer Graphene. PNAS 2015, 112, 11795-11799. 9) Gan, L. Y.; Zhang, Q.; Guo, C. S.; Schwingenschlög, U.; Zhao, Y. Two-Dimensional MnO2/Graphene Interface: Half-Metallicity and Quantum Anomalous Hall State. J. Phys. Chem. C 2016, 120, 2119-2125. 10) Dutta, S.; Pati, S. K. Half-Metallicity in Undoped and Boron Doped Graphene Nanoribbons in the Presence of Semilocal Exchange-Correlation Interactions. J. Phys. Chem. B 2008, 12, 1333-1335. 11) Park, W.; Guo, Y.; Li, X.; Hu, J.; Liu, L.; Ruan, X.; Chen, Y. P. High-performance Thermal Interface Material Based on Few-layer Graphene Composite. J. Phys. Chem. C 2015, 119, 26753-26759. 12) Tan, X.; Shao, H.; Hu, T.; Liu, G.; Jiang, J.; Jiang, H. High Thermoelectric Performance in Two-dimensional Graphyne Sheets Predicted by First-principles Calculations. Phys. Chem. Chem. Phys. 2015, 17, 22872-81. 13) Xiao, Y.; Wang, W.; Lin, T.; Chen, X.; Zhang, Y.; Yang, J.; Wang, Y.; Zhou, Z. Largely Enhanced Thermal Conductivity and High Dielectric Constant of

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105) Kumar, A.; Kumar, A.; Ahluwalia, P. K. Ab initio study of structural, electronic and dielectric properties of free standing ultrathin nanowires of noble metals. Physica E Low Dimens. Syst. Nanostruct. 2012, 46, 259-269.

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Table of Contents Graphic and Synopsis:

46 Environment ACS Paragon Plus

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Figure 1. Optimized structure of doped graphyne with most favorable doping site: (a) graphyne with 1B at ring; (b) graphyne with 2B at ring; (c) graphyne with 3B at ring; (d) graphyne with 1N at chain; (e) graphyne with 2N at chain; (f) graphyne with 3N at chain. The boron or nitrogen atoms are substituted in the unit cell. 177x90mm (300 x 300 DPI)



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Figure 2. Top view of spin density difference ρ = ρ↑ − ρ↓ for B-doped graphyne: (a) graphyne with 1B at chain; (b) graphyne with 2B at chain; (c) graphyne with 3B at chain configurations. 177x65mm (300 x 300 DPI)


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Figure 3. Bandstructure, projected density of states (PDOS) and –COHP plot of (a) graphyne with 1B at chain 177x76mm (250 x 250 DPI)



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Figure 3. Bandstructure, projected density of states (PDOS) and –COHP plot of (b) graphyne with 1N at chain 76x32mm (300 x 300 DPI)


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Figure 3. Bandstructure, projected density of states (PDOS) and –COHP plot of (c) graphyne with 1B at ring 177x76mm (200 x 200 DPI)



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Figure 3. Bandstructure, projected density of states (PDOS) and –COHP plot of (d) graphyne with 1N at ring 177x76mm (200 x 200 DPI)


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Figure 4. Electron density plot of (a) graphyne with 3B at chain; (b) graphyne with 3N at chain; (c) graphyne with 3B at ring; (b) graphyne with 3N at ring. 177x184mm (300 x 300 DPI)



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Figure 5. Comparison of the dielectric function between interband and intraband transition of ‘graphyne with 1B at chain’ for average electric field: (a) real part of dielectric function; (b) imaginary part of dielectric function. 86x42mm (300 x 300 DPI)


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Figure 6. Comparison of absorption spectra with increasing dopant concentration: (a) graphyne with B at chain (b) graphyne with B at ring (c) graphyne with N at chain (d) graphyne with N at ring. ‘GY’ stands for graphyne. 177x166mm (200 x 200 DPI)



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Figure 7. Comparison of real part of optical conductivity with increasing dopant concentration: (a) graphyne with B at chain (b) graphyne with B at ring (c) graphyne with N at chain (d) graphyne with N at ring. ‘GY’ stands for graphyne. 177x172mm (200 x 200 DPI)


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Figure 8. Comparison of reflectivity between interband and intraband transition: (a) graphyne with 1B at chain; (b) graphyne with 2B at chain; (c) graphyne with 3B at chain; (d) graphyne with 1N at chain; (e) graphyne with 2N at chain; (f) graphyne with 3N at chain. ‘GY’ stands for graphyne. 177x119mm (300 x 300 DPI)



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Figure 9. Comparison of the energy loss function due to interband and intraband transitions: (a) graphyne with 1B at chain; (b) graphyne with 2B at chain; (c) graphyne with 3B at chain; (d) graphyne with 1N at chain; (e) graphyne with 2N at chain; (f) graphyne with 3N at chain. ‘GY’ stands for graphyne. 177x129mm (300 x 300 DPI)


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Figure 10. Variation of the imaginary part of dielectric function with respect to photon energy for average, parallel and perpendicular electric field: (a) graphyne with 1B at chain; (b) graphyne with 1B at ring; (c) graphyne with 1N at chain; (d) graphyne with 1N at ring. ‘GY’ stands for graphyne. The average, parallel and perpendicular electric fields are represented by black, red and green lines respectively. 177x166mm (200 x 200 DPI)


The Effect of Boron and Nitrogen Doping in Electronic, Magnetic, and

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