Electronic and magnetic properties of deformed and defective single wall carbon nanotubes

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Electronic and magnetic properties of deformed and defective single wall carbon nanotubes Yaroslav V. Shtogun *, Lilia M. Woods Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, FL 33620-5700, USA

A R T I C L E I N F O

A B S T R A C T

Article history:

The combined effect of radial deformation and defects on the properties of semiconducting

Received 8 May 2009

single wall carbon nanotubes are studied using density functional theory. A Stone–

Accepted 11 July 2009

Thrower–Wales defect, a substitutional nitrogen impurity, and a mono-vacancy at the high-

Available online 23 July 2009

est curvature side of a radially strained nanotube are considered. The energies characterizing the deformation and defect formation, the band gap energies, and various bond lengths are calculated. We find that there is magneto-mechanical coupling behavior in the nanotube properties which can be tailored by the degree of radial deformation and the type of defect. The carbon nanotube energetics and magnetism are also explained in terms of electronic structure changes as a function of deformation and types of defects present in the structure.  2009 Elsevier Ltd. All rights reserved.

1.

Introduction

Single wall carbon nanotubes (CNTs) are cylindrically rolled infinite graphene sheets characterized by a chiral index (n,m), which determines many of their characteristics [1]. Their unique electronic and mechanical properties make them potential building blocks for nanoelectronic devices. At different stages of the CNT growth, purification or device production processes, however, mechanical deformations or defects may occur in their structure. Thus the development of such devices requires fundamental knowledge of structural and electronic properties of not only perfect, but also mechanically altered CNTs. In addition, exploring the modifications of CNT properties by creating defects or deforming the CNT structure intentionally has been viewed as an additional route to control the CNT charge transport [2–5]. Tuning various properties of CNTs through mechanical deformations has drawn substantial interest from researchers. Radial squashing is of particular interest. It has been shown that using an atomic force microscope (AFM) [6] or scanning tunneling microscopy techniques [7] metal–semi-

conductor transitions take place upon radial deformation of the CNT cross-section. Also, the CNT conductance is reduced by two orders of magnitude due to local sp3 bonds formation induced by an AFM tip squashing [8]. Similar changes can be achieved if CNTs are placed under sufficiently high external hydrostatic pressure [9–11]. Radially deformed CNTs have also been studied theoretically. First principle calculations have revealed that important factors, such as the mirror-symmetry breaking, rp hybridization due to higher curvature regions and the interaction between the low curvature regions are responsible for the metal–insulator transitions and electronic structure modulations in CNTs with different chiralities [12– 17]. In addition to radial deformations, CNT properties can be modified by the presence of topological defects in their structure [18–21]. The Stone–Thrower–Wales defect (STW), which is one C–C bond rotated by 90 in the CNT network [22], is one of the most common defects in the CNT structure. Such C–C bond rotations appear during the CNT growth process or during high temperature treatments [23,24]. The effect of the STW defect on the CNT properties has been intensively

* Corresponding author: Fax: +1 813 9745813. E-mail address: [email protected] (Y.V. Shtogun). 0008-6223/$ - see front matter  2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2009.07.042

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investigated in previous works [25–27], which have shown that metal–semiconductor transitions in the CNT electronic structure are induced depending on the STW concentration [28]. On the other hand, the presence of STW defects also increases reactivity of CNT surface upon adsorption of various molecules or atoms [29,30]. Other factors, such as, the interaction with atoms, molecules, or nanoparticles, also cause changes in the CNT electronic properties [31–33]. Studies of even synthesizing new nanotubes (BC4N) from CNT with substitutional atoms have also been reported [34]. In addition, atoms such as boron and nitrogen are common dopants, which can appear in the CNTs during laser-ablation and arc-discharge synthesize processes or during substitutional reaction methods [35–37]. Theoretical studies have shown that the presence of such impurities leads to breaking of the CNT mirror symmetry and shifting of the Fermi level, creating additional impurity states in the energy band structure, improving the carrier conductivity, and increasing CNT reactivity to other compounds [38–40]. Furthermore, vacancies produce significant changes in the CNT transport, mechanical, and optical properties as well. Vacancies can be present as a native defect during synthesis of CNT or can be created intentionally by ion or electron irradiation methods [41,42]. Electronic structure calculations have shown that a single vacancy is characterized by removing a C atom from the carbon network, which leads to the formation of a pentagon and a nonagon with one dangling bond [43]. Also, depending on the vacancy concentration and CNT chirality, the conductance of such defective CNT decreases and new states appear in the energy band structure [44,45]. In addition, the electronic properties of CNT with vacancies can be tuned by external electric field or radial deformation [46,47]. Recently, it has been shown that the application of two external stimuli leads to even richer changes in the CNT properties. For example, the presence of an external electric field in defective [46] or radially deformed CNTs [48], as well as Si doped in radially deformed CNTs [49] have been shown to provide additional ways of tuning their properties. In this work, we investigate another way of tailoring CNT properties by considering the combined effects of radial deformation and a defect located at the highest curvature region of the CNT structure. Two types of radial squashing are studied – narrower than the tube’s cross-section and wider than the tube’s cross-section. The first type corresponds to deformations achieved by narrow hard surfaces, while the second one corresponds to deformations achieved by infinite hard surfaces. Also, three types of defects at the highest curvature of the deformed CNT are investigated here. These are a STW defect, a substitutional N impurity, and a single vacancy. We present first principle calculations and analyze the electronic structure in terms of the type and degree of radial deformation and type of the defect in the CNT structure. Our results show that CNT metal–semiconductor transitions can occur for various combinations of mechanical alterations, and reveal what the important electronic and magnetic structure changes for each case are. In particular, we investigate the evolution of the energy band gap and the various defect formation energies as a function of radial deformation. We

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also explore the possibilities of mechanically induced magnetic properties of the radially deformed and defective CNT. Thus by considering CNTs under two external mechanical stimuli, we show additional ways to tune their properties. Our results are of interest to experimentalists interpreting their data of applying stress to realistic CNTs. Furthermore, this study reveals greater capabilities for CNT applications in new devices.

2.

Computational method and model

The results presented here are obtained using self-consistent density functional theory (DFT) within the local density approximation (LDA) for the exchange-correlation functional implemented in the Vienna Ab Initio Simulation Package (VASP) [50]. This code uses a plane-wave basis set and a periodic supercell method. The core electrons are accounted for either by utilizing ultrasoft Vanderbilt pseudopotentials or by the projector-augmented wave method [51]. Here we use the ultrasoft pseudopotentials. The Brillouin zone is sampled by (1 · 1 · 7) Monkhorst–Pack k-grid with an energy cutoff of 420 eV for all systems. Also, the relaxation criteria for all sys˚ for the tems are 105 eV for the total energy and 0.005 eV/A total force. Spin-polarization effects are included in the calculations of the defective CNT. To illustrate our results, we consider a single wall semiconducting zigzag (8, 0) CNT. The supercell consists of four unit cells along the z-axis of the CNT and for a defect-free ˚ 3 after relaxaCNT it has dimensions (22.12 · 22.12 · 17.03) A tion. Such a supercell helps to avoid interactions between neighboring defects and simulates isolated defects in the CNT network. First, we investigate a radially deformed defect-free (8,0) CNT. The radial deformation is obtained by applying stress to the opposite sides of the CNT cross-section along the ydirection, which causes squeezing in the y-direction and elongation in the x-direction (Fig. 1a–c, e and f). It is characterized by a dimensionless parameter g = (R  Ry)/R (in%), where R is the radius of the perfect CNT and Ry is the semi-minor axis connecting the CNT lowest curvature regions (Fig. 1c). We consider two types of squashing. One is radial deformation between two hard surfaces with a cross-section smaller than the CNT cross-section. In this case, we assume that the extension of the wall along the x-axis is equal to one C– ˚ ). Thus the y-coordinates of the top and botC bond (1.44 A tom rows on the lowest curvature are fixed, and all other coordinates are taken to be free (Fig. 1e). The other one corresponds to radial deformation between two hard surfaces with a cross-section larger than the CNT cross-section. In this case, the y-coordinates of the atoms from the top and bottom flat regions are kept fixed, while all other coordinates are allowed to relax (Fig. 1g). Depending on the degree of deformation, the radial crosssection of the CNT takes different forms. When g < 35%, the CNT has an elliptical-like cross-section after relaxation, regardless of the type of squashing. For g P 35%, the CNT has a ‘‘Peanut’’-like form after deforming between narrow walls (Fig. 1e), and a ‘‘Flat’’-like form after deforming between wide walls (Fig. 1g) after relaxation. We studied radial defor-

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Fig. 1 – (a) Cross-sectional and (b) side view of an undeformed defect-free (8,0) CNT, (c) radially deformed (8,0) CNT with g = 20%, (d) side view of a STW defect, (e) Peanut structure with g = 65%, (f) side view of N impurity, (g) Flat structure with g = 65%, and (h) side view of a MV. Only the symmetry equivalent atoms in the STW and MV defects are shown.

mation of (8,0) CNT up to g = 75% for the Peanut and up to g = 65% for the Flat configurations. In all cases, allowing all coordinates to relax restores the original circular cross-section indicating that these types of deformation are elastic. After the (8,0) CNT was deformed and relaxed, a single defect is created at the highest curvature region. The structure is relaxed again by keeping the appropriate constraints for radial squashing described earlier. We investigate a STW defect by rotating one C–C bond (Fig. 1d), a single N impurity by substituting one C atom (Fig. 1f), and a mono-vacancy (MV) by removing one C atom (Fig. 1h). Releasing all coordinates restores the circular form of the CNTwith a defect in its surface, thus the CNT is elastic regardless of the defects present.

3.

Results and discussion

3.1.

Changes in the deformed and defective CNT structure

Here we present the results from the calculations related to the changes of various bonds in the CNT structure upon deformation and defect introduction. We are particularly interested in the CNT bonds located at the highest curvature sides and the bonds comprising the defects (Fig. 1b, d, f and h). The evo-

lution of the C–C1 and C–C2 distances for the defect-free (8,0) CNT as a function of deformation are shown in Fig. 2a) (C– C2 = C–C3 due to symmetry). The figure indicates that the bond along the CNT axis decreases, while the C–C2 bond increases when g increases. Also, the C–C2 distance changes the most for the Flat configuration, for which the bond is stretched by ˚ (g  0  65%), while there is little difference in C–C1 0.08 A distance between the Peanut and Flat structure. We find that the most stable configuration for the STW defect is when the rotated bond is perpendicular to the CNT axis (Fig. 1d). Fig. 2b) shows the various bond changes as a function of g. It is evident, that there is no significant difference between the corresponding distances for the Peanut and Flat configurations with the exception of the C1–C2 bond. In fact, for larger g the C1–C2 in the Flat CNT is changed the most as compared to the other bonds. Also, the C1–C2 functional behavior is very similar to the one for the C–C2 in the defect-free CNT. Surprisingly the bond located at the highest curvature site and perpendicular to the CNT axis, C6–C7, shows little variation as a function of g. The substitutional N impurity is created at the highest curvature side of the perfect and deformed CNT. Fig. 2c) shows that the N–C1 and N–C2 bonds exhibit similar dependence

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Fig. 2 – Bond lengths as a function of deformation for (a) a defect-free (8,0) CNT, (b) (8,0) CNT with a STW defect, (c) (8,0) CNT with a N impurity, (d) and (e) (8,0) CNT with a MV.

on g as the corresponding C–C bonds in the defect-free CNT (Fig. 2a). Thus not much disturbance in the CNT structure is caused by the N atom. However, due to the larger size of N, ˚ and 0.03 A ˚ than the the N–C1 and N–C2 are smaller by 0.01 A C–C1 and C–C2, respectively, for all g. Our calculations also show that the N–C1 bond decreases slightly as a function of g and it is similar for both types of deformations. Conse˚ for the Flat quently, N–C2 = N–C3 has increased by 0.08 A ˚ for the Peanut one. CNT and by 0.04 A It has been shown, that removing one C atom from CNT network leads to the formation of several metastable MV configurations in CNT [52,53]. The most stable MV configuration is characterized by a pentagon and a nonagon along the CNT axis for zigzag CNTs and is shown in Fig. 1h. Fig. 2d and e shows how the bonds involved in the MV change as a function of g. It is interesting to see that while for the other studied cases (defect-free, STW and N impurity) all C–C distances change in a relatively continuous manner, the C–C bonds comprising the MV for larger g do not. In particular, when the distance be˚ for the Flat tween the two flat portions becomes less than 3.4 A CNT, some bonds are found to experience relatively ‘‘sudden’’ jumps and dips. The biggest changes are found in the bonds lying at the highest curvature regions. For example, C1–C2 is ˚ , C6–C7 by 0.08 A ˚ , while the C5–C8 is deincreased by 0.06 A ˚ for the Flat CNT. Thus the MV causes larger creased by 0.11 A local disturbance in the deformed CNT structure as compared to the other isolated defects.

3.2.

Energetics of the deformed and defective CNT

We also calculate different energies characterizing the deformation and defect formation. The deformation energy of a defect-free CNT is defined as: Efg ¼ Eg  E;

ð1Þ

where Eg is the total energy for the deformed CNT and E is the total energy for the undeformed perfect CNT. The formation energy for the STW defect, N impurity, and MV at the highest curvature of the radially deformed CNT is calculated, respectively, as: f

Eg=STW ¼ Eg=STW  Eg ;

ð2Þ

f Eg=N

ð3Þ

f

¼ Eg=N  Eg  lN þ lC ;

Eg=MV ¼ Eg=MV  Eg þ l;

ð4Þ

where Eg/STW,N,MV are the total energies for the deformed CNT with the appropriate defect, lN,C are the chemical potentials for a free nitrogen and carbon atom, respectively, and l is the chemical potential of a carbon atom from the CNT (energy per C atom in the supercell). Fig. 3a shows the deformation energy as a function of the degree of radial deformation for the two types of squashing. Efg increases non-linearly, however this increase is much steeper for the Flat structure as compared to the Peanut one. It is realized that for higher deformations, we press up to five (35% < g < 65%) rows of carbon atoms on the top and bottom

Fig. 3 – (a) The deformation energy as a function of g for Peanut and Flat CNT structures. (b) The formation energy for the single defects as a function of g for the Peanut and Flat CNT structures. Cross-sectional view of the deformed and defective (8,0) CNT after relaxation for various cases are also shown.

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of the flat regions for the Flat structure, as compared to one row on the top and bottom of the flatter regions for the Peanut structure. Consequently, large distortions at the highest curvature regions and elongations along the x-axis are created for the Flat configurations – Fig. 1 g). However, for the Peanut configurations, mainly the distance between the top and bottom C rows is decreased, while very little elongation along the x-axis and practically no change in the highest curvature regions for g > 35% are found – Fig. 1e). Therefore more energy is needed to account for the larger distortions in the curved regions for the Flat structure as compared to the Peanut one. In addition to the distortion effects, there is a repulsion contribution to the deformation energy from the flat graphene-like regions in the Flat structure for very large deformations. At g P 50% the distance between the flat regions ˚ , which is smaller than the equilibrium becomes 2Ry 6 3.13 A ˚ in graphite [54]. For the Peanut structure, this distance 3.4 A repulsion is smaller since only two rows from the top and bot˚. tom of the CNT network are brought closer than 3.4 A The formation energies for the different defects as a function of g are also shown (Fig. 3b). The energies Eg/STW,N,MV decrease for all types of defects as g increases. Thus less energy is needed to make a defect on a deformed CNT as compared to f a circular one. Our calculations show that Eg=STW is the lowest for the STW defect, and it is very close in value for the Peanut f and Flat structures. Also, Eg=N for the substitutional N impurity is practically the same for both Peanut and Flat configuraf tions. Eg=MV is the largest for MV defect and it differs significantly for the two types of deformation for larger g. f For example, Eg=MV for the Peanut configuration stays at a plaf teau as a function of g, while Eg=MV for the Flat configuration decreases non-linearly. We relate this to the fact that the C– C bonds exhibit more dramatic changes in the Flat CNT (Fig. 2d and e). Thus it is easier to break the three bonds to create a MV after deforming between two wide walls as compared to the case between two narrow walls. Fig. 3b) suggests that it is easier to create a defect on CNT under larger radial strain as compared to a circular or lightly deformed CNT. The least amount of energy is needed to make a STW defect as compared to the greatest amount of energy to make a MV. This is understood by realizing that the STW defect involves the least disturbance in the CNT structure (just one C–C bond is rotated), followed by introducing an impurity (one C is substituted by N) and by creating a MV (one C atom is removed by breaking three bonds, two of them become connected and the third one is a dangling one). The degree of radial deformation and the presence of each isolated defect also affect the band gap energy of the CNT. The perfect defect-free (8,0) CNT is a semiconductor with a relatively large band gap (Eg = 0.55 eV). Squashing the CNT radially leads to decreasing of Eg until the gap is closed at g = 23% (Fig. 4). Thus the CNT becomes a metal [12]. Note that the semiconductor–metal transition corresponds to a rather discontinuous change in the C–C1 and C–C2 bonds (Fig. 2a). One also sees that this transition occurs before the deformed CNT acquires a Flat or a Peanut shape. Further deformation of the defect-free CNT does not result in opening of a band gap. The band gap energy Eg for defective CNT as a function of g is also shown (Fig. 4). Initially (g = 0%) the gap is larger for the CNT with a STW defect and smaller for the CNT with a N

Fig. 4 – The energy band gap Eg of the perfect and defective (8,0) CNT as a function of radial deformation g. impurity and a MV as compared to Eg of the defect-free CNT. The squeezing closes Eg at g = 23% for the CNT with an N impurity or a MV, and at g = 25% with a STW defect. However, further deformation of the (8,0) CNT with the MV results in opening of a band gap with its highest value Eg = 0.2 eV at g = 55% for the Peanut structure. Eg becomes non-zero again following another gap closure at g = 65%. Fig. 4 also shows that Eg = 0 for all g P 25% for the CNT with the N impurity, and that there is a very small gap Eg = 0.01 eV at g = 55% and g = 65% for the STW defect in the Peanut CNT structure.

3.3.

Electronic structure modulations

To further study the combined effect of the radial deformation and isolated defects in the CNT structure, we carry out detailed analysis of the electronic structure changes for various cases. In Fig. 5, we show the band structures for several values of g of a defect-free (8,0) CNT and an (8,0) CNT with a STW defect at its highest curvature side. The applied radial squashing lifts the degeneracy of the energy bands for the defect-free CNT (Fig. 5a). As g increases, the lowest conduction band starts to move towards the Fermi level. At g = 23%, the highest valence band reaches the Fermi level and crosses with the lowest conduction band at a point different than C. The electronic structure analysis shows that rp orbital hybridization due to atoms residing on the higher curvature sides is the main reason for the semiconductor–metal transition here. These results confirm the findings in previous studies reporting electronic structure calculations of CNT under relatively small radial deformation [12–14]. Further increase in g amplifies the effect of r–p admixture and leads to the movement of the point of energy band crossing with EF towards the X point. For sufficiently large radial strain (g > 50%), multiple crossings at the Fermi level from higher conduction and lower valence bands occur, indicating that the squashed CNT has became a better metal. The electronic structure calculations show that for a perfect defect-free CNT, all atoms from the CNT network contribute to the energy bands. As g > 0%, the energy bands around the EF level are mainly composed of orbitals from the atoms

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Fig. 5 – Energy band structure of (a) defect-free (8,0) CNT, (b) (8,0) CNT with a STW defect on its highest curvature site for different degrees of radial deformation g.

located at the highest curvature regions. When g P 55% for the case of Peanut deformation, contribution from the orbitals of the atoms from the top and bottom rows separated by 2Ry (Fig. 1c) is also found in the energy bands around EF. The effect of radial deformation can also be traced in the charge redistribution changes on the carbon network. Fig. 6a–c show that for radial strain g = 25% in the Peanut configuration, the charge redistribution is mainly around the higher curvature CNT sides, while for the Flat configuration charge is redistributed over the flat CNT portions as well. The energy band structure for the deformed (8,0) CNT with a STW defect is similar to the one for the defect-free radially deformed CNT (Fig. 5b). The main differences at g = 0% are the larger band gap and the presence of a relatively flat level asso-

ciated with the defect at E  2.9 eV in the conduction region for the CNT with STW (in red). As g increases, this flat level starts to move away from EF, while the highest valence band and the lowest conduction band start to move towards EF in a similar manner as in the case of the defect-free CNT. A very small energy gap Eg  0.01 eV is found at g = 55% and g = 65% for the Peanut CNT with a STW defect, while Eg = 0 eV for all other g. Our analysis shows that again the r–p hybridization due to the orbitals from the atoms at the highest curvature regions contributes mainly to the energy band structure around EF. We find that the lowest conduction band is mainly composed from the orbitals from the defect, while the highest valence band is composed mainly from orbitals from the rest of the CNT.

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Fig. 6 – Total charge density plots for (8,0) CNT (a) defect-free structure with g = 25%, (b) Peanut structure with g = 65%, (c) Flat structure with g = 65%, (d) STW defect with g = 25%, (e) Peanut structure with STW and g = 65%, and (f) Flat structure with STW ˚ 3. and g = 65%. The isosurface value is 0.0185 e/A

The local disturbance by the STW defect also affects the charge accumulation on the CNT. Fig. 6d–f) shows that even though the defect is at the highest curvature side, little charge accumulation is found on the defect itself except on the C6– C7 bond. Most of the total charge is found on the atoms surrounding the STW defect regardless of the applied radial deformation. The electronic structure of the deformed (8,0) CNTwith a N impurity and a MV is also analyzed. In Fig. 7, we present our results for the total Density of States (DOS) for the various cases. Spin-polarization effects are also included in the calculations in order to study the possibility of magnetic properties of CNT. Such possibility has been suggested by other authors who have considered doped CNT and CNT with vacancies [55– 57]. It has been shown that the DOS and energy band structure of the N-doped CNT depends on the concentration of impurities [57,58,19]. For concentrations more than 1%, a flat level in the energy band gap is found in the 0.2  0.27 eV region below the bottom of the conduction band. Here, the N concentration is 0.78%, and no such flat level between the highest valence and lowest conduction bands is found (Fig. 7a). As g is increased, the lowest conduction and the highest valence bands move towards the EF, thus Eg decreases. The total DOS for the Peanut and Flat structures increase significantly for g > 45% suggesting that the CNT characteristics becomes more metallic-like. The electronic structure analysis reveals that the energy bands in the vicinity of the Fermi level are mainly composed of the px and py orbitals of the atoms from the highest curvature CNT regions. The orbitals from the N atom contribute to the lowest conduction band, which is also partially occupied. For 0 < g < 25% the r–p hybridization increases leading to closing of the energy gap and the extra e is relatively localized in the lowest conduction band. For g > 25%, the EF is located above the crossing point of the conduction and valence bands, which causes multiple crossing of the EF due to the continuing increase in the r–p admixture and the presence of the extra e. It is evident from Fig. 7a) that the extra N e can induce spin-polarization effects in the CNT electronic structure at g = 0%. Around  2.8 eV sharper features in the DOS for spin ‘‘up’’ are found. However, the radial deformation has a profound effect on the spin-polarization effects of the CNT with the N impurity. For g < 25% spin ‘‘up’’ and spin ‘‘down’’ states

show differences in the valence region, but for g P 25%, the total DOS are practically the same, except for the Flat CNT at g = 65%. Fig. 7b) depicts the evolution of the CNT local magnetic moments m as a function of deformation. m experiences a maximum at g = 5%, and it becomes m = 0 (g = 25%) almost when the CNT becomes a metal (g = 23%). However, when g = 65% the Flat CNT has its largest value for m = 0.92 lB (not shown in Fig. 7b) suggesting that the deformation and the N impurity have a complicated inter-relationship. Further insight into the N defective (8,0) CNT can be gained by examining the spin density for various deformations g (Fig. 8a–c). The spin density is maximal on the N atom and the surrounding C atoms. The localization of the e spin shows striking differences for the different g. For the g = 20% case, the unpaired e is much more delocalized as compared to the g = 10% case, where the e spin density localized around the impurity site is much more intense. This behavior is similar to the one found in semiconducting (zigzag) CNT, where the N e is localized around the N impurity. However, for metallic (armchair) CNTs, N e is completely delocalized [58]. At the same time, for g = 65% the Flat CNT is a metal, but the m has its highest value – m = 0.92 lB. Consequently, the e spin is localized around the impurity and neighboring atoms again. The results from the spin-polarized calculations for the radially deformed (8,0) CNT with MV are also shown in Fig. 7c). At g = 0%, there is a sharp localized peak at  3.41 eV in the conduction region of the spin ‘‘up’’ and ‘‘down’’ total DOS. The main contribution to this peak comes from the px and py orbitals of the C atoms comprising the MV. As the CNT is deformed, this peak starts to broaden and move closer to EF. This is due to the increased r–p admixture from the CNT atoms located in the highest curvature locations together with the C atoms forming the MV as g increases. For g = 45%, two such peaks appear for the Peanut and Flat structures, which also become broadened for larger g. The major contribution to this peak comes from the px orbitals of C1, C5 and C8 atoms as well as py orbitals of the C atoms of the pentagon of MV (Fig. 1 h). For g = 65% this broadening continues but with additional sharp features from the MV at higher energy in the conduction region. Comparing the total DOS for spin ‘‘up’’ and ‘‘down’’ states shows that for almost all g there is little difference between them. The exception is the conduction and valence regions

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Fig. 7 – (a) Total Density of States for spin ‘‘up’’ and ‘‘down’’ carriers of (8,0) CNTwith a substitutional N impurity on its highest curvature site at different g for Peanut and Flat structures. (b) The magnetic moment as a function of g for the (8,0) CNT with the N impurity. (c) Total Density of States for spin ‘‘up’’ and ‘‘down’’ carriers of (8,0) CNT with a MV defect on its highest curvature site at different g for Peanut and Flat structures.

Fig. 8 – Spin density isosurface plots for (a) (8,0) CNTwith a N ˚ 3), (b) (8,0) impurity for g = 10% (isosurface value = 0.004 lB/A CNTwith a N impurity for g = 20% (isosurface value = 0.004 ˚ 3), (c) flat (8,0) CNTwith a N impurity for g = 65% lB/A ˚ 3), and (d) Peanut (8,0) CNTwith (isosurface value = 0.0122 lB/A ˚ 3). a MV for g = 65% (isosurface value = 0.018 lB/A

around EF of the g = 65% deformation for the Peanut CNT. For this case, we find that there is a small magnetic moment m = 0.04 lB. These findings lead us to conclude that there is an intricate connection between the electronic structure of the deformed CNT with a mono-vacancy and the CNT magnetic properties. The origin of magnetism in CNT with vacancies is an issue which is still under debate. Several reasons have been shown to be responsible for their spin-polarization effects: under-coordinated C atom with a localized unpaired spin, concentration of vacancies, CNT chirality, sp3 pyramidization and related bond length changes, and vacancy location with respect to the CNT structure [57,59]. Other researchers have found that for the MV orientation investigated here (Fig. 1h), semiconducting (n,0) CNT do not show magnetic properties [59]. We also confirm this for g = 0%. Our calculations show that this behaviour persists even for radially squeezed defective CNT until very large g. Even though the sp3 mixture of the carbon atoms changes signifi-

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cantly as the deformation increases, this effect alone does not seem to be enough to induce magnetism in the CNT, suggested in other studies [59,60]. However, for g = 65% for the Peanut CNT the spin density plot in Fig. 8d) shows that the e– spin is rather localized around the dangling bond of the MV suggesting that in this case the under-coordinated C atom with the unpaired spin is important for the magnetic properties of the defective and deformed CNT. However, no such effect of e– spin localization is found in the cases for other values of g. It has been predicted that localized zigzag states associated with edges of H-terminated graphitic ribbons produce a flat band at the Fermi level [61,62]. The presence of such a flat band leads to electron–electron interactions, and consequently to magnetic polarization with moments localized at the zigzag states. The mono-vacancy is such a zigzag edge. However, the characteristic zigzag edge flat band may not be evident here due to the combined role of the chirality of the CNT, the r–p admixture, and the concentration and orientation of the MV. Applying radial deformation can change the r–p hybridization and bond lengths in such a way that the zigzag edge flat bands are evident again. Examining the energy band structure shows that for the Peanut configuration with g = 65% dispersionless portions of the lowest conduction and highest valence bands composed mainly of the r and p electrons are found at the Fermi level. No such flat bands are obtained for the other values of radial deformation. These observations suggest that the magnetic flat-band theory together with r–p orbital admixture may explain the origin of magnetic polarization of radially deformed zigzag CNT with isolated vacancies [61,62].

4.

Conclusions

In conclusion, we have presented ab initio calculations based on density functional theory revealing the electronic structure modifications of single walled radially deformed and defective CNT. The particular way of mechanically altering the CNT structure investigated here corresponds to first radially deforming the CNT, after which a single defect is created at its highest curvature region. Experimentally this can be done by squashing the CNT between two narrow or between two wide hard walls, and then introducing a rotated C–C bond, a N impurity or a single vacancy, by another experimental technique such as ion or electron irradiation. Our calculations show that in general it is easier to create a defect in the carbon network for CNT with larger degree of applied radial strain. In addition, the amount of energy needed to create a defect in the carbon network involving less disturbance (such as STW defect) is less compared to creating a defect with larger disturbance (such as a mono-vacancy). We also found that for all types of defects, the (8,0) CNT experiences a semiconductor–metal transition at approximately the same value of radial strain regardless of the defects. However, further deformation leads to opening of a smaller energy gap in the CNT electronic structure when a mono-vacancy is present, while for all other defects, no such gap is found. The detailed electronic structure analysis reveals that the main reason for the semiconductor–metal transition is the balance between the r–p hybridization from the radial defor-

mation and from the atoms forming the defect. Furthermore, this study demonstrates that there is dependence between the mechanical and magnetic properties of defective and radially strained CNT. We find that the simultaneous application of radial strain and a defect, such as impurity or vacancy, can induce magnetism in the CNT for certain combinations of g and types of defects. The origin of the magneto-mechanical behavior of the CNT is explained in terms of the interplay between the r–p orbitals admixture, energy band structure, and types of defects in the structure.

Acknowledgements Acknowledgement is made to the donors of the American Chemical Society Petroleum Research Fund for support of this research. L.M.W. was also supported by the US Army Medical Research and Material Command under Award No. W81XWH07-1-0708 during part of this work. Useful conversations with Dr. Thomas Reinecke from the Naval Research Laboratory are also gratefully acknowledged. Finally, we would like to acknowledge the use of the services provided by the Research Computing Core at the University of South Florida, the TeraGrid Advanced Support Program at the University of Illinois, and the High Performance Computing facilities of DoD.

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