Spin-Dependent Electron Transport Induced by Non-Magnetic Adatoms in Metallic Carbon Nanotubes

The spin-dependent electron transport properties of a metallic (5,5) single-walled carbon nanotube with either carbon (C) or boron (B) adatoms were investigated using a non-equilibrium Green’s function technique combined with spin-dependent density functional theory. We find that both of the non-magnetic B and C adatoms cause zero-bias conductance that is highly dependent on the spin states of the conduction electrons. The microscopic origin of this phenomenon is explained by the features of the spin-dependent local density of states in the region of the adatom. From the present calculation it was also determined that the spin-dependent conductance is controllable by tuning the applied gate voltage, which would be a useful property for application in spin filters. [DOI: 10.1380/ejssnt.2008.157]


I. INTRODUCTION
Since the discovery of giant magnetoresistance (GMR) in 1988 [1], a promising path toward a new paradigm for electronics has been followed.The principle is to rely on the electron spin to convey information, in addition to the electron charge.The advantages of spin-based electronics (or spintronics) are low power consumption, small sized systems, high speed and new logic functionalities.Therefore, new materials, experimental techniques and theoretical tools are being currently developed, and spintronics will hopefully reach its full potential within the next decade.A particularly suitable environment for spintronics is found in molecular electronics, another emerging field that aims to replace conventional semiconductors with organic materials, and addresses the properties of electron transport in molecular systems.Nano-carbon materials such as graphene sheets, graphene ribbons and carbon nanotubes can be useful for molecular electronics, due to their remarkable electrical properties.For example, pristine single-walled nanotubes (SWNT) demonstrate ballistic electron transport that has already been extensively studied.Moreover, it has also been demonstrated that a spin-polarized electric current can flow coherently for long distances in carbon nanotubes, making them very interesting and useful for spintronics.In fact, the magnetic properties of carbon nanotubes under various conditions have already attracted a great deal of interest in the past few years.It has been demonstrated that vacancies [2][3][4], metallic chains [5], and adatoms [4,6] on carbon nanotubes, as well as external fields [3], are likely to induce spin-dependent responses in the transport.
Considering this background, we performed theoretical simulations taking the degrees of freedom of spin into account, in order to investigate how various non-magnetic adatoms can induce spin-dependent electron transport in SWNTs.It is shown that carbon and boron adatoms cause spin-dependent dips in the conductance of SWNTs with clear differences in the transport properties between the majority (α-spin) and minority spin states (β-spin ).Our results can be clearly interpreted by considering the features of the spin-dependent local density of states (SL-DOS).Another important finding in the present study is that the spin-dependent electrical conductance can be easily controlled by tuning the gate voltage.

II. METHOD AND MODEL
Firstly, the positions of several adatoms, i.e.B, C, N, O, Si, Ti, Fe and Au on a metallic (5,5) nanotube were optimized using density functional theory in the Perdew-Buke-Ernzerhof generalized-gradient approximation (PBE-GGA) [7] with ultrasoft pseudopotentials [8], as implemented in the QUANTUM-ESPRESSO series of programs [9].A plane wave basis set was used with a cutoff of 30 Ry for the wave functions and 240 Ry for the charge density and a 1×1×4 Monkhorst-Pack mesh for all geometric optimizations.
The zero-bias spin-dependent conductance was then calculated using the non-equilibrium Green's function technique combined with spin-dependent density functional theory (NEGF+DFT) that has been developed for the numerical analysis of open systems under nonequilibrium conditions [10].The premise of this method is to divide the system into three regions, i) the left and ii) right electrodes, and iii) the scattering region in between.In our case, regions i) and ii) are semi-infinite nanotubes and region iii) is a portion of the nanotube containing 60 carbon atoms (3 layers) and the adatom.The Green's function of the scattering region includes the self-energy generated by the leads through a self-consistent DFT scheme.The transmission function T and the density of states are readily available, in addition to the zero-bias conductance G(E), calculated using G σ (E) = G 0 ×T σ (E) where G 0 = e 2 /h is the quantum conductance and σ is the electron spin.In the present calculations we used single-zeta orbitals with polarization.

A. Energetics
According to our calculations, there are no stable geometries on the surface of the SWNT for heavier atoms such as Au, Ti and Fe.The strong curvature of the (5,5) SWNT is probably responsible for this fact, because transition metals are usually adsorbed on the surface of larger tubes [11].On the contrary, lighter atoms (B, C, N, O and Si) are found to be strongly chemisorbed, with a C-C bond broken on the surface and two new chemical bonds formed with the adatoms (see Fig. 1).
It has been predicted that [2+1] cycloaddition of CX 2 moeities should have a small effect on the conductance, since the sp 2 hybridization of the SWNT carbon atoms is preserved [12].However, in this investigation, we examine a slightly different situation with individual atoms; once on the surface, the adatoms have unpaired electrons and dangling bonds.
The electronic ground states of the (5,5) SWNT with the chemisorbed adatoms show that, in the cases of N, O and Si adatoms, the system is not spin-polarized.On the contrary, the C and B adatoms are spin-polarized, as shown in Fig. 2 that displays the 3-dimensional plots of the difference in the spin-dependent electron densities (the red and blue colored densities show the regions with majority spin (α) and minority spin (or β), respectively).The localized features of the spin-polarized electron density is apparent, and can be explained by the fact that the two electrons of the carbon adatom and the lone electron of the boron adatom, which are not involved in the chemical bonding with the nanotube, are distributed in the p z orbital (normal to the tube surface) and in the dangling sp 2 orbital (parallel to tube's surface, along the tube's direction) [13].Indeed, for the carbon atom, the occupation of the sp 2 orbital explains the slight asymmetry in Fig. 2.
Figures 3 and 4 show the results of zero-bias spindependent conductance for the cases of C and B adatoms, respectively.
For the carbon adatom (Fig. 3), the most significant dip is observed in the β-spin transmission curve, above the Fermi energy at E = +0.3eV.Other dips in both the α and β curves are observed at around E = +1.1 eV, and in the α-spin transmission curve only at E = −1.2eV.
In the case of the B adatom (Fig. 4), the main dip position is observed in the α-spin transmission curve, below the Fermi energy at E = −0.6 eV.It should be noted that for each dip, the conductance is reduced from 2 (for a perfect SWNT) to 1 G 0 .This one unit reduction is interpreted by the fact that the adatom breaks the mirror symmetry of the nanotube (along its axe), and the destructive interference results in a perfect reflection.This phenomenon is discussed extensively in Ref. [2].
The dips in the conductance curves of Figs. 3 and 4 cannot be merely explained with the total spin-polarized densities (Fig. 2).In the case of the carbon adatom, one may think that the α-spin conduction electrons would be scattered by the adatom, because an excess of α-spin electrons are observed around it (Fig. 2).However, that is not necessarily the case, because conduction electrons of a particular energy are scattered only by the electronic states of the adatoms with the same energy.Therefore, to understand how the electrons are scattered, the SL-DOS must be considered.Figure 3 (bottom) shows the isosurfaces of the SLDOS in carbon, for E = −1.20 eV and E = +0.30eV.For E = +0.30eV, the α-SLDOS is delocalized along the nanotube, but on the contrary, the β-SLDOS is quite localized around the adatom.This explains why only the β-spin electrons are scattered, resulting in a dip in the β-spin conductance.The conductance dip in the α curve at E = −1.20 eV is explained also by the SLDOS for α-spin electrons.The case for the B atom is also consistent with this interpretation, with the α-and β-SLDOS shown in Fig. 4. At E = −0.6 eV, the SL-DOS for α-spin electrons is localized around the adatom, hence α-spin electrons are scattered, which results in the dip.The zero-bias spin-dependent conductance shown in Figs. 3 and 4

C. Effect of a gate electrode
It is important to note from Figs. 3 and 4 that the conductance at the Fermi energy (E =0) is larger for α-spin electrons than for β-spin electrons in the presence of the C adatom (Fig. 3).In contrast, the B adatom induces almost no difference in the spin-dependent conductance at the Fermi energy, as seen in Fig. 4. For real spintronics applications, the difference between the majority and minority spin electron transport should be as strong as possible, and to a certain extent, should be controllable.It is well known that the bias voltage of a gate electrode can locally modify the electronic states, leading to a remarkable change in electric conduction [14].Therefore, the possibility of controlling spin-dependent conductance was investigated by application of a gate voltage.The effect of gate bias is simulated by shifting the energy of the scattering region in the Hamiltonian, as if the gate bias induces an external potential locally in the scattering region, i.e.H g = V g S, where V g is the electrostatic potential induced by the gate electrode, and S is the overlap matrix between atomic orbitals [14,15].This is an approximate method for simulating the effect of gate bias and considered to give qualitatively correct results but can not be directly compared with the experiments.Results for the case of the B adatom are shown in Fig. 5 It was found that a positive gate voltage shifts the dip in the α-spin conductance toward the Fermi Energy, while a negative gate voltage causes a shift toward the low energies.It was expected that the higher voltages would shift the dip further toward the Fermi energy.The zero-bias conductance of the α-spin electron current becomes half that of the β-spin; therefore, the nanotube could be used as a spin-filter.

IV. SUMMARY
The extent that non-magnetic adatoms on the surface of a metallic carbon nanotube can induce significant changes in its spin-dependent transport properties was investigated using the NEGF+DFT methods.It was demonstrated that carbon and boron adatoms have spin-polarized electronic states upon adsorption, and thus show a clear spin dependence of the electrical conductance.Lastly, it was found that nanotubes may behave as spin-filters by shifting the spin-dependent conductance dips under the influence of a gate bias voltage.Volume 6 (2008) demic Frontier" Project and Grants-in-Aid (#30408695 and #19540411).Some of the numerical calculations were performed on the Hitachi SR11000s at the ISSP, the University of Tokyo.

FIG. 2 :
FIG. 2: Difference in the spin-dependent electron densities in the case of C (upper) and B (lower) adatoms.Red areas indicate an excess of electrons with α-spin and blue areas indicate an excess of electrons with β-spin.The isosurfaces are plotted for a value of +/− 0.001 Å−3 Figures3 and 4show the results of zero-bias spindependent conductance for the cases of C and B adatoms, respectively.For the carbon adatom (Fig.3), the most significant dip is observed in the β-spin transmission curve, above the Fermi energy at E = +0.3eV.Other dips in both the α and β curves are observed at around E = +1.1 eV, and in the α-spin transmission curve only at E = −1.2eV.In the case of the B adatom (Fig.4), the main dip position is observed in the α-spin transmission curve, below the Fermi energy at E = −0.6 eV.It should be noted that for each dip, the conductance is reduced from 2 (for a perfect SWNT) to 1 G 0 .This one unit reduction is interpreted by the fact that the adatom breaks the mirror symmetry of the nanotube (along its axe), and the destructive interference results in a perfect reflection.This phenomenon is discussed extensively in Ref.[2].The dips in the conductance curves of Figs. 3 and 4 cannot be merely explained with the total spin-polarized densities (Fig.2).In the case of the carbon adatom, one may think that the α-spin conduction electrons would be scattered by the adatom, because an excess of α-spin electrons are observed around it (Fig.2).However, that is not necessarily the case, because conduction electrons of a particular energy are scattered only by the electronic states of the adatoms with the same energy.Therefore, to understand how the electrons are scattered, the SL-DOS must be considered.Figure3 (bottom)shows the isosurfaces of the SLDOS in carbon, for E = −1.20 eV and E = +0.30eV.For E = +0.30eV, the α-SLDOS is delocalized along the nanotube, but on the contrary, the β-SLDOS is quite localized around the adatom.This explains why only the β-spin electrons are scattered, resulting in a dip in the β-spin conductance.The conductance dip in the α curve at E = −1.20 eV is explained also by the SLDOS for α-spin electrons.The case for the B atom is also consistent with this interpretation, with the α-and β-SLDOS shown in Fig.4.At E = −0.6 eV, the SL-DOS for α-spin electrons is localized around the adatom, hence α-spin electrons are scattered, which results in the dip.The zero-bias spin-dependent conductance shown in Figs.3 and 4are now understood using the SLDOS.