Ab initio study of spin-dependent transport in carbon nanotubes with iron and vanadium adatoms

We present an ab initio study of spin-dependent transport in armchair carbon nanotubes with transition metal adsorbates: iron or vanadium. The method based on density functional theory and nonequilibrium Green’s functions is used to compute the electronic structure and zero-bias conductance. The presence of the adsorbate causes scattering of electrons of mainly one spin type. The scattering is shown to be due to a coupling of the two armchair band states to the metal $3d$ orbitals with matching symmetry, giving rise to Fano antiresonances appearing as dips in the transmission function. The spin type (majority or minority) being scattered depends on the adsorbate and is explained in terms of $d$-state filling. We contrast the single-walled carbon nanotube results to the simpler case of the adsorbate on a flat graphene sheet with periodic boundary conditions and corresponding width in the zigzag direction, where the $d$-orbital selectivity is easily understood in terms of a simple tight-binding model.

Figure 1

(Color online) The unit cell of the GPB system. The sheet is cut in an armchair structure along the $y$ direction. The adatom, iron, or vanadium is placed in the center. The shaded areas marked $L$ and $R$ are the electrodes, and $C$ is the central region. Periodic boundary conditions are imposed in the transverse direction $\left(x\right)$.

Figure 2

(Color online) Top: Transmission as a function of energy for iron (left) or vanadium (right) on the GPB system. Within a 0.5 eV range of $E_F$ the minority spin channels are suppressed in the case of iron, whereas the majority channels are suppressed for vanadium. Middle: The transmission of the two minority (majority) spin channels for the iron (vanadium) system. The sum of the two channels yields the total transmission in each case. Bottom: The projected density of states (PDOS) of the $3d$ orbitals of the iron (vanadium) adatom for minority (majority) spin.

Figure 3

(Color online) The transmission for the (2,2) GPB system for different iron adatom distances to the sheet plane ranging from 1.50 to $1.77\text{Å}$.

Figure 4

(Color online) The real part of the (left-to-right) eigenchannel scattering states for the vanadium GPB system, stemming from majority spin electrons from both bands, at the energy of the first dip $\left(-0.5\text{eV}\right)$ [(a),(b)] and second dip $\left(-0.1\text{eV}\right)$ [(c),(d)] in the transmission spectrum. Only the solutions in the scattering region are shown. The size of the shapes indicates a cutoff value for the wave function. White indicates a positive sign and blue indicates a negative sign of the wave function. The involved orbitals of the vanadium atom (marked with dotted circle) are seen to be (a): $3d_{x^2-y^2}$ (and a minor presence of $3d_{3z^2-r^2}$); (b): $3d_{xy}$; (c): $3d_{yz}$; and (d): $3d_{zx}$.

Figure 5

(Color online) Top panel: The two $\pi$-band $\left(p_z\right)$ states (not normalized) in a hexagon where the arrow denotes the direction along the armchair GPB ($y$ direction) with $\varphi =e^{i2\pi /3}$. Left and right panel correspond to symmetric and antisymmetric solution on the A, B dimers ($x$ direction). Lower panels: Simple tight-binding model. The sign and relative size of the hopping matrix elements between the ring $\pi$ orbitals and the metal adatom $d$ orbitals when the metal atom is situated $1.7\text{Å}$ above the middle of the ring.

Figure 6

(Color online) The transmission through the symmetric and antisymmetric bands for Fe minority spin (left panels) and V majority spin (right panels) calculated with the simple tight-binding model. Lower panels display the projected density of states onto the $d$ orbitals.

Figure 7

(Color online) An analysis as the one given in Fig. 2 comparing (10,10) GPB and (10,10) SWNT systems for iron(vanadium) in the upper (lower) panel. The transmission for the (10,10) SWNT with iron (vanadium) adatom shown in the upper (lower) panel. As for the (2,2) GPB system, the minority spin channels are suppressed in the case of iron, whereas the majority channels are suppressed for vanadium.