Strongly correlated electron physics in nanotube-encapsulated metallocene chains

The structural, electronic, and transport properties of metallocene molecules $\left(M{\mathrm{Cp}}_2\right)$ and isolated or nanotube-encapsulated metallocene chains are studied by using a combination of density functional theory and nonequilibrium Green’s functions. The analysis first discusses the whole series of isolated $\left(M{\mathrm{Cp}}_2\right)$ molecules, where $M=\mathrm{V}$, Cr, Mn, Fe, Co, Ni, Ru, and Os. The series presents a rich range of electronic and magnetic behaviors due to the interplay between the crystal field interaction and Hund’s rules, as the occupation of the $d$ shell increases. The article then shows how many of these interesting properties can also be seen when $\left(M{\mathrm{Cp}}_2\right)$ molecules are linked together to form periodic chains. Interestingly, a large portion of these chains display metallic, and eventually magnetic, behavior. These properties may render these systems as useful tools for spintronics applications but this is hindered by the lack of mechanical stability of the chains. It is finally argued that encapsulation of the chains inside carbon nanotubes, that is exothermic for radii larger than $4.5\mathrm{\AA }$, provides the missing mechanical stability and electrical isolation. The structural stability, charge transfer, magnetic, and electronic behavior of the ensuing chains, as well as the modification of the electrostatic potential in the nanotube wall produced by the metallocenes are thoroughly discussed. We argue that the full devices can be characterized by two doped, strongly correlated Hubbard models whose mutual hybridization is almost negligible. The charge transferred from the chains produces a strong modification of the electrostatic potential in the nanotube walls, which is amplified in case of semiconducting and endothermic nanotubes. The transport properties of isolated metallocenes between semi-infinite nanotubes are also analyzed and shown to lead to important changes in the transmission coefficients of clean nanotubes for high energies.

Figure 1

(Color online) Densities of states $g_i$ of (a) $\mathrm{V}{\mathrm{Cp}}_2$, (b) $\mathrm{Fe}{\mathrm{Cp}}_2$, and (c) $\mathrm{Co}{\mathrm{Cp}}_2$, projected onto the $d$-shell orbitals of the $3d$-row metal atom $i=d_{x^2-y^2},d_{xz},d_{3z^2-r^2},d_{yz},d_{xy}$. Continuous and dashed lines represent spin-up and spin-down electrons, respectively.

Figure 2

(Color online) Band structure around the Fermi level for chains of vanadocene [(a1) and (a2) for majority and minority spin, respectively] and cobaltocene [(b1) and (b2)] calculated at a lattice constant of $7.5\mathrm{\AA }$. Circles, squares, diamonds, triangles up and triangles down represent $d_{yz}$, $d_{xz}$ ($e_{1g}^{*}$ orbitals), $d_{x^2-y^2}$, $d_{xy}$ ($e_{2g}$ orbitals), and $d_{3z^2-r^2}$ ($a_{1g}^{\prime }$ orbital), respectively.

Figure 3

Energy as a function of the spiral pitch vector for (a) an isolated chain of cobaltocenes and (b) a chain of cobaltocenes inside a (7,7) SWNT grown along the $C_5$ symmetry axis. $q=0$ corresponds to the ferromagnetic configuration and $q=1$ (in units of $\pi ∕a$) to the antiferromagnetic configuration.

Figure 4

(Color online) Cohesive energy for the cases $N=3$ (circles) and $N=4$ (squares) in the parallel (continuous line) and perpendicular (broken line) configurations, calculated without (a) and with (b) BSSE correction.

Figure 5

Band structure of (a) an isolated cobaltocene chain (lattice $\text{constant}=7.5\mathrm{\AA }$), (b) a cobaltocene inside three unit cells of a (7,7) nanotube (the same separation between molecules as before), and (c) a (7,7) nanotube, for spin-up and spin-down electrons.

Figure 6

Band structure of (a) $\mathrm{Co}{\mathrm{Cp}}_2@2(11,0)$, (b) $2\mathrm{Co}{\mathrm{Cp}}_2@(12,4)$, and (c) $2\mathrm{Co}{\mathrm{Cp}}_2@(15,5)$ for spin up and spin down electrons.

Figure 7

(Color online) From top to bottom, projected densities of states on the cobaltocene Co, C, and H atoms for a cobaltocene chain at its equilibrium distance, and a clean (7,7) SWNT. Solid and dashed lines indicate spin up and down components, respectively.

Figure 8

(Color online) From top to bottom, projected densities of states on the cobaltocene Co, C, and H atoms and the nanotube walls in a $\mathrm{Co}{\mathrm{Cp}}_2@3(7,7)$ device. Solid and dashed lines indicate spin up and down components, respectively.

Figure 9

(Color online) From top to bottom, projected densities of states on the cobaltocene Co, C, and H atoms and the nanotube walls in a $\mathrm{Co}{\mathrm{Cp}}_2@4(7,7)$ device. Solid and dashed lines indicate spin up and down components, respectively.

Figure 10

(Color online) $\Delta V$ as a function of the $z$ coordinate for $\mathrm{Co}{\mathrm{Cp}}_2@2(11,0)$ (continuous line) and $\mathrm{Co}{\mathrm{Cp}}_2@4(11,0)$ (dashed line) devices.

Figure 11

(Color online) Unit cell used to calculate the transport properties of a clean nanotube with a metallocene impurity. The atoms of the metallocene have been highlighted for clarity.

Figure 12

Transmission coefficients of isolated ferrocenes, cobaltocenes, and nickelocenes in the parallel configuration between semi-infinite (7,7) SWNT leads. For comparison it is also shown the transmission coefficients of a clean (7,7) SWNT.