RKKY interaction in single-walled nanotubes

The Ruderman-Kittel-Kasuya-Yoshida interaction between magnetic impurities in single-walled nanotubes is studied in the framework of a free electron model. It is found that the interaction decays inversely as axial separation between the impurities as in the case of a purely one-dimensional system. The key feature found is that the inverse-distance interaction is modulated by a nonperiodic function that depends on the size (radius) of the tube. Implications for magnetically doped nanotubes are discussed.

Figure 1

(Color online) Dimensionless Fermi energy ${ϵ}_f$ as a function of the size parameter $\rho$. The inset shows schematically the Fermi wave vectors in different bands ($k_{f2},-k_{f2}$ not shown). Angular momentum quantum numbers $\left(n\right)$ of different bands are as indicated in the inset.

Figure 2

(Color online) The dimensionless RKKY interaction $\mathcal{J}(x,\theta )$ for two different values of $\rho$. All lengths are normalized by the radius $R$; $x=X∕R$ is the dimensionless axial coordinate.

Figure 3

(Color online) A comparison of $\mathcal{J}(x,0)$ and ${\mathcal{J}}^a(x,0)$ for $\rho =1.0$.

Figure 4

Contour used in the evaluation of the integral (A7).