RKKY Interaction In Graphene Research Articles

RKKY interaction in graphene with a line defect

A kind of extended line defect is currently an experimentally available one-dimensional topological structure in graphene lattice. It modifies the electronic properties of graphene in many aspects. For example, it induces an even-parity boundary state which has linear dispersion and breaks the electron–hole symmetry of the graphene electronic structure. In addition, the line defect possesses much stronger adsorption ability to the metal adatoms than the ordinary graphene lattice point. In the present work, by developing an analytical lattice Green's function technique, we theoretically study the RKKY interaction in graphene when two magnetic impurities are adsorbed near the line defect. We find that R−3 decay rate of the RKKY interaction unique to graphene still holds true in the presence of the line defect. But another feature of the RKKY interaction in graphene, referred to as the Saremi's rule, which claims the RKKY interactions between the same or opposite sublattice points are ferro- or antiferromagnetic respectively, is no longer preserved due to the influence of the boundary state around the line defect. More importantly, the RKKY interaction on the line defect is greater than its counterpart in the pristine graphene by about one or two orders of magnitude. The local lattice distortion around the line defect can bring about the transition of the RKKY interaction between ferro- and antiferromagnetic orders. Such a result implies that the presence of the extended line defect provides a feasible platform in graphene to realize the long-range magnetic order even at a high temperature.

Publisher’s Note: RKKY interaction in graphene [Phys. Rev. B84, 115119 (2011)

Publisher’s Note: RKKY interaction in graphene [Phys. Rev. B<b>84</b>, 115119 (2011)

RKKY interaction in graphene

We consider RKKY interaction between two magnetic impurities in graphene. The consideration is based on the perturbation theory for the thermodynamic potential in the imaginary time representation. We analyze the symmetry of the RKKY interaction on the bipartite lattice at half filling. Our analytical calculation of the interaction is based on direct evaluation of real space spin susceptibility.

RKKY interaction in graphene from the lattice Green’s function

We study the exchange interaction $J$ between two magnetic impurities in undoped graphene (the Ruderman-Kittel-Kasuya-Yosida [RKKY] interaction) by directly computing the lattice Green's function for the tight-binding band structure for the honeycomb lattice. The method allows us to compute $J$ numerically for much larger distances than can be handled by finite-lattice calculations as well as for small distances. In addition, we rederive the analytical long-distance behavior of $J$ for linearly dispersive bands and find corrections to the oscillatory factor that were previously missed in the literature. The main features of the RKKY interaction in half-filled graphene are that unlike the $J\ensuremath{\propto}(2{k}_{F}R){}^{\ensuremath{-}2}\mathrm{sin}(2{k}_{F}R)$ behavior of an ordinary two-dimensional metal in the long-distance limit, $J$ in graphene falls off as $1/{R}^{3}$, shows the $1+\mathrm{cos}[(K\ensuremath{-}{K}^{\ensuremath{'}})\ifmmode\cdot\else\textperiodcentered\fi{}R]$-type oscillations with additional phase factors depending on the direction, and exhibits a ferromagnetic interaction for moments on the same sublattice and an antiferromagnetic interaction for moments on the opposite sublattices as required by particle-hole symmetry. The computed $J$ with the full band structure agrees with our analytical results in the long-distance limit, including the oscillatory factors with the additional phases.

Impurity scattering, Friedel oscillations and RKKY interaction in graphene

We investigate Friedel Oscillations (FO) surrounding a point scatterer in graphene. We find that the long-distance decay of FO depends on the symmetry of the scatterer. In particular, the FO of the charge density around a Coulomb impurity show a faster, δρ∼1/ r3, decay than in conventional 2D electron systems. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice decay according to the 1/r2 law. We discuss the consequences of these findings for the temperature dependence of the resistivity of the material and the RKKY interaction between magnetic impurities.