RKKY interaction in disordered graphene

Abstract

We investigate the effects of nonmagnetic disorder on the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction in graphene by studying numerically the Anderson model with on-site and hopping disorder on a honeycomb lattice at half filling. We evaluate the strength of the interaction as a function of the distance R between two magnetic ions, as well as their lattice positions and orientations. In the clean limit, we find that the strength of the interaction decays as 1/R 3 , with its sign and oscillation amplitude showing strong anisotropy. With increasing on-site disorder, the mean amplitude decreases exponentially at distances exceeding the elastic mean free path. At smaller distances, however, the oscillation amplitude increases strongly and its sign changes on the same sublattice for all directions but the armchair direction. For random hopping disorder, no sign change is observed. No significant changes to the geometrical average values of the RKKY interaction are found at small distances, while exponential suppression is observed at distances exceeding the localization length.

RKKY interaction in heavily vacant graphene

“…These equations indicating ferromagnetic (antiferromagnetic) correlation on same (different) sub-lattice were numerically confirmed with the KPM method [7,8]. We have also checked that the KPM results obtained in the clean limit (see Fig.…”

“…in undoped [7] and doped graphene [8]. They found that for strong enough on-site disorders where Anderson localization takes place, the RKKY interaction exponentially decays with distance which is consistent with the picture based on localized spectrum [9].…”

“…[7]: We find that propagation of electron waves in defective environment reduces the exponent α in R α distance dependence of the RKKY interaction from α = −3 to below −4 away from half-filling. The exponent α will not differ from −3 as long as the chemical potential is around energies where the density of states is linear in energy.…”

“…Typical averages are obtained by geometric averages of the form J geo RKKY = exp( (1/2) ln(J RKKY ) 2 ave ). The geometric averages of the above type are known to better represent the propagating nature of waves, and when they become zero indicate the transition to insulating state [7,8]. To ensure the same holds for our particular form of disorder, in appendix A we have compared the statistics of geometric and arithmetic averages.…”

“…The kernel polynomial method (KPM) can be conveniently used to evaluate various spectral functions including A ij (ε) [7,9,22]. In this method, A ij (ε) can be expressed as a series in Chebyshev (or any other complete set of orthogonal) polynomials and the expansion coefficients -the so called moments -are evaluated by repeated operation with powers of the appropriate re-scaled Hamiltonian in such a way that a T n (H) is generated via their recursive relations.…”