RKKY Interaction in Disordered Graphene

TL;DR

This paper studies how nonmagnetic disorder affects the RKKY interaction in graphene, revealing decay patterns, anisotropy, and the influence of different disorder types on magnetic coupling.

Contribution

It provides a numerical analysis of the RKKY interaction in disordered graphene, highlighting the effects of on-site and hopping disorder on interaction decay, sign changes, and anisotropy.

Findings

RKKY interaction decays as 1/R^3 in clean graphene

On-site disorder causes exponential decay beyond the elastic mean free path

Hopping disorder does not induce sign changes in the interaction

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.