Potential and spin-exchange interaction between Anderson impurities in graphene

TL;DR

This paper investigates how Anderson impurities in graphene interact via conduction electrons, revealing that their potential and spin-exchange interactions depend on sublattice positioning, coupling strength, and distance, with complex sign and magnitude behaviors.

Contribution

It provides a detailed analysis of the distance-dependent potential and spin-exchange interactions between Anderson impurities in graphene, highlighting the effects of sublattice configuration and coupling strength.

Findings

Potential interaction varies with sublattice and coupling strength, showing $1/R^3$ or $1/R$ dependence.

Spin-exchange coupling can be ferromagnetic or antiferromagnetic, reversing sign at intermediate distances.

Resonant enhancement occurs at specific distances where energy levels cross the Dirac points.

Abstract

The effective interaction between resonant magnetic Anderson impurities in graphene, mediated by conduction electrons, is studied as a function of the strength of the onsite energy level of the impurities and the amplitude of coupling to conduction electrons. The sign and character of the interaction depend on whether the impurities reside on the same or opposite sublattices. For the same (opposite) sublattice, the potential interaction is attractive (repulsive) in the weak coupling limit with $1/R^3$ dependence on the distance; the interaction reverses sign and becomes repulsive (attractive) in the strong coupling limit and displays $1/R$ behavior. The spin-exchange coupling is ferromagnetic (antiferromagnetic) at both large and small distances, but reverses sign and becomes anti-ferromagnetic (ferromagnetic) for intermediate distances. For opposite sublattices, the effective spin exchange coupling is resonantly enhanced at distances where the energy levels cross the Dirac points.