Local magnetic moment oscillation around an Anderson impurity on graphene

TL;DR

This paper theoretically studies spin-dependent Friedel oscillations and quasiparticle interference caused by an Anderson impurity in graphene, revealing sublattice-specific magnetic moment decay and providing analytic formulas for these phenomena.

Contribution

It introduces a detailed theoretical analysis of spin-resolved FO and QPI in graphene with an Anderson impurity, including analytic expressions and sublattice-specific decay behaviors.

Findings

Spin-dependent FO exhibits a $r^{-2}$ decay at doping.

At half filling, charge density and magnetic moment decay as $r^{-3}$.

Magnetic moment decay occurs only on one sublattice at half filling.

Abstract

We theoretically investigate the spin resolved Friedel oscillation (FO) and quasiparticle interference (QPI) in graphene induced by an Anderson impurity. Once the impurity becomes magnetic, the resulted FO becomes spin dependent, which gives rise to a local magnetic moment oscillation with an envelop decaying as $r^{-2}$ in real space in the doping cases. Meanwhile, at half filling, the charge density and local magnetic moment will not oscillate but decay as $r^{-3}$. Such spin resolved FO has both sublattice and spin asymmetry. Interestingly, the local magnetic moment decay at half filling only occurs at one sublattice of graphene, which is quite like the phenomenon observed in a recent STM experiment [H. Gonzalez-Herrero et al., Science 352, 437 (2016)]. We further give an analytic formula about such spin dependent FO based on the stationary phase approximation. Finally, we study the interference of quasiparticles around the magnetic impurity by calculating the spin-dependent Fourier-transformed local density of states (FT-LDOS). Our work gives a comprehensive understanding about the local magnetic moment oscillation around an Anderson impurity on graphene.