Topological view on magnetic adatoms in graphene

TL;DR

This paper presents a topological approach to analyze magnetic impurities in graphene, revealing how the relativistic dispersion influences occupation and phase shifts, with implications for impurity state stability and susceptibility.

Contribution

It introduces a topological framework using winding numbers within the Anderson model to study magnetic impurities in graphene, highlighting the effects of relativistic dispersion on impurity occupation.

Findings

Winding number analysis links impurity occupation to topological properties.

Relativistic dispersion in graphene leads to integer impurity occupation.

Impurity state stability depends on gate voltage tuning and Fermi level alignment.

Abstract

We study theoretically the physical properties of a magnetic impurity in graphene. Within the Anderson model for a very strong Coulomb interaction on the impurity, we start from the Slave-Boson method and introduce a topological picture consisting of a degree of a map and a winding number (WN) to analyze the phase shift and the occupation on the impurity. The occupation is linked to WN. For a generic normal metal we find a fractional WN. In contrast, the winding is accelerated by the relativistic dispersion of graphene at half-filling leading to an integer occupation. We show that the renormalization parameter that shifts the impurity level is insufficient to invert the sign of the energy level. Consequently, the state at half-filling is stable unless a gate voltage is tuned such that the Fermi level touches the edge of the broadened impurity level. Only in this case the zero field susceptibility is finite and shows a pronounced peak structure with the gate voltage.