Boundary Ferromagnetism in Zigzag Edged Graphene

TL;DR

This paper demonstrates that in zigzag-edged graphene, edge state degeneracy is lifted by interactions, leading to a ferromagnetic ground state with maximal spin, confirmed through perturbation theory.

Contribution

It shows that for a broad class of interaction Hamiltonians, the edge states in zigzag graphene favor a ferromagnetic ground state at first-order perturbation.

Findings

Edge states are resolved into a ferromagnetic ground state.

Ground state has maximal total spin j = N/2.

Degeneracy is lifted by interactions in the model.

Abstract

The flat band of edge states which occur in the simple tight-binding lattice model of graphene with a zig-zag edge have long been conjectured to take up a ferromagnetic configuration. In this work we demonstrate that, for a large class of interaction Hamiltonians which can be added to the tight-binding model, and at the first order in perturbation theory, the degeneracy of the edge states is resolved in such a way that the ground state is in the maximal, spin j = N/2 representation of the spin symmetry where N is the number of edge states.