# Effect of long-range interaction on graphene edge magnetism

## TL;DR

This paper investigates how long-range Coulomb interactions affect edge magnetism in graphene, finding that ferromagnetism persists even with unscreened Coulomb forces, which is crucial for experimental realization.

## Contribution

It introduces a model considering non-local Coulomb interactions on graphene edges and demonstrates that ferromagnetism remains stable under these conditions.

## Key findings

- Ferromagnetism survives with unscreened Coulomb interactions
- Long-range interactions do not destroy edge magnetism in graphene
- The model includes electron, hole, and exciton excitations

## Abstract

It has been proposed that interactions lead to ferromagnetism on a zigzag edge of a graphene sheet. While not yet directly studied experimentally, dramatically improving techniques for making and studying clean zigzag edges may soon make this possible. So far, most theoretical investigations of this claim have been based on mean field theories or more exact calculations using the Hubbard model. But long-range Coulomb interactions are unscreened in graphene so it is important to consider their effects. We study rather general non-local interactions, including of Coulomb $1/r$ form, using the technique of projection to a strongly interacting edge Hamiltonian, valid at first order in the interactions. The ground states as well as electron/hole and exciton excitations are studied in this model. Our results indicate that ferromagnetism survives with unscreened Coulomb interactions.