Magnetism as a mass term of the edge states in graphene

TL;DR

This paper theoretically investigates how edge states in graphene exhibit magnetism, influenced by Coulomb interactions, pseudo-spin order instability, and edge-induced gauge fields, revealing a connection to the parity anomaly.

Contribution

It introduces a theoretical framework linking edge-induced gauge fields and spin-dependent mass terms to magnetism in graphene edge states, highlighting the role of Coulomb interactions.

Findings

Coulomb interactions induce ferrimagnetic order at graphene edges.

Pseudo-spin order stability is affected by next nearest-neighbor hopping.

Edge magnetism correlates with density of states peaks near the Fermi level.

Abstract

The magnetism by the edge states in graphene is investigated theoretically. An instability of the pseudo-spin order of the edge states induces ferrimagnetic order in the presence of the Coulomb interaction. Although the next nearest-neighbor hopping can stabilize the pseudo-spin order, a strong Coulomb interaction makes the pseudo-spin unpolarized and real spin polarized. The magnetism of the edge states makes two peaks of the density of states in the conduction and valence energy bands near the Fermi point. Using a continuous model of the Weyl equation, we show that the edge-induced gauge field and the spin dependent mass terms are keys to make the magnetism of the edge states. A relationship between the magnetism of the edge states and the parity anomaly is discussed.