Bosonic field theory of tunable edge magnetism in graphene

TL;DR

This paper develops a bosonic field theory to describe tunable edge magnetism in graphene, linking effective fermionic models with bosonization and analyzing quantum phase transitions.

Contribution

It introduces a novel bosonic field theory derived from fermionic edge states, capturing the momentum-dependent interactions responsible for edge magnetism in graphene.

Findings

The bosonic theory models the weak edge magnetism in graphene.

Near the quantum phase transition, the theory simplifies to a universal form.

Quantum Monte-Carlo methods can access key terms of the critical behavior.

Abstract

A bosonic field theory is derived for the tunable edge magnetism at graphene zigzag edges. The derivation starts from an effective fermionic theory for the interacting graphene edge states, derived previously from a two-dimensional interacting tight-binding model for graphene. The essential feature of this effective model, which gives rise to the weak edge magnetism, is the momentum-dependent non-local electron-electron interaction. It is shown that this momentum-dependence may be treated by an extension of the bosonization technique, and leads to interactions of the bosonic fields. These interactions are reminiscent of a \phi^4 field theory. Focussing onto the regime close to the quantum phase transition between the ferromagnetic and the paramagnetic Luttinger liquid, a semiclassical interpretation of the interacting bosonic theory is given. Furthermore, it is argued that the universal critical behavior at the quantum phase transition between the paramagnetic and the ferromagnetic Luttinger liquid is governed by a small number of terms in this theory, which are accessible by quantum Monte-Carlo methods.