Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps

TL;DR

This paper investigates the edge states in graphene ribbons under magnetic fields, considering quantum Hall ferromagnetism and Dirac masses, revealing conditions for gapless states with implications for experiments.

Contribution

It combines analytic and numerical methods to analyze edge states in graphene ribbons, accounting for ferromagnetic and Dirac-like gaps, for both zigzag and armchair edges.

Findings

Conditions for gapless edge states are established.

Spectrum features depend on edge type and magnetic effects.

Results aid interpretation of recent experimental data.

Abstract

By combining analytic and numerical methods, edge states on a finite width graphene ribbon in a magnetic field are studied in the framework of low-energy effective theory that takes into account the possibility of quantum Hall ferromagnetism (QHF) gaps and dynamically generated Dirac-like masses. The analysis is done for graphene ribbons with both zigzag and armchair edges. The characteristic features of the spectrum of the edge states in both these cases are described. In particular, the conditions for the existence of the gapless edge states are established. Implications of these results for the interpretation of recent experiments are discussed.