Electron-electron and spin-orbit interactions in armchair graphene ribbons

TL;DR

This paper investigates how intrinsic spin-orbit and Coulomb interactions influence the electronic properties of finite-width graphene armchair ribbons, revealing spin-filtered edge states and a width-dependent charge gap.

Contribution

It provides a detailed analysis of the interplay between spin-orbit and Coulomb interactions in armchair graphene ribbons using a Dirac Hamiltonian approach, highlighting the persistence of metallic edge states.

Findings

Metallic states persist as spin-filtered edge states despite spin-orbit interactions.

A charge gap opens due to Coulomb interactions, decreasing with ribbon width as 1/W.

Weak spin-orbit interactions do not alter the insulating behavior.

Abstract

The effects of intrinsic spin-orbit and Coulomb interactions on low-energy properties of finite width graphene armchair ribbons are studied by means of a Dirac Hamiltonian. It is shown that metallic states subsist in the presence of intrinsic spin-orbit interactions as spin-filtered edge states, in contrast with the insulating behavior predicted for graphene planes. A charge-gap opens due to Coulomb interactions in neutral ribbons, that vanishes as $\Delta\sim 1/W $, with a gapless spin sector. Weak intrinsic spin-orbit interactions do not change the insulating behavior. Explicit expressions for the width-dependent gap and various correlation functions are presented.