Unscreened Coulomb interactions and quantum spin Hall phase in neutral zigzag graphene ribbons

TL;DR

This paper investigates how unscreened Coulomb interactions influence the quantum spin Hall phase in neutral zigzag graphene ribbons, revealing edge state behaviors and the impact of Coulomb interactions on the charge gap.

Contribution

It provides analytic solutions for band structures and edge states considering Coulomb interactions and spin-orbit coupling in zigzag graphene ribbons.

Findings

Coulomb interactions open a charge gap with a gapless spin sector.

Edge states are localized and damped oscillatory, similar to armchair ribbons.

Charge gap decreases exponentially with ribbon width, depending on spin-orbit coupling.

Abstract

A study of the effect of unscreened Coulomb interactions on the quantum spin Hall (QSH) phase of finite-width neutral zigzag graphene ribbons is presented. By solving a tight-binding Hamiltonian that includes the intrinsic spin-orbit interaction (I-SO), exact expressions for band-structures and edge-states wavefunctions are obtained. These analytic results, supported by tight-binding calculations, show that chiral spin-filtered edge states are composed of localized and damped oscillatory wavefunctions, reminiscent of the ones obtained in armchair ribbons. The addition of long-range Coulomb interactions opens a gap in the charge sector with a gapless spin sector. In contrast to armchair terminations, the charge-gap vanishes exponentially with the ribbon width and its amplitude and decay-length are strongly dependent on the I-SO coupling. Comparison with reported ab-initio calculations are presented.