  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.
