Figure 2. Charge gap, spin gap and spin density of half-filled ZGNRs.

(a) The charge gap (Δ_c) behavior over the BZ for ZGNRs with N_z = 4 and 20 (solid lines) and for bulk graphene (dashed line) at half-filling. (b) The minimum of charge gap, Δ_c (min.) (circles) near the Dirac point as a function of N_z and fitted (solid line) with the equation: Δ_c = 1.736/ N_z. The Δ_c at k = π for varying N_z is shown by dashed line with squares. (c) The spin gap (Δ_s) behavior over the BZ for ZGNRs with N_z = 4 and 20 (solid lines) and for bulk graphene (dashed line) at half-filling. (d) and (e) shows the spin density profile of half-filled ZGNR with N_z = 20 for S_z^tot = S₀ and S₀ + 1, respectively as a function of wavenumber (k) along the width (designated by site index). The color bar shows the absolute scale of spin density.