Solitons in magnetic nanographite ribbons investigated with a Peierls-Hubbard model

The hydrogenated nanographite ribbons are numerically investigated with a Peierls-Hubbard model. In the ferrimagnetic ground state, an antiferromagnetic spin density wave and perfect dimerization exist. The dependences of the dimerization and the spin density on the width of the ribbon, electron-phonon coupling $\lambda$, and the on-site Hubbard repulsion $U$ are studied in detail. Because the ground state is degenerate, a domain wall describing the lattice deformation and the spin soliton describing the localization of spin exist. The creation energy of the soliton is much smaller than that in polyacetylene because the localized state of soliton is not in the gap. Due to the interplay between $\lambda$ and $U$, the solitons exist only in a range of $U$, which depends on $\lambda$.

Figure 1

A hydrogenated nanographite ribbon with $M$ zigzag chains each with $N$ carbon atoms. Open circles denote hydrogen atoms and other sites represent carbon atoms. The dashed rectangle denotes a unit cell. The arrow labels the direction of chains.

Figure 2

The energy spectra (a) the ground state and (b) the excited state for the system with $N=120$ and $M=3$. ${ϵ}_{\mu }^{\sigma }$ (with $t_0$ as unit of energy) is $\mu \text{th}$ energy level with spin $\sigma$. (c), (d) the spatial distribution of the wave function of the localized soliton level.

Figure 3

The dimerzation $y_1={(-1)}^i{y}_{1,i}$ on the first chain versus the width $M$ of the ribbon for different $\lambda$ and $U$.

Figure 4

The dimerization $y_1$ versus $U$ for different $\lambda$ and $M$.

Figure 5

The spin densities $⟨S_{l,i}^z⟩$ at different sites in a unit cell (see the sites in the dashed rectangle in Fig. 1) versus $U$ for $M=5$, $\lambda =0.60$ (solid line) and 0.65 (dashed line).

Figure 6

(a), (b) The lattice deformation $d_{l,i}={(-1)}^i{y}_{l,i}$ of the soliton on different chains for $N=120$, $M=3$, $\lambda =0.625$, and $U=2$. (c)–(e) The spin density $⟨S_{l,i}^z⟩$ on the $i\text{th}$ site in $l\text{th}$ chain, which shows the localization of spin in the middle of each chain.

Figure 7

The same as in Fig. 6 but for $M=5$.

Figure 8

The creation energy of soliton $E_s$ versus $U$ for $M=3$ and different $\lambda$ and $N$.