Peierls instability and ferrimagnetic ordering of quasi-one-dimensional carbon chains generated in H-passivated graphene

Using first-principle density-functional calculations, we investigate the competition between Peierls instability and spin ordering in a zigzag C chain generated in an H-passivated graphene. We find that such a quasi-one-dimensional (1D) C chain of infinite length stabilizes a Peierls instability showing bond alternation with a band-gap opening. As the chain length becomes finite, the Peierls distortion is enhanced at even-numbered chains, while a ferrimagnetic spin ordering with the atomic structure of a topological soliton is stabilized at odd-numbered chains. These results indicate the existence of complex interplay between electron-lattice and electron-electron interactions with respect to the parity of the quasi-1D C chains.

Figure 1

(a) Schemetic diagram of the bond-alternated structure of polyacetylene and optimized structures of (b) the H-passivated graphene (graphane) and (c) the 1D infinitely long C chain generated in graphane. The top view of (c) is displayed in (d). Large and small circles represent C and H atoms, respectively. For distinction, C atoms composing the C chain are drawn in dark color. The C–C bond length (in Å) is given in (d).

Figure 2

Calculated band structure of the C-$\infty$ chain. The energy zero represents the Fermi level. The direction of $\Gamma -\mathbf{X}$ line is along the chain. The charge character of the $S_1$ ($S_2$) state at the $\mathbf{X}$ point is shown with an isosurface of 0.2 (0.1) electrons/Å${}^3$. The perspective view of the antibonding $\pi$ character is also shown in the inset.

Figure 3

Top view of the optimized structure of finitely long C chains: (a) C-2, (b) C-3, (c) C-4, and (d) C-5 chains. The numbers denote the C–C bond length (in Å). In the inset of (b) and (d), the majority (minority) spin density is displayed with an isosurface of 0.02(–0.02) electron/Å${}^3$.

Figure 4

Simulated filled-state STM images of (a) C-2, (b) C-3, (c) C-4, (d) C-5, (e) C-6, and (f) C-7 chains. The filled-state images were obtained by integrating the charge from occupied states within 3 eV. All the images were taken at a charge density of 2.3 $\times$ 10${}^{-5}$ electron/Å${}^3$. Open circles represent C atoms composing the chain, whereas black (gray) circles represent H-passivated C atoms positioned above (below) the chain.