Length- and parity-dependent electronic states in one-dimensional carbon atomic chains on C(111)

Using first-principles density-functional theory calculations, we find dramatically different electronic states in the C chains generated on the H-terminated C(111) surface, depending on their length and parity. The infinitely long chain has $\pi$ electrons completely delocalized over the chain, yielding an equal $\text{C}\text{C}$ bond length. As the chain length becomes finite, such delocalized $\pi$ electrons are transformed into localized ones. As a result, even-numbered chains exhibit a strong charge-lattice coupling, leading to a bond-alternated structure, while odd-numbered chains show a ferrimagnetic spin ordering with a solitonlike structure. These geometric and electronic features of infinitely and finitely long chains are analogous to those of the closed (benzene) and open (polyacetylene) chains of hydrocarbons, respectively.

Figure 1

(Color online) (a) Delocalized $\pi$ electrons in benzene, (b) schematic diagram of the bond-alternated structure of polyacetylene, (c) linear C chain fabricated on the H-terminated C(111) surface, (d) delocalized $\pi$ electrons in $\text{CC-}\infty$, and schematic diagrams of (e) CC-4 and (f) CC-5. In (a) and (d), the contour plots of the charge density are also drawn in the vertical plane containing the $\text{C}\text{C}$ bond, where the first line is at $0.04\text{electrons}/{\text{Å}}^3$ with spacings of $0.03\text{electrons}/{\text{Å}}^3$. In (c), the large and small circles represent C and H atoms, respectively. For distinction, the C atoms composing the C chain are drawn in dark color.

Figure 2

Calculated energies of the NM and AF (FI) configurations relative to the ${\text{NM}}_0$ configuration as a function of the chain length.

Figure 3

(Color online) Local spin moments in odd-numbered chains containing up to $N=11$, calculated from the spin-1/2 Heisenberg Hamiltonian. On the $x$ axis, $i=6$ represents the center site of each chain.

Figure 4

(Color online) Calculated band structures of (a) CC-2 and (b) CC-3. The energy zero represents the Fermi level. The direction of $\Gamma \text{-J}$ line is along the chain. In CC-2 (NM configuration), the solid circles represent the subbands due to the DB electrons, while in CC-3 (FI configuration), the solid and open circles represent the subbands of majority and minority spins, respectively. The charge and spin characters of subbands at the $\Gamma$ point are also given in (c) and (d), respectively, where the charge (spin) density isosurface is shown at $0.04\left(0.02\right)\text{electrons}/{\text{Å}}^3$. In (e), the total spin density isosurface is also shown at $0.02\text{electrons}/{\text{Å}}^3$.