Electron-electron interactions on the edge states of graphene: A many-body configuration interaction study

We have studied zigzag and armchair graphene nanoribbons (GNRs), described by the Hubbard Hamiltonian using quantum many-body configuration interaction methods. Due to finite termination, we find that the bipartite nature of the graphene lattice gets destroyed at the edges, making the ground state of the zigzag GNRs a high spin state, whereas the ground state of the armchair GNRs remains a singlet. Our calculations of charge and spin densities suggest that, although the electron density prefers to accumulate on the edges (instead of spin polarization), the up and down spins prefer to mix throughout the GNR lattice. While the many-body charge gap results in insulating behavior for both kinds of GNRs, the conduction upon application of electric field is still possible through the edge channels because of their high electron density. Analysis of optical states suggest differences in quantum efficiency of luminescence for zigzag and armchair GNRs, which can be probed by simple experiments.

Figure 1

The unit cell of GNR. The translations along the $x$ and $y$ axes give the zigzag and armchair edge GNRs. The number of atoms at the zigzag terminal of an armchair GNR is represented by the integers.

Figure 2

The lowest gap in tight-binding calculations as a function of inverse system size $(1∕N)$ for both zigzag (circle) and armchair (square) GNRs with ${ϵ}_{\mathit{\text{edge}}}$ equal to (a) $-2.0$ and (b) 0.

Figure 3

Charge density on each and every site for both (a) zigzag and (b) armchair GNRs with ${ϵ}_{\mathit{\text{edge}}}=-2.0$ (gray lines with circles) and 0 (solid lines without any symbol) on the edge atoms of the system with $N=104$. Insets present the contour plot of the charge density for the corresponding systems with ${ϵ}_{\mathit{\text{edge}}}=-2.0$.