Knots in a graphene nanoribbon

We have investigated the structural and electronic properties of a graphene nanoribbon with topological knotlike defects using first-principles calculations. As the knotted ribbon is stretched, we find two distinct metastable knot configurations. The first one, a self-tied knot configuration, is stable due to interlayer interactions. The second one, a tight-knot configuration, is stable due to the rehybridization of carbons atoms inside the knot, with the formation of additional covalent bonds, and of localized electronic states in the energy bandgap. Also, the tight-knot configuration has a spin-polarized ground state with a nonzero spin dipole moment.