Full analytical solution of finite-length armchair/zigzag nanoribbons

Finite-length armchair graphene nanoribbons can behave as one dimensional topological materials, that may show edge states in their zigzag-terminated edges, depending on width and termination. We here a full solution of Tight-Binding rectangles any length be seen either finite-length or zigzag ribbons. find exact analytical expressions for both bulk eigen-states eigen-energies. write down the Coulomb interactions among introduce Hubbard-dimer model to analyse emergence features different magnetic at whose existence depends ribbon length. ample room experimental testing our predictions N = 5 compare results with ab initio simulations benchmark quality dimer set its parameters. A further detailed analysis Hamiltonian allows us identify those variations parameters affect properties