Width-dependent dimensional crossover in zigzag graphene nanoribbons

The exact solution of a tight-binding Hamiltonian shows that the unusual width- dependent band-structure of zigzag graphene nanoribbons (ZGNR) is caused by spinor wavefunction phase shifts. These results suggest the correct continuum description of these systems to be in terms of effective coupled-chains models. The particular anisotropic continuum limit reproduces the physics of ZGNR with high accuracy while capturing the width-dependence effect. It also reveals the underlying connection between tight-binding ZGNR models and a continuous set of two-dimensional models that include the square lattice and the $\pi$-flux model. The Majorana fermion language used in this approach shows that ZGNRs are physical realizations of various quantum spin chain (QSC) models.