▎ 摘　　要

An exact mapping of the tight-binding Hamiltonian for a graphene nanoribbon under any armchair uniaxial strain into an effective one-dimensional system is presented. As an application, for a periodic modulation we have found a gap opening at the Fermi level and a complex fractal spectrum, akin to the Hofstadter butterfly resulting from the Harper model. The latter can be explained by the commensurability or incommensurability nature of the resulting effective potential. When compared with the zig-zag uniaxial periodic strain, the spectrum shows much bigger gaps, although in general the states have a more extended nature. For a special critical value of the strain amplitude and wavelength, a gap is open. At this critical point, the electrons behave as relativistic Dirac fermions in one direction, while, in the other direction, a nonrelativistic Schrodinger behavior is observed. Also, some topological states were observed which have the particularity of not being completely edge states since they present some amplitude in the bulk. However, these are edge states of the effective system due to a reduced dimensionality through decoupling. These states also present the fractal Chern beating observed recently in quasiperiodic systems.