  We study the properties of flat-bands that appear in a heterostructure
composed of strands of different widths of graphene armchair nanoribbons. One
of the flat-bands is reminiscent of the one that appears in pristine armchair
nanoribbons and has its origin in a quantum mechanical destructive interference
effect, dubbed `Wannier orbital states' by Lin et al. in Phys. Rev. B 79,
035405 (2009). The additional flat-bands found in these heterostructures, some
reasonably closer to the Fermi level, seem to be generated by a similar
interference process. After doing a thorough tight-binding analysis of the band
structures of the different kinds of heterostructures, focusing in the
properties of the flat-bands, we use Density Functional Theory to study the
possibility of magnetic ground states when placing, through doping, the Fermi
energy close to the different flat-bands. Our DFT results confirmed the
expectation that these heterostructures, after being appropriately hole-doped,
develop a ferromagnetic ground state that seems to require, as in the case of
pristine armchair nanoribbons, the presence of a dispersive band crossing the
flat-band. In addition, we found a remarkable agreement between the
tight-binding and DFT results for the charge density distribution of the
so-called Wannier orbital states.
