The flat electronic band has remarkable relevance in the strongly correlated phenomena mainly due to its reduced kinetic energy in comparison to the many-body potential energy. The formation of such bands in cubically structured nanowires is addressed in this article by means of a new independent channel method and a generalized convolution theorem developed for the Green's function including the first, second, and third neighbor interactions. A real-space renormalization method is further applied to address macroscopic-length aperiodic nanowires. We also determined the appearance condition of these flat bands, as well as their degeneracy and robustness in the face of perturbations, such as structural dislocations. Finally, the possible experimental detection of this flat band via the electronic specific heat is analyzed.
Keywords: convolution theorem; flat band; independent channels; nanowire.