Abstract
The electronic states in flat bands possess zero group velocity and null charge mobility. Recently, flat electronic bands with fully localized states have been predicted in nanowires, when their hopping integrals between first, second, and third neighbors satisfy determined relationships. Experimentally, these relationships can only be closely achieved under external pressures. In this article, we study the alternating current (AC) in such nanowires having nearly flat electronic bands by means of a new independent channel method developed for the Kubo-Greenwood formula including hopping integrals up to third neighbors. The results reveal a large AC conductivity sensitive to the boundary conditions of measurement, where the charge carriers resonate with the external electric field by oscillating around their localized positions.