Classical trajectories in quantum transport at the band center of bipartite lattices with or without vacancies

Abstract

Here we report on several anomalies in quantum transport at the band center of a bipartite lattice with vacancies that are surely due to its chiral symmetry, namely: no weak localization effect shows up, and, when leads have a single channel the transmission is either one or zero. We propose that these are a consequence of both the chiral symmetry and the large number of states at the band center. The probability amplitude associated to the eigenstate that gives unit transmission ressembles a classical trajectory both with or without vacancies. The large number of states allows to build up trajectories that elude the blocking vacancies explaining the absence of weak localization.