The resonance structure in a random dimer model

Abstract

The authors have studied a random dimer model using the transfer matrix method and used the Landauer formula to compute conductances of large dimer chains as a function of the Fermi energy of the incident electron. They find very interesting resonance structures in this system around two special energies, namely the site energies (taken from a binary distribution). The localization length around these energies is found to diverge quadratically as a function of the energy difference as one approaches one of these energies from either side. It is also found that the conductance vanishes for this random dimer chain at almost all the allowable energies, just as it does in the case of a random 'monomer' chain. Thus a localization-delocalization transition (and more certainly a mobility edge) is absent in this system as opposed to what is claimed in some recent articles.