Theory of length-dependent conductance in one-dimensional chains

The length-dependent conductance of molecular wires and quantum dot array has been theoretically investigated based on finite size one-dimensional model. It has been clarified that the dependences of the conductance on the length of the chain have qualitatively different characteristics even for noninteracting electrons as the Fermi energy of the lead is varied relative to the energy spectra of atoms. It has also been found that the relative magnitude of the transfer integrals in the chain and the electrode, and those between the electrode and the chain plays a crucial role on the conductance. We have found length dependence in these cases have more physics besides the even-odd oscillatory behavior, which has been studied in a special case of the atomic wire system. The dephasing effects and the effects of strong correlation in the dot have been briefly investigated based on the Hubbard chain. A simple formula for the conductance given here may be useful to analyze band calculation results and experimental results.