Analytical results on coherent conductance in a general periodic quantum dot: Transfer matrix method

In this work, we study the conductance of a general periodic quantum dot (QD) attached to ideal semi-infinite uniform metallic leads (nanocrystals), fully analytically. We propose a new general formula which relates conductance to transfer matrix (TM) for an isolated cell in the periodic dot. The equation describes exactly the dependence of the transmission coefficient (TC) on Fermi energy, dot-size, dot-lead coupling, and gate voltage for an arbitrary periodic dot. Then, we derive a nonlinear equation which gives the resonance, bound, and surface state energies. Finally, the TC has been calculated for gapless, single, and double gap models exactly. Moreover, we have also calculated the effects of the cross-section of the leads, which were separated by a polymer chain on the conductance. Our calculations can be generalized to any type of QD and quantum wire (QW) within the one-electron approximation, and, can be applied to, e.g., molecular, polymer, and nanocrystal junctions, where these results may be useful in designing future molecular electronic devices.