Quantum transport in a chain of quantum dots with inhomogeneous size distribution and manifestation of 1D Anderson localization

The effect of inhomogeneous quantum dot (QD) size distribution on the electronic transport of one-dimensional (1D) QD chains (QDCs) is theoretically investigated. The non-equilibrium Green function method is employed to compute the electron transmission probabilities of QDCs. The ensemble averaged transmission probability shows a close agreement with the conductivity equation predicted by Anderson et al. for a disordered electronic system. The fidelity of quantum transport is defined as the transmission performance of an ensemble of QDCs of length N (N-QDCs) to assess the robustness of QDCs as a practical electronic device. We found that the fidelity of inhomogeneous N-QDCs with the standard deviation of energy level distribution σ(ε) is a Lorentzian function of variable Nσ(ε)(2). With these analytical expressions, we can predict the conductance and fidelity of any QDC characterized by (N, σ(ε)). Our results can provide a guideline for combining the chain length and QD size distributions for high-mobility electron transport in 1D QDCs.