A model is presented for the quantum transport of electrons, across finite atomic wire nanojunctions between electric leads, at zero bias limit. In order to derive the appropriate transmission and reflection spectra, familiar in the Landauer-Büttiker formalism, we develop the algebraic phase field matching theory (PFMT). In particular, we apply our model calculations to determine the electronic conductance for freely suspended monatomic linear sodium wires (MLNaW) between leads of the same element, and for the diatomic copper-cobalt wires (DLCuCoW) between copper leads on a Cu(111) substrate. Calculations for the MLNaW system confirm the correctness and functionality of our PFMT approach. We present novel transmission spectra for this system, and show that its transport properties exhibit the conductance oscillations for the odd-and even-number wires in agreement with previously reported first-principle results. The numerical calculations for the DLCuCoW wire nanojunctions are motivated by the stability of these systems at low temperatures. Our results for the transmission spectra yield for this system, at its Fermi energy, a monotonic exponential decay of the conductance with increasing wire length of the Cu-Co pairs. This is a cumulative effect which is discussed in detail in the present work, and may prove useful for applications in nanocircuits. Furthermore, our PFMT formalism can be considered as a compact and efficient tool for the study of the electronic quantum transport for a wide range of nanomaterial wire systems. It provides a trade-off in computational efficiency and predictive capability as compared to slower first-principle based methods, and has the potential to treat the conductance properties of more complex molecular nanojunctions.
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