  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-B\"{u}ttiker 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.
