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Equivalence of wave function matching and Green's functions methods for quantum transport: generalized Fisher-Lee
Hocine Boumrar1, Mahdi Hamidi1, Hand Zenia1
1Laboratoire de Physique et Chimie Quantique, FacultÉ des Sciences, UniversitÉ Mouloud Mammeri Tizi-Ouzou BP 17 RP, 15000 Tizi-Ouzou, Algeria.
None:
We present a proof of an exact equivalence of the two approaches that are most used in computing conductance in quantum electron and phonon transport: the wave function matching and Green's functions methods. We can obtain all the quantities defined in one method starting from those obtained in the other. This completes and illuminates the work started by Ando (1991Phys. Rev. B448017) and continued later by Khomyakovet al(2005Phys. Rev. B72035450). The aim is to allow for solving the transport problem with whichever approach fits most the system at hand. One major corollary of the proven equivalence is our derivation of a generalized Fisher-Lee formula for resolving the transmission function into individual phonon mode contributions. As an illustration, we applied our method to a simple model to highlight its accuracy and simplicity.
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