1. Equivalence of wave function matching and Green's functions methods for quantum transport: generalized Fisher-Lee relation
- Author
-
Samir Lounis, Hand Zenia, Hocine Boumrar, and Mahdi Hamidi
- Subjects
Matching (graph theory) ,Phonon ,02 engineering and technology ,Function (mathematics) ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,01 natural sciences ,Corollary ,Simple (abstract algebra) ,0103 physical sciences ,General Materials Science ,ddc:530 ,010306 general physics ,0210 nano-technology ,Wave function ,Equivalence (measure theory) ,Quantum ,Mathematics ,Mathematical physics - Abstract
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 (1991 Phys. Rev. B 44 8017) and continued later by Khomyakov et al (2005 Phys. Rev. B 72 035450). 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.
- Published
- 2020