2019/12/24 by Hocine Boumrar, Boumrar, Hocine, Mahdi Hamidi +5 · 1 citation
Engineering · Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Molecular Junctions and Nanostructures #Quantum and electron transport phenomena #Surface and Thin Film Phenomena
paper · pdf · doi:10.48550/arxiv.1912.11506
openalex publication_date 2019/12/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We present a proof of an exact equivalence of the two approaches that are\nmost used in computing conductance in quantum electron and phonon transport:\nthe wave function matching and Green's functions methods. We can obtain all the\nquantities defined in one method starting from those obtained in the other.\nThis completes and illuminates the work started Ando[Ando T 1991 Phys. Rev. B\n44 8017] and continued later by Komyakov et al.[Khomyakov P A, Brocks G, Karpan\nV, Zwierzycki M and Kelly P J 2005 Phys. Rev. B 72 035450]. The aim is to allow\nfor solving the transport problem with whichever approach fits most the system\nat hand. One major corollary of the proven equivalence is our derivation of a\ngeneralized Fisher-Lee formula for resolving the transmission function into\nindividual phonon mode contributions. As an illustration, we applied our method\nto a simple model to highlight its accuracy and simplicity.\n