Mode-detailed analysis of transmission based directly on Green’s functions

Fisher-Lee relation \hbox{$\bm{t}= {i}\bm{\Gamma}_L^{1/2}\bm{G}\bm{\Gamma}^{1/2}_R$} t = i Γ L 1 / 2 G Γ R 1 / 2 is a well-established tool to decode the mode information from Green’s function and coupling parameters. Using the Bloch eigen-modes of the leads, we show that the \hbox{$\bm{\Gamma}^{1/2}_{L/R}$} Γ L / R 1 / 2 term can be expressed by the Bloch eigen-mode vectors and the wave velocities which give unambiguous algorithm of \hbox{$\bm{\Gamma}^{1/2}_{L/R}$} Γ L / R 1 / 2 in the Fish-Lee relation. Using this approach, we present an accurate and convenient technique to analyze all transport modes and also the dominant channels of an electronic transport system in tight-binding model. We study graphene nanoribbon structures to demonstrate the typical application of our technique.