Transmission eigenchannels from nonequilibrium Green’s functions

The concept of transmission eigenchannels is described in a tight-binding nonequilibrium Green’s function (NEGF) framework. A simple procedure for calculating the eigenchannels is derived using only the properties of the device subspace and quantities normally available in a NEGF calculation. The method is exemplified by visualization in real space of the eigenchannels for three different molecular and atomic wires.

Figure 1

The generic two probe system which couples the left $\left(L\right)$ and right $\left(R\right)$ leads through an intermediate “device” region $\left(D\right)$.

Figure 2

Overview of the different states used in this paper. Note that the scattering states which are nonzero in the device subspace are all spanned by the $\mid {\tilde{\Psi }}_l⟩$ states. We can, therefore, find the eigenchannels by studying the wave functions spanned by the $\mid {\tilde{\chi }}_l⟩=P_D\mid {\tilde{\Psi }}_l⟩$.

Figure 3

(Color online) Left eigenchannel for a seven-atom Au atomic chain connected by four atom pyramids to Au (100) surfaces. The complex phase of the eigenchannel, indicated and shown in color, is similar that of a Bloch wave at the Fermi level in the infinite atomic gold chain (half-filled $6s$ band).

Figure 4

(Color online) Left eigenchannel for an OPV molecule bound by thiols to the hollow sites on Au (111) surfaces. The colors correspond to the two different signs of the almost real-valued wave function.

Figure 5

(Color online) (a) Left and (b) right eigenchannels for an OPE molecule strongly bound by a thiol to the left surface and weakly interacting with the right lead.