Calculation of electron transport in multiterminal systems using complex absorbing potentials

A method to calculate the transmission coefficient in multiterminal systems is presented. By adding a complex absorbing potential to the Hamiltonian of the semi-infinite leads, the problem of inverting an infinite dimensional matrix is transformed into a finite dimensional eigenvalue problem. Using this approach transmission coefficients are calculated for all energies at once. The accuracy of the approach is demonstrated with an analytically solvable model system. Numerical examples of a four-terminal graphene cross junction and six-terminal carbon nanotube junction are presented.

Figure 1

$n$-terminal junction. The CAP is added between the two dashed lines and the shaded area represents the center region.

Figure 2

Four-terminal junction.

Figure 3

Transmission in a four-terminal junction. The results of the CAP and the analytical calculation are in complete agreement and cannot be distinguished in the resolution of the figure.

Figure 4

Eight-terminal junction.

Figure 5

Transmission ($T_{12}$) in an eight-terminal junction. The results of the CAP and the analytical calculation are in complete agreement and cannot be distinguished in the resolution of the figure.

Figure 6

Transmission ($T_{14}$ and $T_{15}$) in an eight-terminal junction. The results of the CAP and the analytical calculation are in complete agreement and cannot be distinguished in the resolution of the figure.

Figure 7

Graphene cross-junction device.

Figure 8

The transmission coefficient of a graphene cross-junction device.

Figure 9

Six-terminal CNT junction.

Figure 10

Transmission in a six-terminal CNT junction.

Figure 11

Transmission in a six-terminal CNT junction.

Figure 12

Transmission in a monoatomic gold chain cross. The transmission coefficients are calculated by both the CAP approach and by the conventional NEGF method using the decimation technique[48] to obtain the self-energies. The results of the two approaches are in complete agreement and cannot be distinguished in the resolution of the figure.

Figure 13

Potential distribution in a monoatomic gold chain cross.

Figure 14

Current-voltage characteristics in the monoatomic gold chain cross.