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First-principles methodology for quantum transport in multiterminal junctions
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View: Figures


Image of FIG. 1.
FIG. 1.

Schematic diagram of a multiterminal junction. The barrier region is divided into -number of blocks . The leads are connected to blocks , respectively, whereas the remaining leads are connected to block .

Image of FIG. 2.
FIG. 2.

(Left) Schematic of a four-terminal system. The leads , , , and are connected to the molecular barrier via the subregions , , , and , respectively. The subregions and the molecular region are considered together as a single region shown by the blue-dotted box. The black-dotted box shows the extended-scattering region . (Right) Tridiagonal matrix representation of this system. Any matrix-element in the lower off-diagonal-blocks is the complex conjugate of the corresponding element in the upper off-diagonal-blocks and therefore one can avoid storing the lower off-diagonal-blocks. The shaded blocks of the matrix are directly connected to the leads and hence these contain the same matrix-elements as in the respective leads.

Image of FIG. 3.
FIG. 3.

An initial bias profile (size ) for a four-terminal junction to be applied to the system at the beginning of a nonequilibrium calculation. For the planar molecules considered here, it has been generated by solving a 2D Laplace’s equation with appropriate boundary conditions (see text for details). An identical bias voltage 0.8 V is applied through all four leads , , ,and . The leads are denoted by the numbers 1–4, respectively, and the scale bar of the potential is in electron volt.

Image of FIG. 4.
FIG. 4.

Flowchart of the SC loop used to calculate characteristics. The terminology is explained in the text.

Image of FIG. 5.
FIG. 5.

Charge convergence of the radialene system with SC steps at zero bias. In the inset, a schematic view of the central region of the four-terminal radialene junction is shown, with the number 1–4 marking the positions of the leads. The size of the system is .

Image of FIG. 6.
FIG. 6.

(Left) SC converged potential profile (same as system size, i.e., ) at zero bias of the four-terminal radialene system, plotted 4.88 Bohr above the atomic plane. (Right) The converged potential profile after applying an identical bias at 0.8 V through all the leads. Both the images are shown in same color scale (in electron volt), to compare the relative heights of the potentials.

Image of FIG. 7.
FIG. 7.

(Left) Converged potential profile of the radialene system with a nonuniform bias voltage. (The color scale is in electron volt.) An identical bias of 0.8 V is applied through three of the leads (denoted by 1, 2, 3) and no bias is applied through the fourth lead. (Right) Potential drop along the central line between the leads 3 and 4.

Image of FIG. 8.
FIG. 8.

Transmission curves of the four-terminal radialene system with different bias voltages. The is the Fermi energy of the lead 4. The bias geometry is the same as in Fig. 7. The left and right panels show transmission through the leads and , respectively.

Image of FIG. 9.
FIG. 9.

Current-voltage characteristics of the four-terminal radialene junction. The bias geometry is as shown in Fig. 7. The current contributions through the leads , are displayed.

Image of FIG. 10.
FIG. 10.

A schematic diagram of the crossed-carbon-chains system. Three cases are considered, with distances between the chains of 7.5, 5.0 and 2.5 Bohr.

Image of FIG. 11.
FIG. 11.

(a) and (c) Comparison of the converged potential profiles of the crossed-carbon-chains system when the distances between the two carbon chains are 7.5 and 5.0 Bohr. In both the cases, we apply same bias 0.5 V through the leads , and and bias −0.5 V through the fourth lead . The plotting passing through one of the chains. (b) and (d) Potential drops between the leads to for (a) and (c) case.

Image of FIG. 12.
FIG. 12.

Comparison of transmission curves in all three cases, where the distances between the chains are 7.5, 5.0 and 2.5 Bohr, of the crossed-carbon-chain system with zero and nonzero biases (as in Fig. 11). The left and right panels show transmission through leads and , respectively.

Image of FIG. 13.
FIG. 13.

Comparison of curves with varying distances between the chains of the crossed-carbon-chain system. The left and right panels show the current contributions through leads and , respectively, with the bias voltage.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: First-principles methodology for quantum transport in multiterminal junctions