Journal
APPLIED SCIENCES-BASEL
Volume 11, Issue 24, Pages -Publisher
MDPI
DOI: 10.3390/app112411696
Keywords
all-carbon devices; source-and-sink potential; ballistic conduction; molecular graph; characteristic polynomial; vertex-deleted subgraphs; hyperdeterminants
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A fully analytical model for ballistic conduction in a multi-lead device is presented, based on a pi-conjugated carbon framework and specifying transmission in terms of combinations of structural polynomials. The model allows insight into many-lead devices through constituent two-lead devices, structural polynomials, molecular orbital channels, and selection rules for active and inert leads and orbitals. In the wide-band limit, transmission is expressed in terms of characteristic polynomials of vertex-deleted graphs, and complete symmetric devices (CSD) and complete bipartite symmetric devices (CBSD) are defined and solved analytically as limiting cases of maximum connection.
A fully analytical model is presented for ballistic conduction in a multi-lead device that is based on a pi-conjugated carbon framework attached to a single source lead and several sink leads. This source-and-multiple-sink potential (SMSP) model is rooted in the Ernzerhof source-and-sink potential (SSP) approach and specifies transmission in terms of combinations of structural polynomials based on the molecular graph. The simplicity of the model allows insight into many-lead devices in terms of constituent two-lead devices, description of conduction in the multi-lead device in terms of structural polynomials, molecular orbital channels, and selection rules for active and inert leads and orbitals. In the wide-band limit, transmission can be expressed entirely in terms of characteristic polynomials of vertex-deleted graphs. As limiting cases of maximum connection, complete symmetric devices (CSD) and complete bipartite symmetric devices (CBSD) are defined and solved analytically. These devices have vanishing lead-lead interference effects. Illustrative calculations of transmission curves for model small-molecule systems are presented and selection rules are identified.
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