A Simple Model of Ballistic Conduction in Multi-Lead Molecular Devices

A fully analytical model is presented for ballistic conduction in a multi-lead device that is based on a π-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.

A Study of Graphene Applications

Carbon is unique in its own ways, the most special attribute of carbon is that it can make rings and long chain; even life on the earth is possible due to this property of carbon. Graphene is the first two dimensional material and it has many outstanding properties which have resulted in many exciting applications. Graphene is claimed to be so versatile that it will be able to replace present day materials. It is thought to be the perfect two-dimensional carbon crystal as it is the unique blend of properties both mechanical and electronics. Graphene is the thinnest, highly elastic, am bipolar, chemically inert, and hydrophobic, possesses record electron conductivity, high value of mobility, high thermal conductivity, high opacity, low resistivity and shows fractional quantum Hall effect and ballistic conduction and many other interesting properties that are yet be explored. Recently it has been found that the magnetic field of grapheme can be switched on and off. In this paper, I have done a comparative study of properties of grapheme and tried to produce an application of grapheme in two fields which affect us most, that are, Medicine and Electronics.