Electron Transport through Models for Small-World Nanomaterials

We investigate the quantum transport of (spinless) electrons through simplified models related to small-world nanomaterials. We employ a tight-binding Hamiltonian, and obtain the transmission coefficient from a matrix solution of the associated time-independent Schr\"{o}dinger Equation. The system studied corresponds to $d=1$ semi-infinite input and output leads, connected to a `blob' of $N$ atoms. We first present exact results for $N$ inter-connected atoms, a fully-connected graph. The exact solution, for any $N$, is given both for symmetric and non-symmetric connections between the `blob' and the input/output. We then present numerical results obtained by removing some of the connections within the $N$-site `blob', thereby approaching transport through a small-world nanomaterial [1-4]. \newline [1] S. \c{C}ali\c{s}kan, M.A. Novotny, and J.I. Cerd\'{a}, J. Appl. Phys., \textbf{102}, 013707 (2007). \newline [2] M.A. Novotny \textit{et al.}, J. Appl. Phys., \textbf{97}, 10B309 (2005). \newline [3] M.A. Novotny and S.M. Wheeler, Braz. J. Physics \textbf{34}, 395 (2004). \newline [4] J. Yancey, M.A. Novotny, and S.R. Gwaltney, 2008 March Meeting presentation.