Tight-binding implementation of the microcanonical approach to transport in nanoscale conductors: Generalization and analysis

Abstract

Bushong, Sai, and Di Ventra (BSD) recently demonstrated that steady-state transport can emerge solely from quantum dynamics in a globally closed system consisting of a nanoscale conductor bridging two electrodes by Bushong et al. [Nano Lett. 5, 2569 (2005)]. They reported calculations, based on a simple tight-binding implementation of the “microcanonical” approach (TBIMCA) by Di Ventra and Todorov [J. Phys.: Condens. Matter 16, 8025 (2004)], in which a steady-state conductor current consistent in magnitude with the quantum conductance G0=2e2/h is established after an initial bias-induced imbalance in electrode populations begins to equalize. In this work, BSD’s TBIMCA is generalized, and their expressions for the time-dependent current and local occupation functions are shown to apply only to a restricted class of structures. Calculations of the current dynamics and local occupation functions, based on the generalized formalism, are then presented for a wide variety of electrode-conductor-electrode geometries. These calculations provide a more comprehensive characterization of the TBIMCA, enable identification of the conditions under which signature features of nanoscale transport emerge, and show that the emergence of these features hinges critically on details of the structure geometry. This structure dependence represents an important consideration for application of the TBIMCA to the modeling of transport through nanostructures and should be recognized in any attempt to identify and explain signature features of nanoscale transport within this approach.