Non Equilibrium Green's Function Approach for Modeling Carbon Nanotube Devices

We introduce a comprehensive theoretical framework to explore a non-equilibrium nanoelectromechanical system (NEMS) based on a fully suspended carbon nanotube (CNT) device. This complex system presents several significant modeling challenges, most notably: (1) the lifetime broadening of the electronic energy level; (2) Coulomb interactions; (3) the mechanical motion of the CNT and its influence on electronic states; and (4) operation away from equilibrium.

Our approach innovatively addresses these challenges through the use of non-equilibrium Green's function (NEGF) formalism coupled with perturbation theory. Specifically, the lifetime broadening is encapsulated within the retarded Green's function by integrating energy-dependent self-energies, that account for strong coupling with source and drain Fermi reservoirs. Coulomb interactions are systematically included via additional self-energy terms thereby capturing electron-electron interactions. The mechanical motion of the CNT is modeled, introducing an explicit displacement-dependent term that enables us to derive equations for effective resonance frequencies.

The framework is mathematically rigorous and allows for the derivation of the spectral function for the density of available electronic states and current flowing through the device.

By meticulously incorporating lifetime broadening, Coulomb interactions, mechanical displacements, and out of equilibrium effects, our theoretical construct provides a robust and comprehensive approach to analyze the transport phenomena in NEMS, laying the groundwork for future experimental validations and technological applications.