Role of electron-electron interactions in electron emission from nanotube materials

Nanotubes and nanorods have been recently established as very good materials to work as electron sources in a field emission (FE) process. These are one-dimensional materials and electron-electron interactions are expected to play a crucial role in their physics. Here we study the influence of electron-electron interactions on the field emission. We study the problem in the low energy regime; thus we need to abandon the antiadiabatic approximation and derive tunneling amplitude for a finite duration of the tunneling process. In this work we identified the parameters when exact analytic expression for tunneling current can be given. We obtained formalism that enables one to capture the collective effects due to electron-electron interactions and thermionic emission. Our results reveal that different types of nanotubes, and their minigap/compressibility parameters, can be easily distinguished based on FE measurements on these materials.