Analytic solution of charge density of single wall carbon nanotube in conditions of field electron emission

TL;DR

This paper presents an analytic solution for the electrostatic potential and charge density of single wall carbon nanotubes under field electron emission conditions, assuming constant density of states.

Contribution

It provides a novel analytic approach to determine charge density in carbon nanotubes under external electric fields, enhancing understanding of their emission properties.

Findings

Derived explicit formulas for electrostatic potential and charge density.

Showed the linear relationship between excess charge and external field.

Assumed constant density of states for simplification.

Abstract

We derived the analytic solution of induced electrostatic potential along single wall carbon nanotubes. Under the hypothesis of constant density of states in the charge-neutral level, we are able to obtain the linear density of excess charge in an external field parallel to the tube axis.