Energy Anomaly and Polarizability of Carbon Nanotubes

TL;DR

This paper investigates the energy anomaly in Dirac fermions on a circle and relates it to the polarizability of carbon nanotubes, revealing universal and scale-invariant electronic responses influenced by external fields.

Contribution

It establishes a theoretical connection between energy anomaly and polarizability in carbon nanotubes, highlighting universality and predicting strong-field electron band transformations.

Findings

Energy anomaly is a universal function of applied field.

Polarizability of nanotubes is expressed via the anomaly, showing universality.

Electron band transformation occurs under strong fields.

Abstract

The energy of electron Fermi sea perturbed by external potential, represented as energy anomaly which accounts for the contribution of the deep-lying states, is analyzed for massive d = 1+1 Dirac fermions on a circle. The anomaly is a universal function of the applied field, and is related to known field-theoretic anomalies. We express transverse polarizability of Carbon nanotubes via the anomaly, in a way which exhibits the universality and scale-invariance of the response dominated by pi-electrons and qualitatively different from that of dielectric and conducting shells. Electron band transformation in a strong-field effect regime is predicted.