One-dimensional semirelativity for electrons in carbon nanotubes

TL;DR

This paper demonstrates that the electronic behavior in single-wall semiconducting carbon nanotubes can be described using a one-dimensional semirelativistic model, revealing phenomena like Zitterbewegung that are more observable than in free electrons.

Contribution

It introduces a semirelativistic framework for electrons in CNTs, showing their band structure parallels relativistic electrons and predicting observable Zitterbewegung effects.

Findings

Electrons in CNT exhibit relativistic-like band structure.

Zitterbewegung is predicted to be observable in CNTs.

The model replaces light speed with a maximum velocity of 10^8 cm/s.

Abstract

It is shown that the band structure of single-wall semiconducting carbon nanotubes (CNT) is analogous to relativistic description of electrons in vacuum, with the maximum velocity $u$= $10^8$cm/s replacing the light velocity. One-dimensional semirelativistic kinematics and dynamics of electrons in CNT is formulated. Two-band k.p Hamiltonian is employed to demonstrate that electrons in CNT experience a Zitterbewegung (trembling motion) in absence of external fields. This Zitterbewegung should be observable much more easily in CNT than its analogue for free relativistic electrons in vacuum.