Topological Casimir effect in nanotubes and nanoloopes

TL;DR

This paper studies the topological Casimir effect in carbon nanotubes and nanoloopes, revealing how their electronic properties influence the Casimir energy and forces, with implications for nanoscale physics and device design.

Contribution

It introduces a Dirac-like model analysis of the topological Casimir effect in nanotubes, highlighting the dependence on metallic or semiconducting properties and boundary conditions.

Findings

Casimir energy is positive for metallic nanotubes and negative for semiconducting ones.

Toroidal compactification affects Casimir energy differently based on boundary conditions.

Casimir forces are attractive for finite metallic nanotubes and vary with length for semiconducting nanotubes.

Abstract

The Casimir effect is investigated in cylindrical and toroidal carbon nanotubes within the framework of the Dirac-like model for the electronic states. The topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. The toroidal compactification of a cylindrical nanotube along its axis increases the Casimir energy for metallic-type (periodic) boundary conditions along its axis and decreases the Casimir energy for the semiconducting-type compactifications. For finite length metallic nanotubes the Casimir forces acting on the tube edges are always attractive, whereas for semiconducting-type ones they are attractive for small lengths of the nanotube and repulsive for large lengths.