Hall conductance from Berry curvature in carbon nanotubes

TL;DR

This paper demonstrates that applying perpendicular electric and magnetic fields to carbon nanotubes induces a topologically non-trivial gapped state that supports a quantized Hall effect, with observable electron transport phenomena.

Contribution

It analytically shows how external fields induce a topological gap and Hall conductance in carbon nanotubes, revealing a new quantum Hall effect in quasi-one-dimensional systems.

Findings

A gap of a few meV can be induced by realistic fields.

The gapped state has a non-zero topological invariant.

Variation of flux results in quantized electron transport.

Abstract

We analytically show that a gap is induced around the Dirac point in the electronic spectrum of a previously metallic nanotube, in the presence of electric and magnetic fields perpendicular to the tube axis. For realistic values of the fields, a gap of at least a few meV can appear. Despite the quasi-one dimensional nature of the system, the gapped state is associated with a non-zero topological invariant and supports a Hall effect. This is revealed when the flux through the tube is varied by one flux quantum, which leads to exactly one electron per spin being transported between the ends of the tube.