Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes

TL;DR

This paper calculates the vacuum fermionic current in spacetimes with compactified dimensions, revealing effects like the Aharonov-Bohm phenomenon and applying results to nanotube models, highlighting topological influences on quantum currents.

Contribution

It provides new analytical formulas for fermionic currents in toroidally compactified spacetimes with gauge fields, applicable to nanotube physics and higher-dimensional models.

Findings

Fermionic current exhibits Aharonov-Bohm oscillations with magnetic flux.

In nanotubes, total fermionic current cancels out without magnetic flux.

Derived formulas are applicable to Kaluza-Klein and nanotube models.

Abstract

The vacuum expectation value of the fermionic current is evaluated for a massive spinor field in spacetimes with an arbitrary number of toroidally compactified spatial dimensions in presence of a constant gauge field. By using the Abel-Plana type summation formula and the zeta function technique we present the fermionic current in two different forms. Non-trivial topology of the background spacetime leads to the Aharonov-Bohm effect on the fermionic current induced by the gauge field. The current is a periodic function of the magnetic flux with the period equal to the flux quantum. In the absence of the gauge field it vanishes for special cases of untwisted and twisted fields. Applications of the general formulae to Kaluz-Klein type models and to cylindrical and toroidal carbon nanotubes are given. In the absence of magnetic flux the total fermionic current in carbon nanotubes vanishes, due to the cancellation of contributions from two different sublattices of the graphene hexagonal lattice.