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

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.

18 pages, 5 figures, explicit regularization procedure added

References in corpus (13)

• The electronic properties of graphene
• Substrate-induced band gap opening in epitaxial graphene
• Electron fractionalization in two-dimensional graphenelike structures
• Persistent currents in normal metal rings
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect
• Supersymmetry in carbon nanotubes in a transverse magnetic field
• Casimir effect in de Sitter spacetime with compactified dimension
• Fermionic Casimir effect in toroidally compactified de Sitter spacetime
• Quantum Hall effect in carbon nanotubes and curved graphene strips
• Wightman function and vacuum densities in de Sitter spacetime with toroidally compactified dimensions
• Fermionic vacuum polarization by a composite topological defect in higher-dimensional space-time
• Fermionic vacuum densities in higher-dimensional de Sitter spacetime

Cited by in corpus (3)

• Fermionic current densities induced by magnetic flux in a conical space with a circular boundary
• Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
• Fermionic condensate in a conical space with a circular boundary and magnetic flux