Excitons in narrow-gap carbon nanotubes

Abstract

We calculate the exciton binding energy in single-walled carbon nanotubes with narrow band gaps, accounting for the quasi-relativistic dispersion of electrons and holes. Exact analytical solutions of the quantum relativistic two-body problem are obtain for several limiting cases. We show that the binding energy scales with the band gap, and conclude on the basis of the data available for semiconductor nanotubes that there is no transition to an excitonic insulator in quasi-metallic nanotubes and that their THz applications are feasible.

11 pages, 3 figures. Several references and an additional appendix added

References in corpus (6)

• The electronic properties of graphene
• Electronic States of Graphene Nanoribbons
• Luminescence Decay and the Absorption Cross-Section of Individual Single-Walled Carbon Nanotubes
• Atomic collapse, Lorentz boosts, Klein scattering, and other quantum-relativistic phenomena in graphene
• Exciton storage in a nano-scale Aharonov-Bohm ring with electric field tuning
• Exciton Hierarchies in Gapped Carbon Nanotubes

Cited by in corpus (33)

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• Fundamental Optical Processes in Armchair Carbon Nanotubes
• One-dimensional Coulomb problem in Dirac materials
• Collective Antenna Effects in the Terahertz and Infrared Response of Highly Aligned Carbon Nanotube Arrays
• Bielectron vortices in two-dimensional Dirac semimetals
• Searching for confined modes in graphene channels: the variable phase method
• Optical selection rules of zigzag graphene nanoribbons
• Electric dipole moment oscillations in Aharonov-Bohm quantum rings
• Strong Light-Matter Coupling in Carbon Nanotubes as a Route to Exciton Brightening
• Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons
• Localization of massless Dirac particles via spatial modulations of the Fermi velocity
• On zero energy states in graphene
• Generalized Dirac Oscillators with position-dependent mass
• Two-body problem for two-dimensional electrons in Bernervig-Hughes-Zhang model
• Exciton oscillator strength in two-dimensional Dirac materials
• Pair states in one-dimensional Dirac systems
• Bipolar electron waveguides in graphene
• Zero-energy vortices in Dirac materials
• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• mKdV equation approach to zero energy states of graphene
• One-dimensional Van Hove polaritons
• Anomalous magnetization of a carbon nanotube as an excitonic insulator
• Trapping charge carriers in low-dimensional Dirac materials
• A new type of optical biosensor from DNA wrapped semiconductor graphene ribbons
• Coherent exciton transport in semiconductors
• Momentum alignment and the optical valley Hall effect in low-dimensional Dirac materials
• Dirac equation with complex potentials
• Particle-hole pair states of layered materials
• Radiative decay of bound electron pairs into unbound interacting electrons in 2D materials with two-band spectrum
• Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime