Pair states in one-dimensional Dirac systems
arXiv:1706.04886 · doi:10.1103/PhysRevA.95.062110
Abstract
Analytic solutions of the quantum relativistic two-body problem are obtained for an interaction potential modeled as a one-dimensional smooth square well. Both stationary and moving pairs are considered and the limit of the δ-function interaction is studied in depth. Our result can be utilized for understanding excitonic states in narrow-gap carbon nanotubes. We also show the existence of bound states within the gap for a pair of particles of the same charge.
14 pages and 6 figures
References in corpus (31)
- The electronic properties of graphene
- Chiral tunneling and the Klein paradox in graphene
- Size, Shape and Low Energy Electronic Structure of Carbon Nanotubes
- Dirac materials
- Kondo physics in carbon nanotubes
- Exciton binding energies in carbon nanotubes from two-photon photoluminescence
- Quasi-exactly solvable quartic potential
- Terahertz Science and Technology of Carbon Nanomaterials
- Quasi-bound states of quantum dots in single and bilayer graphene
- The Fock-Darwin States of Dirac Electrons in Graphene-based Artificial Atoms
- Band gaps of primary metallic carbon nanotubes
- Smooth electron waveguides in graphene
- Excitations from Filled Landau Levels in Graphene
- On a solution of the Schrodinger equation with a hyperbolic double-well potential
- The 192 Solutions of the Heun Equation
- Quasi-exact solution to the Dirac equation for the hyperbolic secant potential
- Two-body problem in graphene
- Excitons in narrow-gap carbon nanotubes
- One-dimensional Coulomb problem in Dirac materials
- Electron-electron interactions in bilayer graphene quantum dots
- Coupling of two Dirac particles
- Bound states in a hyperbolic asymmetric double-well
- Excitonic Effects in Two-Dimensional Massless Dirac Fermions
- Collective properties of magnetobiexcitons in quantum wells' and graphene superlattices
- Size Quantization in Planar Graphene-Based Heterostructures: Pseudospin Splitting, Interface States, and Excitons
- Metastable electron-electron states in double-layer graphene structures
- Moving zero-gap Wannier-Mott excitons in graphene
- Two-body problem for two-dimensional electrons in Bernervig-Hughes-Zhang model
- New quantum-mechanical phenomenon in a model of electron-electron interaction in graphene
- Two-electron bound states near a Coulomb impurity in gapped graphene
- Exciton absorption in narrow armchair graphene nanoribbons
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- Two-dimensional Dirac particles in a Pöschl-Teller waveguide
- Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons
- Zero-energy vortices in Dirac materials
- Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
- Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones
- Trapping charge carriers in low-dimensional Dirac materials
- Momentum alignment and the optical valley Hall effect in low-dimensional Dirac materials