Supersymmetric twisting of carbon nanotubes

Abstract

We construct exactly solvable models of twisted carbon nanotubes via supersymmetry, by applying the matrix Darboux transformation. We derive the Green's function for these systems and compute the local density of states. Explicit examples of twisted carbon nanotubes are produced, where the back-scattering is suppressed and bound states are present. We find that the local density of states decreases in the regions where the bound states are localized. Dependence of bound-state energies on the asymptotic twist of the nanotubes is determined. We also show that each of the constructed unextended first order matrix systems possesses a proper nonlinear hidden supersymmetric structure with a nontrivial grading operator.

10 pages, 5 figures; analysis extended, fig.5 added. Typos corrected, references added

References in corpus (12)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Magnetic confinement of massless Dirac fermions in graphene
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• A Twisted Kink Crystal in the Chiral Gross-Neveu model
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Hidden supersymmetry in quantum bosonic systems
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Klein tunneling in carbon nanostructures: a free particle dynamics in disguise
• Magnetic field barriers in graphene: an analytically solvable model
• Exact propagators for SUSY partners
• Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians

Cited by in corpus (21)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Spectral singularities in PT-symmetric periodic finite-gap systems
• Dirac electron in graphene under supersymmetry generated magnetic fields
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Trends in supersymmetric quantum mechanics
• Spectrally isomorphic Dirac systems: graphene in electromagnetic field
• Qualitative analysis of trapped Dirac fermions in graphene
• Twisted kinks, Dirac transparent systems and Darboux transformations
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Extended supersymmetry of the self-isospectral crystalline and soliton chains
• Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators
• Supersymmetric Dirac-Hamiltonians in $(1+1)$ dimensions revisited
• Carbon nanotubes in almost homogeneous transverse magnetic field: exactly solvable model
• Tunneling dynamics in exactly-solvable models with triple-well potentials
• Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry
• Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations
• Nonlinear supersymmetry as a hidden symmetry
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• SUSY design of smooth quantum rings in graphene