Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry

Abstract

We consider radially twisted nanotubes in the low-energy approximation where the dynamics is governed by a one-dimensional Dirac equation. The mechanical deformation of the nanotubes is reflected by the presence of an effective vector potential. We discuss twisted carbon and boron-nitride nanotubes, where deformations give rise to periodic and nonperiodic finite-gap Hamiltonians. The intimate relation of these systems with the integrable Ablowitz-Kaup-Newell-Segur hierarchy is exploited in the study of their spectral properties as well as in the computation of the (local) density of states. We show that a nonlinear hidden supersymmetry generated by local supercharges arises naturally in the finite-gap configurations of twisted nanotubes with time-reversal symmetry. The properties of the van Hove singularities are encoded in its structure.

Discussion extended, references added. Published version

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Cited by in corpus (5)

• Dirac electron in graphene under supersymmetry generated magnetic fields
• 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
• Carbon nanotubes in almost homogeneous transverse magnetic field: exactly solvable model