Carbon nanotubes in almost homogeneous transverse magnetic field: exactly solvable model

Abstract

A class of exactly solvable models describing carbon nanotubes in the presence of an external inhomogeneous magnetic field is considered. The framework of the continuum approximation is employed, where the motion of the charge carriers is governed by the Dirac- Weyl equation. The explicit solution of a particular example is provided. It is shown that these models possess nontrivial integrals of motion that establish N = 2 nonlinear supersymmetry in case of metallic and maximally semiconducting nanotubes. Remarkable stability of energy levels with respect to small fluctuations of longitudinal momentum is demonstrated

17 pages, 6 figures, misprints corrected, references added

References in corpus (8)

• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Hidden supersymmetry in quantum bosonic systems
• Supersymmetry in carbon nanotubes in a transverse magnetic field
• Hidden nonlinear supersymmetry of finite-gap Lame equation
• Supersymmetric twisting of carbon nanotubes
• Exactly solvable associated Lame potentials and supersymmetric transformations
• New supersymmetric partners for the associated Lame potentials
• Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry

Cited by in corpus (8)

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• Pseudo-Hermitian Dirac operator on the torus for massless fermions under the action of external fields
• The solutions of Dirac equation on the hyperboloid under perpendicular magnetic fields
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field