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

TL;DR

This paper presents an exactly solvable model for carbon nanotubes under inhomogeneous magnetic fields, revealing supersymmetry and stable energy levels, advancing theoretical understanding of nanotube quantum behavior.

Contribution

It introduces a new exactly solvable continuum model for carbon nanotubes in inhomogeneous magnetic fields, highlighting supersymmetry and stability properties.

Findings

Models exhibit N=2 nonlinear supersymmetry.

Energy levels are stable against small momentum fluctuations.

Explicit solutions demonstrate the model's solvability.

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