Supersymmetric twisting of carbon nanotubes

TL;DR

This paper develops exactly solvable models of twisted carbon nanotubes using supersymmetry and matrix Darboux transformations, revealing how twist affects local density of states and bound states.

Contribution

It introduces a supersymmetric approach to modeling twisted carbon nanotubes, providing explicit solutions and analyzing the effects of twisting on electronic properties.

Findings

Back-scattering is suppressed in the models.

Bound states are localized with decreased local density of states.

Bound-state energies depend on the asymptotic twist.

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.