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

TL;DR

This paper explores the spectral properties of twisted carbon nanotubes modeled by a Dirac equation, revealing a hidden supersymmetry linked to finite-gap Hamiltonians and integrable systems.

Contribution

It introduces a novel connection between finite-gap Hamiltonians of twisted nanotubes and a hidden supersymmetry arising from integrable hierarchy structures.

Findings

Finite-gap Hamiltonians characterize twisted nanotubes with specific spectral features.

A nonlinear hidden supersymmetry naturally emerges in these systems.

The structure encodes properties of van Hove singularities.

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.