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We consider radially twisted nanotubes in the low-energy approximation wherethe dynamics is governed by a one-dimensional Dirac equation. The mechanicaldeformation of the nanotubes is reflected by the presence of an effectivevector potential. We discuss twisted carbon and boron-nitride nanotubes, wheredeformations give rise to periodic and nonperiodic finite-gap Hamiltonians. Theintimate relation of these systems with the integrableAblowitz-Kaup-Newell-Segur hierarchy is exploited in the study of theirspectral properties as well as in the computation of the (local) density ofstates. We show that a nonlinear hidden supersymmetry generated by localsupercharges arises naturally in the finite-gap configurations of twistednanotubes with time-reversal symmetry. The properties of the van Hovesingularities are encoded in its structure.

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