Nanohelicenes [1] or graphene spirals are examples of helically periodic nanostructures, which can be considered as a generalization of the idea of polymeric [∞]helicene. It is known that variations in the shape (hexagonal or trigonal), edge termination (zig-zag or arm-chair), ribbon width or inner shaft lead to the manifestation of metallic or semiconductor properties in nanohelicenes, as well as ferromagnetic or antiferromagnetic ordering. The unique spring topology of such structures makes it possible to manipulate the electronic and magnetic properties by reversible mechanical strains.

So far the properties of nanohelicenes under axial deformations have been studied, ignoring the importance of torsion strains. The study of the latter requires the use of the line symmetry groups [2] which can be written in two factorizations: the crystallographic one L = TF (T is translation subgroup of L) and L = ZP (Z includes screw axis rotations while P is point group). Moreover, using of line groups makes it possible to describe the symmetry of one-periodic structures having no translational periodicity but with helical one.

A general algorithm for ab initio modeling of helically periodic nanostructures was recently successively applied by us to nanohelicenes. Calculations were performed using CRYSTAL17 [3] computer code based on the atomic basis sets and using built-in possibility to take into account the helical symmetry operations of one-periodic systems. By this way it was shown in [4] that the true nanohelicenes symmetry groups differ from the traditionally accepted L6_{1} or L3_{1} rod groups. The superposition of torsional and axial deformations was used to obtain the two-parameter maps of the electronic and magnetic properties of nanohelicenes. It was also shown that torsion, as well as axial, deformations are reversible in a large region, which is a consequence of the spring topology. The electronic band gap depends to a large extent on the magnitude of the strains. In particular, the torsion regulates the type of metal-insulator transition (Mott-Hubbard or Peierls) which occur in metallic nanohelicenes [5].

[1] V.V.Porsev, A.V.Bandura, S.I.Lukyanov, R.A.Evarestov, Carbon 152 (2019) 755.

[2] M.Damnjanovic, I.Milosevic, “Line Groups in Physics. Theory and Applications to Nanotubes and Polymers” Lect. Notes in Phys., 801. Berlin: Springer, 2010.

[3] R.Dovesi, A.Erba, R.Orlando, C.M.Zicovich-Wilson, B.Civalleri, L.Maschio, M.Rerat, S.Casassa, J.Baima, S.Salustro, B.Kirtman, WIREs Comput.Mol.Sci. 8 (2018) e1360.

[4] V.V.Porsev, R.A.Evarestov, Comp.Mat.Sci. 203 (2022) 111063.

[5] V.V.Porsev, R.A.Evarestov, Comp.Mat.Sci. 213 (2022) 111642.

This research has been supported by the Russian Science Foundation (grant 22-23-00247).

The authors appreciate the assistance of Saint Petersburg State University Computer Center in high-performance computing.