A first principles informed machine learning model for helical nanostructures

Helical nanostructures constitute an important class of low-dimensional matter and include nanotubes of arbitrary chirality, nanowires, nanoribbons, nanoassemblies and other miscellaneous chiral structures. The fascinating electronic, optical and magnetic properties of these materials offer unparalleled opportunities for impacting the design of novel quantum, photonic and electromagnetic devices. We present a first-principles informed machine learning model that can predict the electronic structure of such materials in their natural or distorted states, while they are being subjected to deformation modes such as torsion and extension/compression. The model includes structural symmetries, atomic relaxation effects and uses a symmetry-adapted version of Kohn-Sham Density Functional Theory in helical coordinates to generate the input data. We use armchair single wall carbon nanotubes as a prototypical example, and demonstrate the use of the model to predict various electronic fields when the radius of the nanotube, its axial stretch, and the twist per unit length are specified as inputs. Our model is likely to find applications in areas where the interplay of strain and electronic properties at the nanoscale (i.e., strain engineering) plays an important role.