Real-space density functional theory adapted to cyclic and helical symmetry: Application to torsional deformation of carbon nanotubes

Abstract

We present a cyclic and helical symmetry-adapted formulation and large-scale parallel implementation of real-space Kohn-Sham density functional theory for one-dimensional (1D) nanostructures, with application to the mechanical and electronic response of carbon nanotubes subject to torsional deformations. Specifically, employing a semilocal exchange correlation and a local formulation of the electrostatics, we derive symmetry-adapted variants for the energy functional, variational problem governing the electronic ground state, Kohn-Sham equations, atomic forces, and axial stress, all posed on the fundamental domain. In addition, we develop a representation for twisted nanotubes of arbitrary chirality within this framework. We also develop a high-order finite-difference parallel implementation capable of performing accurate cyclic and helical symmetry-adapted Kohn-Sham calculations in both the static and dynamic settings, and verify it through numerical tests and comparisons with established codes. We use this implementation to perform twist-controlled simulations for a representative set of achiral and chiral carbon nanotubes, in both the small and large deformation regimes. In the linear regime, we find that the torsional moduli are proportional to the cube of the diameter; metallic nanotubes undergo metal-insulator transitions; and both the band gap as well as effective mass of charge carriers are proportional to the shear strain and sine of three times the chiral angle. In the nonlinear regime, we find that there is significant Poynting effect, particularly at the ultimate strain, the value of which is determined by the chiral angle; torsional deformations provide a possible mechanism for the irreversible phase transformation from armchair to zigzag nanotubes; and both the band gap as well as effective mass have an oscillatory behavior, with the period for metal-insulator transitions being inversely proportional to the square of the diameter and sine of three times the chiral angle. Wherever available, the results are in good agreement with experimental observations and measurements. Overall, this opens an avenue for the highly accurate and efficient first-principles study of 1D nanostructures that have cyclic and/or helical symmetry, as well as their response to torsional deformations.

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.035101