Ab initio framework for systems with helical symmetry: theory, numerical implementation and applications to torsional deformations in nanostructures

TL;DR

This paper introduces Helical DFT, a first-principles simulation method for nanostructures with helical symmetry, enabling detailed analysis of their electronic properties and mechanical responses, including torsional deformations.

Contribution

The paper develops a rigorous ab initio framework for helical nanostructures, including mathematical formulation, numerical implementation, and application to nanotubes, which was not previously available.

Findings

Accurate modeling of helical nanostructures using Helical DFT.

Observation of an insulator-to-metal transition under twisting.

Evaluation of torsional stiffness in zigzag nanotubes.

Abstract

We formulate and implement Helical DFT -- a self-consistent first principles simulation method for nanostructures with helical symmetries. Such materials are well represented in all of nanotechnology, chemistry and biology, and are expected to be associated with unprecedented material properties. We rigorously demonstrate the existence and completeness of special solutions to the single electron problem for helical nanostructures, called helical Bloch waves. We describe how the Kohn-Sham Density Functional Theory equations for a helical nanostructure can be reduced to a fundamental domain with the aid of these solutions. A key component in our mathematical treatment is the definition and use of a helical Bloch-Floquet transform to perform a block-diagonalization of the Hamiltonian in the sense of direct integrals. We develop a symmetry-adapted finite-difference strategy in helical coordinates to discretize the governing equations, and obtain a working realization of the proposed approach. We verify the accuracy and convergence properties of our numerical implementation through examples. Finally, we employ Helical DFT to study the properties of zigzag and chiral single wall black phosphorus (i.e., phosphorene) nanotubes. We use our simulations to evaluate the torsional stiffness of a zigzag nanotube ab initio. Additionally, we observe an insulator-to-metal-like transition in the electronic properties of this nanotube as it is subjected to twisting. We also find that a similar transition can be effected in chiral phosphorene nanotubes by means of axial strains. Notably, self-consistent ab initio simulations of this nature are unprecedented and well outside the scope of any other systematic first principles method in existence. We end with a discussion on various future avenues and applications.