UCLA

We formulate and implement Helical Density Functional Theory (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 prominent examples include nanotubes, nanosprings, nanowires, miscellaneous chiral structures and important proteins. The overwhelming preponderance of such helical structures in all of science and engineering and the likelihood of these systems being associated with exotic materials properties, provides the motivation to develop systematic and predictive tools for their study. Following this line of thought, we develop a mathematical and computational framework in this contribution, that allows helical structures to be studied ab initio, using Kohn–Sham theory. We first show that the electronic states in helical structures can be characterized by means of special solutions to the single electron problem called helical Bloch waves. We rigorously demonstrate the existence and completeness of such solutions, and then describe how they can be used to reduce the Kohn–Sham Density Functional Theory (KS-DFT) equations for helical structures to a suitable fundamental domain. Next, we develop a symmetry-adapted finite-difference strategy in helical coordinates to discretize the governing equations, and obtain a working realization of our 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. Specifically, 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. The strong dependence of the band gap of these materials on various modes of strain suggests their possible use as nanomaterials with tunable electronic and transport properties. 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.