Symmetry-adapted real-space density functional theory for large nanotubes and bending deformations of thin sheets

Dear Colleagues,

Here is our recently published article on Symmetry-adapted real-space density functional theory for large nanotubes and bending deformations of thin sheets

Title: Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-IV nanotubes

 Authors: Swarnava Ghosh, Amartya S. Banerjee, Phanish Suryanarayana*

Concise summary

This work presents a symmetry-adapted real-space formulation of Kohn-Sham density functional theory (DFT). The formulation and implementation is used to simulate the band structure and bending properties of group IV nanotubes and sheets. Scaling laws of bandgap with respect to the radius of the nanotube, and bending moduli of sheets is reported. We also demonstrate the efficiency of the proposed approach and shows that even micron-sized nanotubes can be simulated with modest computational effort. Overall, this work provides an efficient framework for ab-initio simulations of 1D nanostructures with large radii as well as 1D/2D nanostructures under uniform bending, which are currently intractable using standard DFT methods, and opens an avenue for the ab initio study of the flexoelectric effect.

 Link to the paper:  https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.125143

Abstract

We present a symmetry-adapted real-space formulation of Kohn-Sham density functional theory for cylindrical geometries and apply it to the study of large X (X=C, Si, Ge, Sn) nanotubes. Specifically, starting from the Kohn-Sham equations posed on all of space, we reduce the problem to the fundamental domain by incorporating cyclic and periodic symmetries present in the angular and axial directions of the cylinder, respectively. We develop a high-order finite-difference parallel implementation of this formulation, and verify its accuracy against established planewave and realspace codes. Using this implementation, we study the band structure and bending properties of X nanotubes and Xene sheets, respectively. Specifically, we first show that zigzag and armchair X nanotubes with radii in the range 1 to 5 nm are semiconducting, other than the armchair and zigzag type III carbon variants, for which we find a vanishingly small bandgap, indicative of metallic behavior. In particular, we find an inverse linear dependence of the bandgap with respect to the radius for all nanotubes, other than the armchair and zigzag type III carbon variants, for which we find an inverse quadratic dependence. Next, we exploit the connection between cyclic symmetry and uniform bending deformations to calculate the bending moduli of Xene sheets in both zigzag and armchair directions, while considering radii of curvature up to 5 nm. We find Kirchhoff-Love type bending behavior for all sheets, with graphene and stanene possessing the largest and smallest moduli, respectively. In addition, other than graphene, the sheets demonstrate significant anisotropy, with larger bending moduli along the armchair direction. Finally, we demonstrate that the proposed approach has very good parallel scaling and is highly efficient, enabling ab initio simulations of unprecedented size for systems with a high degree of cyclic symmetry. In particular, we show that even micron-sized nanotubes can be simulated with modest computational effort. Overall, the current work opens an avenue for the efficient ab-initio study of 1D nanostructures with large radii as well as 1D/2D nanostructures under uniform bending.