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

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.

Torsional moduli of transition metal dichalcogenide nanotubes from first principles

“…We utilize the Cyclix-DFT code 44 -adaptation of the state-of-the-art real-space DFT code SPARC [57][58][59] to cylindrical and helical coordinate systems, with the ability to exploit cyclic and helical symmetry in one-dimensional nanostructures 44,60,61 -to calculate the torsional moduli of the aforementioned TMD nanotubes in the low twist limit. Specifically, we consider three-atom unit cell/fundamental domains that has one metal atom and two chalcogen atoms, as illustrated in Fig.…”

Self-Consistent Schrödinger-Poisson Study of Electronic Properties of GaAs Quantum Well Wires with Various Cross-Sectional Shapes

“…It is worth mentioning here that this is the typical SC scheme of working within a single-band or multiband environment in semiconductor physics. However, there are very recent reports on the adaptation of density functional theory which is, intrinsically, self-consistent to deal with nanowire-type systems or with nanotubes; thus opening a way to a powerful, although more computationally demanding, microscopic calculation tool for this particular kind of systems [ 46 , 47 ].…”

“…Their findings were in good agreement with experimental observations and measurements. Their numerical tools and formalism were previously applied to the study of band structure and bending properties of large X ( C, Si, Ge, Sn) nanotubes and X ene sheets [ 46 , 47 ].…”

M-SPARC: Matlab-Simulation Package for Ab-initio Real-space Calculations

“…KSSOLV [10] is one such Matlab code for the planewave method, traditionally the discretization of choice in Kohn-Sham DFT [11,12,13,14,15,16]. However, to the best of our knowledge, no such counterpart exists for real-space methods, which have gained significant attention recently [17,18,19,20,21,22,23,24], in part due to their high scalability for large-scale parallel computing [25,23,24], flexibility in the choice of boundary conditions [26,27,28], and amenability to the development of linear scaling methods [29,8]. Motivated by this, in this work we develop M-SPARC: Matlab-Simulation Package for Ab-initio Realspace Calculations.…”