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Symmetry-adapted real-space density functional theory for cylindrical geometries: application to large X (X=C, Si, Ge, Sn) nanotubes

Ghosh, Swarnava and Banerjee, Amartya S. and Suryanarayana, Phanish (2019) Symmetry-adapted real-space density functional theory for cylindrical geometries: application to large X (X=C, Si, Ge, Sn) nanotubes. . (Unpublished)

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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 real-space parallel implementation of this formulation, and verify its accuracy against established 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. We find an inverse linear dependence of the bandgap with respect to 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. We find Kirchhoff-Love type bending behavior, 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 effort. Overall, the current work opens an avenue for the ab-initio study of 1D nanostructures with large radii as well as 2D nanostructures under uniform bending.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:S.G. acknowledges support from the Army Research Laboratory which was accomplished under Cooperative Agreement Number W911NF-12-2-0022. A.S.B acknowledges support from the Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences, while at the Lawrence Berkeley National Laboratory. A.S.B also acknowledges support from the Minnesota Supercomputing Institute (MSI) for some of the computational resources that were used in this work. P.S. gratefully acknowledges the support of the National Science Foundation (CAREER-1553212). This research was supported in part through research cyberinfrastructure resources and services provided by the Partnership for an Advanced Computing Environment (PACE) at the Georgia Institute of Technology, Atlanta, Georgia, USA. Some of the computations presented here were conducted on the Caltech High Performance Cluster partially supported by a grant from the Gordon and Betty Moore Foundation.
Funding AgencyGrant Number
Army Research LaboratoryW911NF-12-2-0022
Department of Energy (DOE)UNSPECIFIED
Georgia Institute of TechnologyUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20190528-081936267
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95801
Deposited By: Tony Diaz
Deposited On:28 May 2019 16:28
Last Modified:28 May 2019 16:28

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