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

arXiv comment24 pages, 8 figures, 4 tables

References in corpus (36)

• Electric Field Effect in Atomically Thin Carbon Films
• Optimized norm-conserving Vanderbilt pseudopotentials
• Doping graphene with metal contacts
• A real-space grid implementation of the Projector Augmented Wave method
• Epitaxial Growth of Two-Dimensional Stanene
• Perspective on density functional theory
• Germanene: a novel two-dimensional Germanium allotrope akin to Graphene and Silicene
• Quasiparticle Self-Consistent GW Theory
• Excitonic Effects and Optical Spectra of Single-Walled Carbon Nanotubes
• Ab-initio structural, elastic, and vibrational properties of carbon nanotubes
• Nearsightedness of Electronic Matter
• O(N) methods in electronic structure calculations
• Real-Space Mesh Techniques in Density Functional Theory
• Elastic Bending Modulus of Monolayer Graphene
• Multiresolution analysis of electronic structure: semicardinal and wavelet bases
• First-principles theory and calculation of flexoelectricity
• Real-Space Adaptive-Coordinate Electronic Structure Calculations
• Large Scale Electronic Structure Calculations with Multigrid Acceleration
• Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations
• Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
• Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters
• Basis Functions for Linear-Scaling First-Principles Calculations
• Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations
• Characterization of Thin Film Materials using SCAN meta-GGA, an Accurate Nonempirical Density Functional
• SQDFT: Spectral Quadrature method for large-scale parallel $\mathcal{O}(N)$ Kohn-Sham calculations at high temperature
• Collapse of Double-Walled Carbon Nanotube Bundles under Hydrostatic Pressure
• Coarse-graining Kohn-Sham Density Functional Theory
• Quantum thermal transport in stanene
• Augmented Lagrangian formulation of Orbital-Free Density Functional Theory
• Cyclic Density Functional Theory : A route to the first principles simulation of bending in nanostructures
• On nearsightedness in metallic systems for $\mathcal{O}(N)$ Density Functional Theory calculations: A case study on Aluminum
• On the calculation of the stress tensor in real-space Kohn-Sham Density Functional Theory
• Ewald Sums for One Dimension
• On real-space Density Functional Theory for non-orthogonal crystal systems: Kronecker product formulation of the kinetic energy operator

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