[Paper Review] Stone-Wales graphene: A Two Dimensional Carbon Semi-Metal with Magic Stability

Hengchuang Yin, Xizhi Shi+8 more|arXiv (Cornell University)|Jan 9, 2019

Graphene research and applications4 citations

TL;DR

This paper proposes Stone-Wales graphene, a two-dimensional carbon allotrope formed by 90° bond rotations in a √8 × √8 graphene supercell, which exhibits exceptional stability due to a 'magic size' effect. First-principles calculations confirm it is a dynamically stable semimetal with distorted, anisotropic Dirac cones and lower energy than previously proposed allotropes like phagraphene and ψ-graphene.

ABSTRACT

A two-dimensional carbon allotrope, Stone-Wales graphene, is identified in stochastic group and graph constrained searches and systematically investigated by first-principles calculations. Stone-Wales graphene consists of well-arranged Stone-Wales defects, and it can be constructed through a 90$^\circ$ bond-rotation in a $\sqrt{8}$$ imes$$\sqrt{8}$ super-cell of graphene. Its calculated energy relative to graphene, +149 meV/atom, makes it more stable than the most competitive previously suggested graphene allotropes. We find that Stone-Wales graphene based on a $\sqrt{8}$ super-cell is more stable than those based on $\sqrt{9} imes \sqrt{9}$, $\sqrt{12} imes \sqrt{12}$ and $\sqrt{13} imes \sqrt{13}$ super-cells, and is a "magic size" that can be further understood through a simple "energy splitting and inversion" model. The calculated vibrational properties and molecular dynamics of SW-graphene confirm that it is dynamically stable. The electronic structure shows SW-graphene is a semimetal with distorted, strongly anisotropic Dirac cones.

Motivation & Objective

• To identify new two-dimensional carbon allotropes beyond graphene using stochastic and graph-constrained searches.
• To investigate the energetic stability and structural properties of allotropes formed by Stone-Wales defects in graphene supercells.
• To determine whether Stone-Wales graphene exhibits dynamic stability and unique electronic properties such as semimetallicity.
• To explain the origin of enhanced stability in the √8 × √8 supercell through a novel 'energy splitting and inversion' model.
• To explore the electronic structure across a family of SW-graphene allotropes and identify which exhibit Dirac-cone behavior.

Proposed method

• Employed stochastic group and graph-constrained searches using the RG2 code to explore stable 2D carbon structures with up to 24 atoms per unit cell.
• Performed first-principles density functional theory (DFT) calculations with the PBE exchange-correlation functional in VASP to compute structural, energetic, and electronic properties.
• Used a 2s²2p² PAW pseudopotential for carbon and set a 50 Ry energy cutoff for electronic convergence.
• Conducted phonon dispersion and molecular dynamics simulations to assess dynamical stability.
• Systematically analyzed the energy evolution across √N × √N supercells with a single Stone-Wales defect, comparing fixed-configuration, ionic-relaxed, and fully relaxed states.
• Developed a theoretical 'energy splitting and inversion' model to explain the enhanced stability of the √8 × √8 supercell by analyzing relaxation energy contributions (ΔE₁, ΔE₂, ΔE₃).

Experimental results

Research questions

• RQ1 Is there a 2D carbon allotrope based on Stone-Wales defects that is more stable than previously proposed graphene allotropes?
• RQ2 What is the origin of the exceptional stability observed in the √8 × √8 supercell of Stone-Wales graphene?
• RQ3 Does Stone-Wales graphene exhibit dynamic stability under thermal and vibrational fluctuations?
• RQ4 What is the electronic structure of Stone-Wales graphene, and does it host Dirac cones with anisotropic Fermi velocity?
• RQ5 How do the electronic properties of the broader family of SW-graphene allotropes vary with supercell size and symmetry?

Key findings

• Stone-Wales graphene based on a √8 × √8 supercell is 50 meV/atom more stable than the √9 × √9 supercell and more stable than other supercells up to √13 × √13.
• The √8 × √8 SW-graphene structure is energetically more favorable than phagraphene (+201 meV/atom) and ψ-graphene (+165 meV/atom) relative to graphene.
• The structure is dynamically stable, as confirmed by phonon dispersion and molecular dynamics simulations showing no soft modes.
• The electronic band structure reveals SW-graphene as a semimetal with strongly anisotropic, distorted Dirac cones and a nontrivial Berry phase of π.
• The 'magic stability' of the √8 × √8 supercell arises from maximal energy release during ionic relaxation (ΔE₂), explained by the 'energy splitting and inversion' model.
• Among the SW-graphene allotropes, only √8-Cmmm, √16, √24-Cmmm, √25, √27, and √32-Cmmm exhibit semimetallic behavior with Dirac cones; others are semiconductors with direct or indirect gaps.