Cationic vacancies as defects in honeycomb lattices with modular symmetries

Abstract

Layered materials tend to exhibit intriguing crystalline symmetries and topological characteristics based on their two dimensional (2D) geometries and defects. We consider the diffusion dynamics of positively charged ions (cations) localized in honeycomb lattices within layered materials when an external electric field, non-trivial topologies, curvatures and cationic vacancies are present. The unit (primitive) cell of the honeycomb lattice is characterized by two generators, $J_1,J_2\in \mathrm{S}{\mathrm{L}}_2(\mathbb{Z})$ of modular symmetries in the special linear group with integer entries, corresponding to discrete re-scaling and rotations respectively. Moreover, applying a 2D conformal metric in an idealized model, we can consistently treat cationic vacancies as topological defects in an emergent manifold. The framework can be utilized to elucidate the molecular dynamics of the cations in exemplar honeycomb layered frameworks and the role of quantum geometry and topological defects not only in the diffusion process such as prediction of conductance peaks during cationic (de-)intercalation process, but also pseudo-spin and pseudo-magnetic field degrees of freedom on the cationic honeycomb lattice responsible for bilayers.

44 pages, 5 figures, single column

References in corpus (16)

• Two-Dimensional Matter: Order, Curvature and Defects
• Engineering symmetry breaking in two-dimensional layered materials
• Diluted Graphene Antiferromagnet
• Tuning the pseudospin polarization of graphene by a pseudo-magnetic field
• Synthesis, structure and magnetic properties of honeycomb-layered Li3Co2SbO6 with new data on its sodium precursor, Na3Co2SbO6
• Temperature Dependent Na-ion Conduction and its Pathways in the Crystal Structure of the Layered Battery Material Na${}_2$Ni${}_2$TeO${}_6$
• Mixed Alkali-Ion Transport and Storage in Atomic-Disordered Honeycomb Layered $\mathrm{NaKN}{\mathrm{i}}_2\mathrm{Te}{\mathrm{O}}_6$
• Unique Phase Transition on Spin-2 Triangular Lattice of Ag2MnO2
• An Idealised Approach of Geometry and Topology to the Diffusion of Cations in Honeycomb Layered Oxide Frameworks
• Topological Defects and Unique Stacking Disorders in Honeycomb Layered Oxide ${\mathrm{K}}_2\mathrm{N}{\mathrm{i}}_2\mathrm{Te}{\mathrm{O}}_6$ Nanomaterials: Implications for Rechargeable Batteries
• Magnetic and electronic ordering phenomena in the [Ru${}_2$O${}_6$] honeycomb lattice compound AgRuO${}_3$
• RKKY Interactions in Graphene Landau Levels
• Honeycomb Layered Oxides With Silver Atom Bilayers and Emergence of Non-Abelian SU(2) Interactions
• Implications of Coordination Chemistry to Cationic Interactions in Honeycomb Layered Nickel Tellurates
• On local conservation of information content in Schwarzschild black holes
• Renormalization of Electromagnetic Quantities in Small Josephson Junctions

Cited by in corpus (4)

• Honeycomb Layered Oxides With Silver Atom Bilayers and Emergence of Non-Abelian SU(2) Interactions
• Implications of Coordination Chemistry to Cationic Interactions in Honeycomb Layered Nickel Tellurates
• Advances in honeycomb layered oxides: Part I -- Syntheses and Characterisations of Pnictogen- and Chalcogen-Based Honeycomb Layered Oxides
• Pseudo-spin model of argentophilicity in honeycomb bilayered materials