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.

arXiv comment44 pages, 5 figures, single column

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• 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