An Idealised Approach of Geometry and Topology to the Diffusion of Cations in Honeycomb Layered Oxide Frameworks

31 July 2020, Version 4
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

Honeycomb layered oxides are a novel class of nanostructured materials comprising alkali or coinage metals intercalated into transition metal slabs. The intricate honeycomb architecture and layered framework endows this family of oxides with a tessellation of features such as exquisite electrochemistry, unique topology and fascinating electromagnetic phenomena. Despite having innumerable functionalities, these materials remain highly underutilised as their underlying atomistic mechanisms are vastly unexplored. Therefore, in a bid to provide a more in-depth perspective, we propose an idealised diffusion model of the charged alkali cations (such as lithium, sodium or potassium) in the two-dimensional (2D) honeycomb layers within the multi-layered crystal of honeycomb layered oxide frameworks. This model not only explains the correlation between the excitation of cationic vacancies (by applied electromagnetic fields) and the Gaussian curvature deformation of the 2D surface, but also takes into consideration, the quantum properties of the cations and their inter-layer mixing through quantum tunnelling. Through this work, we offer a novel theoretical framework for the study of multi-layered materials with 2D cationic diffusion currents, as well as providing pedagogical insights into the role of topological phase transitions in these materials in relation to Brownian motion and quantum geometry.

Keywords

Layered Materials
Cationic Diffusion
Quantum Tunneling
Brownian Motion
Chern-Simons
Charge Vortices
BKT transitions
Honeycomb Layered Oxide Frameworks
Curvature
Quantum Geometry
Riemannian Manifold
Geodesic Equation

Comments

Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.