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

TL;DR

This paper presents a theoretical model combining geometry, topology, and quantum mechanics to understand cation diffusion in honeycomb layered oxides, revealing links between electromagnetic excitation, surface curvature, and quantum tunneling.

Contribution

It introduces an idealised diffusion model that integrates topological and quantum effects to explain cation behavior in layered oxides, a novel approach in this field.

Findings

Correlation between cationic vacancies and Gaussian curvature deformation.

Quantum tunnelling influences inter-layer cation mixing.

Topological phase transitions affect cation diffusion dynamics.

Abstract

Honeycomb layered oxides are a novel class of nanostructured materials comprising alkali or alkaline earth 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 underutilized 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 three-dimensional (3D) 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 3D 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.