Cationic vacancies as defects in honeycomb lattices with modular symmetries

TL;DR

This paper models cation diffusion in honeycomb layered materials using modular symmetries and topological defects, revealing how quantum geometry influences conductance and magnetic properties.

Contribution

It introduces a novel framework combining modular symmetries and topological defects to analyze cation dynamics in layered honeycomb structures.

Findings

Prediction of conductance peaks during cation intercalation

Identification of topological defects as vacancies affecting diffusion

Role of quantum geometry in pseudo-spin and magnetic fields

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, $J_1, J_2 \in \rm SL_2(\mathbb{Z})$ 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.