Two-Dimensional Diffusion in the Presence of Topological Disorder

TL;DR

This paper investigates how topological defects influence particle diffusion in two-dimensional crystals, revealing that weak disorder reduces diffusion rates while long-range disorder causes subdiffusive behavior over time.

Contribution

It introduces a combined approach of perturbation theory, renormalization group analysis, and simulations to understand the impact of topological disorder on diffusion in 2D materials.

Findings

Weak, short-range disorder reduces diffusion coefficient.

Long-range disorder induces subdiffusive behavior.

Numerical simulations support theoretical predictions.

Abstract

How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder leads to a finite reduction of the diffusion coefficient. Renormalization group theory and numerical simulations suggest that longer-ranged disorder, such as that from randomly placed dislocations or random disclinations with no net disclinicity, leads to subdiffusion at long times.