Fractional Statistics and Electron Transfer at Topological Defects

TL;DR

This paper presents a theoretical model for electron transfer at graphene defects, incorporating fractional quasiparticle statistics and vibrational effects, revealing how topology influences surface reactivity.

Contribution

It introduces a novel framework combining polaron transformation and fractional statistics to analyze electron transfer at topological defects in graphene.

Findings

Fractional statistics suppress low-energy electron transfer near resonance.

Tunable deviations from Marcus-like kinetics are introduced by fractionalized quasiparticles.

Strain and defect engineering can stabilize fractional excitations, affecting surface reactivity.

Abstract

We develop a theoretical framework for electron transfer (ET) at graphene defects, treating the surface as a Dirac cone with a localized defect state coupled to a vibrational environment. Using a polaron transformation combined with a modified density of states, we derive an explicit expression for the ET rate that incorporates both vibrational reorganization and fractionalized quasiparticle statistics. We show that fractional statistics, modeled through a power-law density of states, suppress low-energy ET near resonance and introduce tunable deviations from conventional Marcus-like kinetics. Our results suggest that strain, defect engineering, or chemical modification could stabilize fractional excitations in graphene-based catalysts, offering new strategies for controlling surface reactivity. These findings provide a foundation for future experimental and computational investigations into the role of topology and fractional statistics in chemical electron transfer.