Fractional Statistics and Electron Transfer at Topological Defects

Eric R. Bittner

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arXiv · 2505.05617

Fractional Statistics and Electron Transfer at Topological Defects

Eric R. Bittner

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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.

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Eric R. Bittner. 2025-05-08. Fractional Statistics and Electron Transfer at Topological Defects. https://arxiv.org/abs/2505.05617

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