Quantum Confinement of Electron-Phonon Coupling in Graphene Quantum Dots

TL;DR

This study uses first-principles calculations to reveal how quantum confinement affects phonon-induced gap renormalization in graphene quantum dots, providing insights for engineering temperature-dependent electronic properties.

Contribution

It introduces a correction to the Allen-Heine theory for GQDs and presents momentum-resolved spectral functions, advancing understanding of electron-phonon interactions in quantum dots.

Findings

Strong quantum confinement of zero-point renormalization (20-250 meV)

Correction to Allen-Heine theory exceeds 50% of gap renormalization

Momentum-resolved spectral functions of GQDs provided

Abstract

On the basis of first-principles calculations and the special displacement method, we demonstrate the quantum confinement scaling law of the phonon-induced gap renormalization of graphene quantum dots (GQDs). We employ zigzag-edged GQDs with hydrogen passivation and embedded in hexagonal boron nitride. Our calculations for GQDs in the sub-10 nm region reveal strong quantum confinement of the zero-point renormalization ranging from 20 to 250 meV. To obtain these values we introduce a correction to the Allen-Heine theory of temperature-dependent energy levels that arises from the phonon-induced splitting of 2-fold degenerate edge states. This correction amounts to more than 50% of the gap renormalization. We also present momentum-resolved spectral functions of GQDs, which are not reported in previous contributions. Our results lay the foundation to systematically engineer temperature-dependent electronic structures of GQDs for applications in solar cells, electronic transport, and quantum computing devices.