Quantum Confinement of Electron-Phonon Coupling in Graphene Quantum Dots
2021
Based on 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 sub-10 nm 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 twofold degenerate edge states. This correction amounts to more than 50% of the gap renormalization. We also present momentum-resolved spectral functions of GQDs, not reported in previous works. Our results lay the foundations to systematically engineer temperature-dependent electronic structures of GQDs for applications in solar cell, electronic transport, and quantum computing devices.
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