Phonon mediated tunneling into graphene

TL;DR

This paper provides a theoretical explanation for the observed tunneling gap in graphene, attributing it to phonon-mediated processes, supported by ab-initio calculations and a developed electron-phonon interaction model.

Contribution

The study introduces a detailed model of electron-phonon coupling in graphene that explains the tunneling spectra and the observed energy gap, aligning well with experimental data.

Findings

Good agreement between model and experimental tunneling spectra

Identification of phonon-mediated tunneling as the gap origin

Quantitative analysis of electron-phonon self-energy effects

Abstract

Recent scanning tunneling spectroscopy experiments [V. W. Brar et. al., Appl. Phys. Lett. 91, 122102 (2007), Y. Zhang et. al., arXiv:0802.4315 (2008)] on graphene reported an unexpected gap of about $\pm 60$meV around the Fermi level. Here, we give a theoretical investigation explaining the experimentally observed spectra and confirming the phonon mediated tunneling as the reason for the gap: We study the real space properties of the wave functions involved in the tunneling process by means of ab-initio theory and present a model for the electron-phonon interaction, which couples the graphene's Dirac electrons with quasi free electron states at the Brillouin zone center. The self-energy associated with this electron-phonon interaction is calculated and its effects on tunneling into graphene are discussed. In particular, good agreement of the tunneling density of states within our model and the experimental[V. W. Brar et. al., Appl. Phys. Lett. 91, 122102 (2007), Y. Zhang et. al., arXiv:0802.4315 (2008)] dI/dU spectra is found.