Born-Oppenheimer Breakdown in Graphene

TL;DR

This paper demonstrates the breakdown of the Born-Oppenheimer approximation in graphene, showing that electron dynamics near the Fermi level do not follow phonon oscillations, leading to observable phonon frequency changes.

Contribution

It reveals a fundamental failure of the Born-Oppenheimer approximation in graphene due to slow electron relaxation, impacting the understanding of phonon-electron interactions.

Findings

Raman G peak stiffening with gate voltage in graphene

BO approximation invalid for describing phonon behavior in graphene

Electrons do not adiabatically follow Dirac-cone oscillations

Abstract

The Born-Oppenheimer approximation (BO) has proven effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Graphene, recently discovered in the free state, is a zero band-gap semiconductor, which becomes a metal if the Fermi energy is tuned applying a gate-voltage Vg. Graphene electrons near the Fermi energy have twodimensional massless dispersions, described by Dirac cones. Here we show that a change in Vg induces a stiffening of the Raman G peak (i.e. the zone-center E2g optical phonon), which cannot be described within BO. Indeed, the E2g vibrations cause rigid oscillations of the Dirac-cones in the reciprocal space. If the electrons followed adiabatically the Dirac-cone oscillations, no change in the phonon frequency would be observed. Instead, since the electron-momentum relaxation near the Fermi level is much slower than the phonon motion, the electrons do not follow the Dirac-cone displacements. This invalidates BO and results in the observed phonon stiffening. This spectacular failure of BO is quite significant since BO has been the fundamental paradigm to determine crystal vibrations from the early days of quantum mechanics.