Non-adiabatic Kohn-anomaly in a doped graphene monolayer

TL;DR

This paper investigates how doping affects the phonon frequency in graphene, revealing that dynamic effects cause significant deviations from adiabatic predictions due to a Kohn anomaly.

Contribution

It demonstrates the failure of the adiabatic approximation in doped graphene by comparing it with time-dependent perturbation theory results.

Findings

Adiabatic approximation underestimates doping effects on phonon frequency.

Dynamic calculations show rapid phonon frequency variation with doping.

Kohn anomaly causes significant non-adiabatic effects in doped graphene.

Abstract

We compute, from first-principles, the frequency of the E2g, Gamma phonon (Raman G-band) of graphene, as a function of the charge doping. Calculations are done using i) the adiabatic Born-Oppenheimer approximation and ii) time-dependent perturbation theory to explore dynamic effects beyond this approximation. The two approaches provide very different results. While, the adiabatic phonon frequency weakly depends on the doping, the dynamic one rapidly varies because of a Kohn anomaly. The adiabatic approximation is considered valid in most materials. Here, we show that doped graphene is a spectacular example where this approximation miserably fails.