Fermi energy dependence of first- and second-order Raman spectra in graphene: Kohn anomaly and quantum interference effect

TL;DR

This study investigates how the Fermi energy influences first- and second-order Raman spectra in graphene, highlighting the roles of Kohn anomaly and quantum interference effects in spectral intensity and phonon frequency shifts.

Contribution

It provides a detailed theoretical analysis of the Fermi energy dependence of Raman spectra, emphasizing the different mechanisms affecting first- and second-order processes in graphene.

Findings

First-order Raman peak frequency disperses with Fermi energy due to phonon renormalization.

Second-order Raman spectra show a different dispersive behavior influenced by electron-hole excitations.

Raman intensity is highly sensitive to Fermi energy, indicating quantum interference effects are significant.

Abstract

Intensity of the first- and the second-order Raman spectra are calculated as a function of the Fermi energy. We show that the Kohn anomaly effect, i.e., phonon frequency renormalization, in the first-order Raman spectra originates from the phonon renormalization by the interband electron-hole excitation, whereas in the second-order Raman spectra, a competition between the interband and intraband electron-hole excitations takes place. By this calculation, we confirm the presence of different dispersive behaviors of the Raman peak frequency as a function of the Fermi energy for the first- and the second-order Raman spectra, as observed in experiments. Moreover, the calculated results of the Raman intensity sensitively depend on the Fermi energy for both the first- and the second-order Raman spectra. These results thus also show the importance of quantum interference effect phenomena.