In-plane optical phonon modes of current-carrying graphene

TL;DR

This paper investigates how in-plane optical phonon modes in current-carrying graphene are affected by electron flow, revealing symmetry breaking and shifts in phonon frequencies due to electron-phonon interactions.

Contribution

It provides a theoretical analysis of phonon mode shifts and symmetry breaking in graphene under DC current, highlighting the impact on Raman spectral features.

Findings

DC current causes different frequency shifts in $ ext{TO}$ and $ ext{LO}$ modes.

Breaking of rotational symmetry results in splitting of the Raman G peak.

Strong electron-phonon coupling influences phonon dispersion under current.

Abstract

In this work, we study the in-plane optical phonon modes of current-carrying single-layer graphene whose coupling to the $\pi$ electron gas is strong. Such modes are expected to undergo a frequency shift compared to the non-current-carrying state due to the non-equilibrium occupation of the Dirac cone electronic eigen-states with the flowing $\pi$ electron gas. Large electron-phonon coupling (EPC) can be identified by an abrupt change in the slope of the phonon mode dispersion known as the Kohn anomaly, which mainly occurs for (i) the in-plane longitudinal/transverse optical (LO/TO) modes at the Brillouin zone (BZ) center ($\Gamma$ point), and (ii) the TO modes at the BZ corners ($K$ points). We show that the breaking of the rotational symmetry by the DC current results in different frequency shifts to the $\Gamma$-TO and $\Gamma$-LO modes. More specifically, the DC current breaks the TO-LO mode degeneracy at the $\Gamma$ point which ideally would be manifested as the splitting of the Raman G peak.