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In-plane optical phonon modes of current-carrying graphene

In this work, we study the in-plane optical phonon modes of current-carrying single-layer graphene whose coupling to the $π$ 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 $π$ 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 ($Γ$ 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 $Γ$-TO and $Γ$-LO modes. More specifically, the DC current breaks the TO-LO mode degeneracy at the $Γ$ point which ideally would be manifested as the splitting of the Raman G peak.