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 pi electron gas is strong. Such modes are expected to undergo a frequency shift compared to the non-current-carrying state due to the nonequilibrium occupation of the Dirac cone electronic eigenstates with the flowing pi electron gas. Large electron-phonon coupling 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 optical (LO) and transverse optical (TO) modes at the Brillouin zone (BZ) center (K 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 K-TO and K-LO modes. More specifically, the DC current breaks the TO-LO degeneracy at the K point which ideally would be manifested as the splitting of the Raman G peak.