Emergence of Plasmaronic Structure in the Near Field Optical Response of Graphene

The finite momentum optical response $\sigma({\boldsymbol{q}},\omega)$ of graphene can be probed with the innovative technique of infrared nanoscopy where mid-infrared radiation is confined by an atomic force microscope cantilever tip. In contrast to conventional $q\sim 0$ optical absorption which primarily involves Dirac fermions with momentum near the Fermi momentum, $k\sim k_F$, for finite $q$, $\sigma({\boldsymbol{q}},\omega)$ has the potential to provide information on many body renormalizations and collective phenomena which have been found at small $k< k_F$ near the Dirac point in electron-doped graphene. For electron-electron interactions, the low energy excitation spectrum characterizing the incoherent part of the quasiparticle spectral function of Dirac electrons with $k\sim k_F$ consists of a flat, small amplitude background which scales with chemical potential and Fermi momentum. However, probing of the states with $k$ near $k=0$ will reveal plasmarons, a collective state of a charge carrier and a plasmon. These collective modes in graphene have recently been seen in angle-resolved photoemission spectroscopy and here we describe how they manifest in near field optics.