Acoustic plasmons in extrinsic free-standing graphene

An acoustic plasmon is predicted to occur, in addition to the conventional twodimensional(2D) plasmon, as the collective motion of a system of two types ofelectronic carriers coexisting in the very same 2D band of extrinsic (doped orgated) graphene. The origin of this novel mode stems from the anisotropypresent in the graphene band structure near the Dirac points K and K’. Thisanisotropy allows for the coexistence of carriers moving with two distinct Fermivelocities along the ΓK and ΓK′ directions, which leads to two modes ofcollective oscillation: one mode in which the two types of carriers oscillate inphase with one another (this is the conventional 2D graphene plasmon, which atlong wavelengths (q → 0) has the same dispersion, q1/2, as the conventional 2Dplasmon of a 2D free electron gas), and the other mode found here correspondingto a low-frequency acoustic oscillation (whose energy exhibits at longwavelengthsa linear dependence on the 2D wavenumber q) in which the twotypes of carriers oscillate out of phase. This prediction represents a realization of acoustic plasmons originated in the collective motion of a system of two types ofcarriers coexisting within the very same band.