A century-long argument made by Lord Kelvin that all swimming objects have an effective Mach number of 3, corresponding to a Kelvin angle of 19.5° for ship waves, has been challenged recently with the conclusion that the Kelvin angle should gradually transit to the Mach angle as the ship's velocity increases. Here we show that a similar phenomenon can happen for graphene plasmons. By analyzing the caustic wave pattern of graphene plasmons stimulated by a swift charged particle moving uniformly above graphene, we show that at low velocities of the charged particle, the caustics of graphene plasmons form the Kelvin angle. At large velocities of the particle, the caustics disappear and the effective semiangle of the wave pattern approaches the Mach angle. Our study introduces caustic wave theory to the field of graphene plasmonics, and reveals a physical picture of graphene plasmon excitation during electron energy-loss spectroscopy measurements.

• Received 19 March 2015
• Revised 28 July 2015

DOI:https://doi.org/10.1103/PhysRevB.92.081404