Edge plasmon polaritons on a half-plane

The effect of electromagnetic retardation on the spectrum of edge plasmons in a semi-infinite two-dimensional electron system is considered. The problem is reduced to complicated integral equations for the potentials, which are solved upon a major simplification of the kernel. The spatial distribution of the potentials, charges, and currents is analyzed. It is shown that edge plasmon polaritons in the high-conductivity two-dimensional system are characterized by a high $Q$ factor at all frequencies, including those lower than the reciprocal electron relaxation time $\tau^{-1}$.