Second harmonic generation at the edge of a two-dimensional electron gas

We show that driving a two-dimensional electron gas by an in-plane electric field oscillating at the frequency $\omega$ gives rise to an electric current at $2\omega$ flowing near the edge of the system. This current has both parallel and perpendicular to the edge components, which emit electromagnetic waves at $2\omega$ with different polarizations. We develop a microscopic theory of such an edge second harmonic generation and calculate the edge current at $2\omega$ in different regimes of electron transport and electric field screening. We also show that at high frequencies the spatial profile of the edge current contains oscillations caused by excitation of plasma waves.