Edge Photogalvanic Effect in a Collisionless Electron Gas: Quantum-Mechanical and Kinetic Descriptions

We study the surface photogalvanic effect in a degenerate collisionless electron gas. The surface direct current induced by electromagnetic radiation and flowing along a rigid smooth boundary is calculated for a two-dimensional gas in a semi-infinite quantum well and a three-dimensional gas in a semi-infinite metal slab. The calculations employ two microscopic approaches, namely, the single-particle Schrödinger equation and the Boltzmann kinetic equation. Both approaches yield identical nonzero values of the net surface (edge) current under elliptically polarized radiation. For a linearly polarized wave, the total surface current is zero, marking a key distinction from cases where electron scattering processes are significant. Spatial profiles of the direct current are calculated, revealing that its density decreases as a power law with distance from the edge of the half-plane or semi-infinite slab containing the gas. The exponent varies with the dimensionality of the system and differs between the two approaches. Additionally, the current density exhibits spatial oscillations with a period given by the product of the Fermi velocity and the oscillation period of the radiation field.