This paper presents an analysis of the energy loss of a fast-charged-particle probe of a two-dimensional (2D) collisionless solid-state plasma. The fast-particle motion is taken to be parallel to the 2D plasma sheet, and the plasma is taken to be in a degenerate state (zero temperature). The 2D plasma response dynamics are described in the random-phase approximation (RPA), and our calculation is a 2D analogue of the well-known Nozières-Pines energy-loss calculation, but with the particle’s trajectory at a fixed distance H from the plane of the 2D plasma sheet. Our calculation includes a determination of the part of the fast particle’s energy loss which can be ascribed to the excitation of electron-hole pairs in the 2D plasma, as well as the part which can be ascribed to 2D plasmons (of all wave numbers). We determine the energy loss as a function of the distance of the fast particle from the 2D plasma plane, and its velocity.

• Received 6 February 1987

DOI:https://doi.org/10.1103/PhysRevB.36.1588