Theory of Plasmons for Two-Dimensional Materials in the Random Phase Approximation

Abstract: A theory is derived for plasmons in two-dimensional (2D) materials by using three-dimensional (3D) plasmon theory, which was reported previously in the random phase approximation under high frequency conditions. When the 3D local electron density is expressed by the 2D local electron density n2D multiplied by the delta function in the thickness direction, a self-consistent integral equation for the scalar potential is derived using only n2D and the 2D Coulomb potential. The integral equation consists of the edge and planar plasmon terms which give their resonant frequencies. These frequencies are analytically calculated for uniform 2D atomic layers and nanodisks with step function-like electron densities at their edges. The light emission intensities from the nanodisks are also calculated. These frequencies are compared with those for the 2D and 3D Weyl fermions, i.e., massless Dirac fermions.