Theory of Plasmons in Two-dimensional Multilayer Structures

A theory of plasmons in two-dimensional (2D) multilayer structures is derived from three-dimensional (3D) plasmon theory that was reported in the random phase approximation under the collective electron excitation condition. When the 3D local electron density is expressed by the 2D uniform local electron density n2D multiplied by the delta functions in the thickness direction, an integral equation for the scalar potential is derived using n2D and the Coulomb potential. The integral equation is transformed into simultaneous linear equations for the scalar potential. The plasmon frequencies are derived from eigenvalues of the linear equations. Studies on plasmon excitations in monolayer, bilayer, trilayer, and multilayer structures show that planar, acoustic, and bulk plasmons are excited depending on the interlayer electron-electron interactions. Inelastic scattering probabilities of electron beams by these plasmon excitations are also calculated.