Basab B. Dasgupta

A simple dispersion relation for the surface plasmon: Dependence on electron density profile

Abstract We know from the quantum-mechanical, random-phase-approximation (RFA) calculations for the surface plasmon that the electron density profile at the surface plays an important role in determining the dispersion relation. The full RPA calculations are very difficult to perform, and we present a simple expression for the dispersion relation which depends on the electron density profile at the surface. Our derivation is essentially semi-classical and parallels that of Ritchie and Marusak. The validity of our expression for the dispersion relation is assessed by computing the dispersion relations for different electron density profiles and comparing them with those obtained in the full RPA calculations.

Surface plasmon dispersion for very small metallic spheres: A quantum mechanical formulation

We have derived a pair of matrix equations describing the surface plasmon dispersion for a very small spherical metal particle, using the quantum mechanical random-phase approximation (RPA). The surface of the sphere is represented by an infinite spherical potential well for the conduction electrons and the positive ions are assumed to be uniformly distributed into a “jellium”. The dispersion relation is obtained as the condition that a solution of the RPA integral equation for charge fluctuation would exist for the particle.

Random phase approximation theory of higher surface plasma modes

Using the random phase approximation and analytical calculation we show that a “higher” surface plasma mode can exist near a plane metal-vacuum interface provided the oscillation is “sufficiently” localized. This conclusion is confirmed for the infinite potential barrier model of the surface where a mode with long-wavelength frequencyω≃ωp in sodium is predicted.

Hydrodynamic theory of plasma oscillations in quasi-two-dimensional systems

Abstract We show that a hydrodynamic theory can be applied to calculate the dispersion relation of plasma oscillations in a quasi-two-dimensional system. It also leads to the conclusion that additional “multipole” modes may exist in the system.

Effects of a perpendicular electric field on a quasi-two-dimensional system: Hydrogenic model

Abstract The properties of a quasi-two-dimensional system are affected by the presence of an electric field applied perpendicular to the surface. These changes are investigated analytically within the “hydrogenic” model and a theory linear in the field. Both the static and dynamic fields are considered and the dynamic case is treated in the dipole approximation by following the approach of Luban and Nudler-Blum.

Interband damping of long-wavelength bulk plasmons

Abstract The contribution of interband transitions of electrons to the damping of plasma oscillations in a metal is investigated in the long-wavelength limit using two different approximation schemes: (i) a method using sum rules and (ii) a perturbative approach. We show that the first method leads to unphysical results, but the perturbation theory is justified for those metals in which the lattice periodicity can be represented by a weak pseudopotential. The numerical value of damping is computed for aluminium. The calculated frequency dependence of the imaginary part of the dielectric constant of Al is shown to be in good agreement with the same curve obtained from optical data.