Quantum Oscillation Effects of Electrons in Metal Nanostructures on Localized Plasmons

Abstract

Quantum oscillation effects of electrons in metal nanostructures on localized plasmons are investigated using the random phase approximation at high frequency condition. The scalar potentials for electrons can be calculated by the integral equations with the local electron densities in metal nanostructures. The scalar potentials and light emission intensities are calculated in the quasi-static approximation using local electron densities in Na nanospheres showing quantum oscillations. The integral equations for the scalar potentials are transformed into simultaneous linear equations and the resonant frequencies of localized plasmons are obtained by the eigenvalues of the matrices derived from the linear equations. The quantum oscillations produce multiple resonant frequencies, which is different from the case for the local electron density with step function shape that gives only the surface plasmon frequency. The quantum oscillations at inside areas of Na nanospheres contribute to producing higher resonant frequencies than the classical surface plasmon frequency, while those at surface areas contribute to producing lower resonant frequencies.