Electronic properties of small metallic particles

Abstract

Metallic particles with linear dimensions d small compared with other characteristic lengths (like the wavelength of electromagnetic radiation, the de Broglie wavelength of the conduction electrons, the coherence length or the penetration depth in the superconducting state, etc.) show interesting effects which are usually unobservable in bulk metals. The electronic properties of these particles with diameters of a few nm can be analysed by considering the microcrystals not as “giant molecules” but as “small solids”, i.e. by using the familiar methods of solid state physics with some properly defined boundary conditions. Due to the smallness of the particles, the customary quasi-continuous electronic excitation spectrum splits up into discrete energy levels with an average energy splitting δ of a few meV. If then the relevant energies (like the thermal energy kT, the Zeeman energy μ 0 μ B H, the electrostatic energy edE, the photon energy h ̵ ω , the condensation energy for the superconducting state Δ, etc.) are comparable with δ, novel effects are to be expected, called “quantum size effects” (QSE). In an ensemble of small particles, it is expected that the discrete energy levels are statistically distributed; therefore, methods of level statistics can be employed to calculate the different electronic properties of small particles. In this report, the more phenomenological aspects of the physics of small particles are discussed, where e.g. the interaction of the electromagnetic radiation with the particle is described by a dielectric constant, also characteristic for the bulk metal. The more microscopic quantum size effects in small particles are then analysed theoretically, mainly from the point of view of the statistics of discrete energy levels, and the existing experimental results are discussed. Superconductivity in small metallic particles is reviewed with emphasis on the critical fields in small particles, the magnetic field dependence of their microscopic properties (e.g. density of states), the problem of a lower size limit of a superconductor, and fluctuations in small superconductors. Finally, the most commonly used experimental methods to produce small particles are described.