Quantum size effects in metal particles

W. P. Halperin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1255 Scopus citations


The subject of small metallic particle properties is outlined with emphasis on quantum electronic effects. The theoretical background for interpretation of experiments is discussed beginning with the work of Kubo. More recent amendments to this have been included, taking into account the techniques of random matrix theory and effects of the spin-orbit interaction. A general review of experimental work is presented in order to permit a comprehensive evaluation of current understanding of the quantum size effect on the electronic spectrum. This survey includes magnetic susceptibility, nuclear magnetic resonance, electron spin resonance, heat capacity, optical, and infrared absorption measurements. These are discussed in many instances from the point of view of there being competing size effects arising from a reduced volume contrasted with those from the surface. A number of stimulating and provocative results have led to the development of new areas of research involving metallic clusters such as cluster beam techniques, far-infrared absorption by particle clusters, adsorbate NMR, and particle-matrix composites. Although there is little question that the experiments themselves indicate the existence of quantum effects, there are as yet, insufficient results to test the theoretical predictions for electron-level distribution functions based on fundamental symmetries of the electron Hamiltonian. A new suggestion for measurement of the electron-level correlation function is made using the magnetic field dependence of the NMR Knight shift. Particle preparation methods are also reviewed with commentary on the problems and advantages of these techniques for investigation of quantum electronic effects.

Original languageEnglish (US)
Pages (from-to)533-606
Number of pages74
JournalReviews of Modern Physics
Issue number3
StatePublished - 1986

ASJC Scopus subject areas

  • General Physics and Astronomy


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