Thermodynamic Properties of Electrons in Small Metal Particles

The electronic properties of an assembly of small metal particles are determined by and reflect their distribution of discrete electronic energy levels. With the absence of strong correlations (arising from, for example, the presence of localized impurities or surface states), it is reasonable to treat the energy-level distribution statistically. The level distribution is determined by the symmetry of the dynamics which governs the three ensembles of the statistical theory of spectra and characterized by a mean single-electron-level spacing $\delta$ for particles of a certain size. In this paper we confine our attention to the thermodynamics of small particles. The exact solution of a model is presented which consists of electrons in equally spaced levels and which includes magnetic field and short-range-interaction effects. We report on detailed calculations of the heat capacity and magnetic spin susceptibility. Here, the statistics of level distributions is applied in the whole temperature range, thus generalizing the work done originally by Kubo and Gor'kov and Eliashberg for the limiting case in which $\mathrm{kT}\ll \delta$.