Abstract
Statistical and electrical properties of the conduction electrons of a silver or gold sphere with a radius from 1 to 2 nm are shown to differ drastically from the properties of electrons in a bulk metal sample. If the radius of a noble metal sphere decreases from 10 to 1 nm, its conductivity oscillates around the bulk metal value with increasing amplitude and drops at the 'magic’ numbers of electrons. These numbers are equal to 186, 198, 254, 338, 440, 556, 676, 832, 912, 1,284, 1,502, and 1,760, in agreement with various experimental data. We show that the conductivity and capacitance of a metal nanosphere can be changed by several orders of magnitude by adding or removing just a few electrons.
Highlights
In the past, a measurement of optical absorption by silver nanoparticles embedded in glass showed that the particles had normal metallic properties when their diameters were decreased down to 2.2 nm [1]
It was understood that the metal-insulator transition (MIT) is gradual so that particles with certain ‘magic’ numbers of electrons become insulating while others remain conducting [4]
In [29], we examined the properties of the conduction electrons in grand canonical ensembles where the chemical potential μ0 was fixed
Summary
A measurement of optical absorption by silver nanoparticles embedded in glass showed that the particles had normal metallic properties when their diameters were decreased down to 2.2 nm [1]. Contrary to this finding, metal particles with sizes below 2 nm cannot be conducting according to more recent papers [2,3]. The averaged occupation numbers of the electron energy levels and the variances of the occupation numbers were computed for both isolated metal nanoparticles and those in equilibrium with
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