Statistical and electrical properties of the conduction electrons of a metal nanosphere in the region of metal-insulator transition

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.