Charging spectrum of a small Wigner crystal island

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Abstract
Charging of a clean two-dimensional island is studied in the regime of small concentration of electrons when they form the Wigner crystal. The number of electrons in the island is assumed to be not too big (N < 100). It is shown that the total energy of the island as a function of N has a quasi-periodic component of a universal shape, that is independent of the form of electron-electron interactions. These oscillations are caused by the combination of the geometric effects associated with packing of the triangular lattice into the circular island. These effects are: the shell effect, associated with starting a new crystalline row, and the so-called confinement polaronic effect. In the presence of close metallic gates, which eliminate the long-range part of the electron-electron interactions, the oscillations of the energy bring about simultaneous entering of the dot by a few electrons.
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