Charging Spectrum of a Small Wigner Crystal Island

TL;DR

This paper investigates the charging behavior of a small two-dimensional Wigner crystal island, revealing universal energy oscillations caused by geometric packing effects and electron interactions, with implications for electron addition in gated systems.

Contribution

It demonstrates that the energy of a small Wigner crystal island exhibits universal quasi-periodic oscillations due to geometric and confinement effects, independent of interaction specifics.

Findings

Energy oscillations are universal and shape-independent.

Oscillations are caused by shell and confinement polaronic effects.

Multiple electrons can enter simultaneously in gated environments.

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.