Electron and boson clusters in confined geometries: symmetry breaking in quantum dots and harmonic traps

TL;DR

This paper investigates symmetry breaking and crystalline pattern formation in electron clusters within quantum dots and boson clusters in harmonic traps, revealing localization phenomena and energy behaviors beyond mean-field approximations.

Contribution

It presents new calculations demonstrating electron localization in quantum dots and boson crystallization in traps, advancing understanding beyond traditional mean-field models.

Findings

Electrons form molecular dimers in elliptic quantum dots.

Bosons localize into polygonal-ring-like patterns in traps.

Crystalline phases exhibit saturation of total energy.

Abstract

We discuss the formation of crystalline electron clusters in semiconductor quantum dots and of crystalline patterns of neutral bosons in harmonic traps. In a first example, we use calculations for two electrons in an elliptic quantum dot to show that the electrons can localize and form a molecular dimer. The calculated singlet-triplet splitting (J) as a function of the magnetic field (B) agrees with cotunneling measurements, with its behavior reflecting the effective dissociation of the dimer for large B. Knowledge of the dot shape and of J(B) allows determination of the degree of entanglement. In a second example, we study strongly repelling neutral bosons in two-dimensional harmonic traps. Going beyond the Gross-Pitaevskii (GP) mean-field approximation, we show that bosons can localize and form polygonal-ring-like crystalline patterns. The total energy of the crystalline phase saturates in contrast to the GP solution, and its spatial extent becomes smaller than that of the GP condensate.