Vortices in Quantum Dots

Stephanie Reimann

LTH, Lund University


When a system consisting of many interacting particles is set rotating, it may form vortices. Famous examples of vortices are superconducting films and rotating bosonic He-4 or fermionic He-3 liquids. Vortices are also observed in rotating Bose-Einstein condensates in atomic traps and are predicted to exist for paired fermionic atoms. Here we show that the rotation of trapped particles with a repulsive interaction leads to a similar vortex formation, regardless of whether the particles are bosons or (unpaired) fermions. The exact, quantum mechanical many-particle wave function provides evidence that in fact, the mechanism of this vortex formation is the same for boson and fermion systems.
An example for vortex formation are two-dimensional quantum dots in high magnetic fields. In non-symmetric external potentials we find off-electron vortices that are localized giving rise to charge deficiency or holes in the electron density with rotating currents around them. We discuss the role of quantum fluctuations and show that vortex formation is observable in the energetics of the system. Our findings suggest that vortices can be used to characterize the solutions in high magnetic fields, giving insight into the underlying internal structure of the electronic wave function.
In anharmonic quantum dots, "giant vortices" may form. Here, the vortices accumulate in the center of the dot, leading to large cores in the electron and current densities. The phenomenon is analogous to what was recently found in rotating Bose-Einstein condensates. The giant-vortex states leave measurable signatures in the ground-state energetics. The conditions for the giant-vortex formation as well as the internal structure of the vortex cores are discussed.