Giant vortices in rotating electron droplets

We predict the formation of giant vortices in quasi-two-dimensional quantum dots at high magnetic fields, i.e., in rapidly rotating electron droplets. Our numerical results for quantum dots confined by a flat, anharmonic potential show ground states where vortices are accumulated in the center of the dot, thereby 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.

Figure 1

(Color online) Electron densities (SDFT) of $N=10$ quantum dots containing seven flux quanta in both (a) and (b) but having different distributions of vorticity. The state in (a) is calculated using a parabolic external potential ($\hslash \omega =4\mathrm{meV}$, $B=13\mathrm{T}$) and shows a cluster of seven vortex holes. The state in (b) is calculated in a hard-wall potential well ($R=100\mathrm{nm}$, $B=25\mathrm{T}$) and shows a giant core (eye) of a vortex comprising seven flux quanta close to the center of the rotation.

Figure 2

(Color online) (a) Phase diagram of the vortex solutions in a six-electron quantum dot defined by a parabolic-plus-quartic confining potential [Eq. (2)]. The results have been calculated with the CI method. The roman and arabic numerals mark the number of multiple and clustered vortices in the ground states, respectively. The total angular momenta $L$ are marked by circled numbers. (b) Magnetization of a quantum dot with $\lambda =0.18$ corresponding to the dashed line in (a).

Figure 3

(Color online) Left panel: Total electron densities (gray scale) and current densities (arrows) of double-vortex (II), triple-vortex (III), and eightfold giant-vortex (VIII) states in a six-electron quantum dot. The states II and III have been calculated with the CI in a quadratic-plus-quartic potential as in Fig. 2. The state VIII has been calculated with the SDFT in a circular hard-wall well of radius $R=70\mathrm{nm}$. Right panel: Corresponding conditional densities (contours) and the phases (gray scale) of the conditional wave function. The phase of the SDFT result (VIII) is calculated from the single-determinant auxiliary wave function constructed from the Kohn-Sham states. At the lines where the shadowing changes from darkest gray to white the phase jumps from $-\pi$ to $\pi$. The crosses (blue) and circles (red) mark the most probable electron positions and vortex positions, respectively. The Pauli vortices at the electron positions are not marked by circles for clarity. The probing electron has its maximum probability downright.

Figure 4

(Color online) SDFT results for the total angular momenta of $N=12$ (a) and 20 (b) hard-wall quantum dots. (Red and blue) dashed lines mark the $L$ plateaus for multiple vortices (roman numerals) and vortex clusters (arabic numerals), respectively. The black dashed line corresponds to the single-vortex solution and the dotted line marks the MDD state.