Half-Integer Filling-Factor States in Quantum Dots

The emergence of half-integer filling-factor states, such as $\nu =5/2$ and $7/2$, is found in quantum dots by using numerical many-electron methods. These states have interesting similarities and differences with their counterstates found in the two-dimensional electron gas. The $\nu =1/2$ states in quantum dots are shown to have high overlaps with the composite fermion states. The lower overlap of the Pfaffian state indicates that electrons might not be paired in quantum dot geometry. The predicted $\nu =5/2$ state has a high spin polarization, which may have an impact on the spin transport through quantum dot devices.

Figure 1

(a) Ground-state spin of quantum dots with $N=12$, 30, 48, and 60 electrons, respectively. The magnetic fields are scaled linearly to filling-factor range $2\le \nu \le 3$. (b) Spin densities of the $N=60$ quantum dot at $\nu =5/2$. The spin-polarized second Landau level gives rise to high spin polarization in the core region of the dot. (c) Occupation of the single-electron (Kohn-Sham) states on different Landau levels in the $N=60$ quantum dot at $2\le \nu \le 7/2$.

Figure 2

Electron positions (crosses), conditional electron densities (contours), and phases (gray scale) of the $N=8$, $L=52$ state from the (a) ED and (b),(c) PF models. We probe with the rightmost electron, and densities are on logarithmic scale. The phase changes from $\pi$ to $-\pi$ on the lines where the shadowing changes from the darkest gray to white. In (a) and (c) electrons are on the most probable positions, and in (b) we use ED coordinates for PF.

Figure 3

Ground-state magnetization (upper curves) and total spins (lower curves) of 60-electron quantum dots in (a) parabolic and (b) infinite-well potentials. The finite-size counterparts of the integer and fractional quantum Hall states are marked in the panels (dashed lines).