Many-electron quantum dots in the fractional quantum Hall regime

We perform configuration-interaction calculations in quantum dots with $N=8,10$ electrons in the fractional quantum Hall regime by using an optimized basis which takes into account interaction effects. In the $N=10$ phase diagram we find two very stable configurations which are precursor of the bulk $\nu =2∕3$ and $\nu =3∕5$ states observed in the Hall resistance of the two-dimensional electron gas, and many quasidegenerate configurations which can be related to the quasistable states experimentally found around the $\nu =1∕2$ region.

Figure 1

Convergence of the energy for the $L=42$ many-body state of the $N=8$ dot as a function of the number of configurations used in the diagonalization with a FD basis (dotted-dashed line) and a LSDA basis (full line). The dots in the FD curve give the change of slope when configurations from the third Landau level are added in the calculation. The horizontal thin lines mark the energies given by a fixed phase DMC calculation (solid line) and a mean field LSDA calculation (dotted line).

Figure 2

Lowest energy many-body states of the $N=10$ dot at $B=7\mathrm{T}$ as a function of angular momentum starting from a FD basis (dashed line) and a LSDA basis (full line). The dotted line shows the result obtained using only the LLL in the LSDA basis.

Figure 3

Calculated many-body states (crosses) of the $N=10$ dot as a function of the magnetic field $B$ starting from a LSDA basis (upper figure). The full lines give the interpolated evolution with $B$ of the low energy configurations. The gap, very large for the $\nu =3∕5$ phase, is computed from the energy difference between the ground state and the first excited state. Ground state angular momenta and magnetic field ranges corresponding to $\nu =2∕3,3∕5,1∕2$ are also indicated. The ground state configurations obtained with the FD basis are reported in the lower figure for comparison.

Figure 4

Radial electron densities of the $N=10$ dot calculated starting from a LSDA basis. The values of $B$ and $L$ indicated in the figure correspond to the filling factors $\nu =2∕3,3∕5,1∕2,1$, respectively.