Incompressible states in double quantum dots

Incompressible (magic) states that result from many-body effects in vertically coupled quantum dots submitted to strong magnetic fields such that only the lowest Landau level is relevant are studied within an exact diagonalization calculation for $N=3,$ 5, and 6, electrons. We find that the sequences of total angular momentum M for which these incompressible states exist depend on the interplay between the interdot hopping parameter ${\Delta }_t$ and the interdot distance d. For d of the order of the magnetic length and for all values of ${\Delta }_t,$ we conclude that, in contrast to previous claims, these incompressible states appear at magic values of M which do not differ from those obtained for a single dot: namely, $M=N\left(N-1\right)/2+jN,$ where j is a positive integer number. For large interdot distance and simultaneously small interdot hopping parameter, new sequences of magic values of M are observed. These new sequences can be easily understood in terms of a transition regime towards a system of two decoupled single dots. However, important differences in the nature of the incompressible ground states are found with respect to those of a single dot.