Incompressible States in Double Quantum Dots

TL;DR

This study investigates incompressible states in double quantum dots under strong magnetic fields, revealing how inter-dot parameters influence the existence and nature of these states, with new sequences emerging under certain conditions.

Contribution

It demonstrates that incompressible states occur at the same magic angular momentum values as single dots for certain parameters, and identifies new sequences for large inter-dot distances and small hopping.

Findings

Incompressible states appear at the same M values as single dots for typical parameters.

New sequences of M are observed for large d and small t, indicating a transition to decoupled dots.

Differences in ground state nature compared to single quantum dots are identified.

Abstract

Incompressible (magic) states of 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 incompressible states exists depend on the interplay between the inter-dot hopping parameter \Delta_t and the inter-dot 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, the incompressible states appear at magic values of M which do not differ from those obtained for a single dot, namely M=N(N-1)/2+jN where j is a positive integer number. For large inter-dot distance and simultaneously small inter-dot 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.