Wave function for quantum-dot ground states beyond the maximum-density droplet

Abstract

Semiconductor quantum dots ~QD! are small devices containing a tunable number of electrons in an external confinement potential. There has been significant progress in the fabrication of QD’s during the last few years, which has stimulated an increasing interest in investigating the properties of such systems. From the theoretical point of view, a QD is an ideal many-electron object for theoretical study of fundamental physical properties of correlated systems. One of the major theoretical goals is to understand the nature of the many-body ground states for various magnetic-field strengths. We use the usual model for a quantum dot: electrons with an effective mass m* are moving in two dimensions and are confined by a parabolic potential 1/2v0 r2. The one-body problem is similar to the harmonic oscillator one ~with frequency v5v0 11/4vc 2 , where vc5eB/m*c) and is easily solved for an arbitrary magnetic field B. As we concentrate on the strong magnetic-field limit, the relevant one-particle states are on the lowest Landau level ~LLL!, and these states can be labeled by the angular momentum eigenvalue l. The interaction between electrons is included in the Hamiltonian by the terms e/eri j , where e is the dielectric constant of the material. The fully spin polarized N-electron state built from LLL states of angular momentum l50, . . . ,N21 is the maximum-density droplet ~MDD! state. In the thermodynamic limit, the MDD corresponds to an integer quantum Hall state with filling factor n51. The total angular momentum L is equal to LMDD5N(N21)/2. The many-body states for n.1, corresponding to lowest energy states in the weaker magnetic fields, can be easily obtained from a modified one-electron picture as presented in Ref. 4. In the stronger magnetic-field values, the angular momentum is larger than LMDD and this region corresponds to the fractional quantum Hall regime in the thermodynamic limit, with filling factor defined as n5LMDD /L,1. The L values of these possible lowest energy states, marked by L* in this paper, do not contain all possible L values of the system, but only some of them. There is no theory to rigorously predict the L* values. There are a number of previous theoretical studies on this n,1 or post-MDD region. Recently, high quality experiments with a symmetric QD have been done for this