Exact e–e (exchange) correlations of 2-D quantum dots in magnetic field: Size extensive N=3,4,…,′n′-electron systems via multi-pole expansion

• Published in: Physica. E, Low-dimensional systems & nanostructures Vol. 88; pp. 26 - 34
• Main Authors: Aggarwal, Priyanka, Sharma, Shivalika, Singh, Sunny, Kaur, Harsimran, Hazra, Ram Kuntal
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2017
• ISSN: 1386-9477; 1873-1759
• DOI: 10.1016/j.physe.2016.11.015

Inclusion of coulomb interaction emerges with the complexity of either convergence of integrals or separation of variables of Schrödinger equations. For an N-electron system, interaction terms grow by N(N-1)/2 factors. Therefore, 2-e system stands as fundamental basic unit for generalized N-e systems. For the first time, we have evaluated e–e correlations in very simple and absolutely terminating finite summed hypergeometric series for 2-D double carrier parabolic quantum dot in both zero and arbitrary non-zero magnetic field (symmetric gauge) and have appraised these integrals in variational methods. The competitive role among confinement strength, magnetic field, mass of the carrier and dielectric constant of the medium on energy level diagram, level-spacing statistics, heat capacities (Cv at 1K) and magnetization (T∼(0–1)K) is studied on systems spanning over wide range of materials (GaAs,Ge,CdS,SiO2 and He, etc). We have also constructed an exact theory for generalized correlated N-e 2-D quantum dots via multi-pole expansion but for the sake of compactness of the article we refrain from data. •e–e interactions in absolutely terminating and finitely summed Lauricella function has been evaluated beyond question of convergence.•Exact treatment of generalized N-e systems is proposed using multi-pole expansion.•Unusual stabilization intensified from 2-e to N-electron systems due to enhanced exchange correlations.•Our integral of coulomb correlation limits to 1|m| of Laughlin's prediction for fractional quantum Hall effect.•Level spacing statistics, heat capacity measurement and magnetization (T∼1K) confirms shuffling states of 2-D 2-e quantum dots.•Size of the system, N=2,3,4,‥,10,‥,′n′ for both carrier electron and hole.