Addition energy and magnetization of 3-D multicarrier anisotropic quantum dots in magnetic field by exact multi-pole expansion of coulomb correlations

• DOI: 10.1016/j.physe.2018.07.033
• Publication Date: 2018-07-29T07:59:40Z
• Authors: Shivalika Sharma; Priyanka Aggarwal; Harsimran Kaur; Sambhav Yadav; Ram Kuntal Hazra
• Keywords: 0103 physical sciences; 01 natural sciences; 7. Clean energy

Abstract Coulomb interactions replicates in N(N − 1)∕2 terms for interacting 3-D N − e confined quantum dots leading to non-trivial Schr odinger equations. For the systems having N > 3, e − e interaction reciprocating to both lateral (electrical) and transverse (magnetic) confinements in moderate fields causes acute interplay in anisotropic quantum dots. As DFT, Hartree-Fock and other perturbative methods have certain limitations, recasting Schrodinger equations into self-adjoint Whittaker-M functions addresses coulomb (exchange) integrals as simplest, finite and single-summed analytical Lauricella functions (F2) via Chu-Vandermonde identity. In case of higher ′N′ , expansion of coulomb correlations in terms of multi-pole expansion facilitates the convergences for bound states upto quadrapole and octopole terms. Although, fermionic exchange symmetry of many electron systems could be included in terms of various two-electron integrals, for the sake of brevity we have aimed to reproduce experimental results without spin. Level clustering/accidential degeneracies manifest on energy level spectra due to competitive role among anisotropic confinement strength, magnetic field , mass of the carrier and dielectric constant of the medium. It triggers orbital induced paramagnetism ( T ∼ (0 − 1)K ), signature of fractional quantum Hall effect (FQHE) in chemical potential cusps ( μ) and formation of different ′shell structures′ in capacitive energy respectively, spanning over wide dielectric range of materials (atomic like quantum dots, ZnO , GaAs and PbSe (Lead Chalcogenide) etc).