Strongly Correlated Excitons of Regular/Irregular Planar Quantum Dots in Magnetic Field: Size-Extensive Bi- and Triexciton (e–h–e–h and e–e–h/e–h–h) Systems by Multipole Expansion

Abstract

Excitons in parabolically confined planar quantum dots with a transverse magnetic field have been studied in various model systems. The correlations between e–h, e–e, and h–h have been incorporated in terms of exact, simply elegant, and absolutely terminating finite summed Lauricella functions which eliminate the secular divergence problem and pave way for a comprehensive understanding of certain exotic phenomena of various two-dimensional regular and irregular quantum dots. A simple yet highly accurate and exact variational wave function in terms of Whittaker- M function extensible to multiexcitonic systems has been propounded. We have also presented a formulation extending the size of the systems to triexcitonic (e–e–h/e–h–h), biexcitonic (e–h–e–h), and multiexcitonic (“N” e–h pair) planar dots by mono-, di-, quadru-, and octopole expansions. As a benchmark, we have examined the energy spectra, level-spacing statistics, heat capacities ( C v at 1 K), and magnetization ( T ≈ 0–1 K) of He/SiO 2 /BN/GaAs model systems for different lateral confinements, magnetic fields, mass ratios of e–h, and dielectric constants (ϵ).

Electronic spectra and chemical potential of 2-D multi-electron quantum dots in magnetic field: exact multi-pole expansion of coulomb correlation

“…Other magnificent contributions in solving 2-D multi-electron systems have been improvised by Chakraborty et al, Hamaguchi et al and Taut [8][9][10][11][12][13][14][15][16]. Recently, our group proposed a modest alternate to many-body approximation methods for strong e-e and e-h correlations of 2-D quantum dots in magnetic field [17][18][19]. As many-body physics holds great importance, we have designed a prototype to solve exactly generalized N-e systems using multi-pole expansion (section 2) [20].…”