Binding energies and chemical potential of neutral and charged exciton-complexes of transition metal dichalcogenides/anisotropic 2-D quantum dots in magnetic field by exact multi-pole expansion of coulomb correlations

摘要

Anisotropy is inevitable fate of charged excitonic complexes due to difference in dielectric constants, effective masses, charges of carriers, magnetic field, applied gate voltage etc along in-plane and out-of-plane directions of transition metal dichalcogenides (TMDCs-MX2; M = Mo, W; X = S, Se, Te) as well as in anisotropic quantum dots. In the present paper, the multi-dynamic attractive and scattering interactions among neutral and charged exciton-complexes (N-excitonic, N = 2,3,4, ....) amongst the various charge carriers, i.e., e - h, e - e, h - h has been elegantly accounted for by the use of Lauricella functions and the subsequent application of Chuvandermonde identity. An exact variational treatment for such complex and intertwined interactions in presence of anisotropy has been achieved by employing multi-pole expansion. The result of which emerges as a unique single-summed, finite, exact and absolutely terminating integrals. The calculated binding energies for various N-excitonic systems have been found to be consistent with the previous experimental and computational studies. A discussion of energy spectra, chemical potential (mu) and addition energy (Delta mu) are presented. The results thus obtained indicate increase in binding energy and bosonic character of the multi-excitonic complexes with magnetic field. The effects of anisotropy are manifested through the interplay between many-body coulomb interactions resulting in the dissolution of degeneracy of excitonic states.