Heavy-hole bilayer trions of transition metal dichalcogenides by analytical treatment to model He-isoelectronic ions upto dipole factor of Green’s function expansion of Coulomb interaction

• Published in: Physics open Vol. 11; p. 100107
• Main Authors: Sharma, Shivalika, Kapil, Bharti, Aggarwal, Priyanka, Hazra, Ram Kuntal
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2022; Elsevier
• Subjects: Binding energy of trions; Coulomb interaction; Current-density; Green’s function expansion; He-isoelectronic ions’ ground state; Third order Perturbation; He-isoelectronic ions’ ground state; Binding energy of trions; Green’s function expansion; Third order Perturbation; Coulomb interaction; Current-density
• ISSN: 2666-0326; 2666-0326
• DOI: 10.1016/j.physo.2022.100107

Electronic structures of heavy-hole trions and He-isoelectronic ions show dependence on transitions among two-electron bound states constituted of hydrogenic orbitals for which Coulomb (exchange) interaction causes nontrivial secular divergence to Schrödinger equation (SE). Coulomb interaction between a pair of electrons triggers nonadiabatic transitions due conical intersections and larger vibrational amplitudes of nuclei. Therefore, existing state-of-art theories ubiquitously urge analytical integrals for multipoles of electrostatic Green’s function expansion. Born–Oppenheimer (BO) approximation separates the hamiltonian into electronic and nuclear coordinates at adiabatic limit. Employing associated Laguerre polynomial and Whittaker-M function basis sets of hydrogenic orbitals for the pair of electrons (electronic coordinate) furnishes analytical, terminable, simple and finitely summed integrals in terms of Lauricella functions. The exact integrals also remedy the difficulty arisen from different scaling factors of bound states for higher order perturbation calculations. Analytical perturbation calculations for monopole and dipole factors using singly and doubly excited states (|n2sn4s〉, |n2pn4p〉) with spherical and dumbbell symmetries show sufficient convergence of ground-state energy correction of He-isoelectronic series within 0.20–6.89% of reported results. Calculation of current-density with ground-state upto first order perturbation correction clearly shows that singly and doubly excited spherically symmetric states do not contribute to local current of He-isoelectronic series for monopole factor. Binding energies of heavy-hole trions of transition metal dichalcogenides (TMDCs) are found to be in good agreement with experimentally observed values. •Exact analytical treatment to Coulomb interactions in terms of Green’s function expansion upto third order perturbation calculations for all bound hydrogenic orbitals upto dipole factor (l=0,1; s- and p-orbitals) for He-isoelectronic species.•Ground state energies of He-isoelectronic species map excellently with experimental values.•Current-density of ground-state upto first and second order perturbation corrections inducting monopole factor only which clearly shows that singly and doubly excited spherically symmetric states do not contribute to local current of He-isoelectronic series.•Binding energies of heavy-hole trions of bilayer TMDCs. [Display omitted]