Eur. Phys. J. Plus (2022) 137: 809
https://doi.org/10.1140/epjp/s13360-022-02970-7

Regular Article

Binding energies and current density of heavy-hole trions of monolayer transition metal dichalcogenides: analytical perturbation treatment of Coulomb interaction with 2D H-like basis set

¹ Physical Division, Department of Chemistry, University of Delhi, 110007, Delhi, India
² Asia Pacific Center for Theoretical Physics, POSTECH, 37673, Pohang, Korea

^d pcrkhiacs@gmail.com, rkhazra@chemistry.du.ac.in

Received: 21 March 2022
Accepted: 17 June 2022
Published online: 12 July 2022

Abstract

Heavy-hole trions of transition metal dichalcogenides (TMDCs) have 2D counterpart $H^{-}$. Thus, 2D He-isoelectronic ions can be the ideal model for it even within Born–Oppenheimer (BO) approximation depending on versatile mass ratios. Schr$\ddot{o}$dinger equation of such systems is a long-standing problem because of secular divergence of Coulomb interactions. Analytical description of Coulomb (exchange) potential by algebraic-calculus Green’s function multipole expansion for ground-state energy (GSE) of 2D He-isoelectronic ions and binding energies of TMDCs has become one of indispensable methods. Employing associated Laguerre polynomial and Whittaker-M or Bessel functions in planar hydrogenic orbitals furnishes exact, terminable, simple and finitely summed integrals in terms of Lauricella functions for multipoles and also remedies the difficulties due to different scaling factors of higher-order perturbation calculations. Monopole and dipole factors are exploited upto third-order perturbation corrections of GSE with singly and doubly excited hydrogenic orbitals. The orbitals with circular and dumbbell symmetries exhibit GSEs differing 1.82% from reported results for 2D He atom. Binding energies of heavy-hole trions of TMDCs are observed to be in good agreement with the experimentally reported results.