Binding energies of trions and biexcitons in two-dimensional semiconductors from diffusion quantum Monte Carlo calculations

Abstract

Excitonic effects play a particularly important role in the optoelectronic behavior of twodimensional (2D) semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide statistically exact diffusion quantum Monte Carlo binding-energy data for Mott-Wannier models of excitons, trions, and biexcitons in 2D semiconductors. We also provide contact pair densities to allow a description of contact (exchange) interactions between charge carriers using first-order perturbation theory. Our data indicate that the binding energy of a trion is generally larger than that of a biexciton in 2D semiconductors. We provide interpolation formulas giving the binding energy and contact density of 2D semiconductors as functions of the electron and hole effective masses and the in-plane polarizability. PACS numbers: 78.20.Bh, 73.20.Hb, The optical properties of two-dimensional (2D) semiconductors such as monolayer MoS 2 , MoSe 2 , WS 2 , WSe 2 , InSe, and phosphorene have recently attracted a great deal of interest [1][2][3][4][5][6][7][8]. Numerous observations have been made of the rich structure of the luminescence spectra of these 2D materials, in which the most pronounced features have been interpreted in terms of neutral excitons [9][10][11][12][13][14], charged excitons (trions) [15][16][17][18][19][20], and biexcitons [21][22][23], while recent experiments on higher-quality monolayer transition-metal dichalcogenide (TMDC) samples have revealed additional structure in their spectra [24][25][26][27].In this work we study a Mott-Wannier model of excitons and excitonic complexes in monolayer 2D semiconductors, taking into account the polarizability of the 2D crystal [28][29][30] and providing data to allow for a perturbative treatment of contact interactions between carriers. We use the diffusion quantum Monte Carlo (DMC) approach [31-33] to find the energies of trions and biexcitons, and we provide approximate formulas for the exciton (U), trion (E T ), and biexciton (E XX ) binding energies as functions of the in-plane polarizability and the electron and hole effective masses, which fit the DMC data to within 5%. We calculate and report contact pair densities, enabling the evaluation of perturbative corrections to the energies of charge-carrier complexes, as well as intervalley scattering, due to contact (exchange) interactions between charge carriers. The strength of the contact interactions could in principle be determined from first-principles calculations for different 2D semiconductors; alternatively, the strengths of the contact interactions can be regarded as parameters to be determined using experimental data in conjunction with the contact pair densities reported here.The energy −U − E T of a trion with one hole (h) and two electrons (e 1 and e 2 ) can be found by solving the Schrödinger equation (in Gaussian units)where m e and m h are the electron and hole effective masses and r ij = r i − r j is the position of particle i relative to particle j. The Keldysh po...

Tensor network strategies for calculating biexcitons and trions in monolayer two-dimensional materials beyond the ground state

“…Overall the order of magnitude of the calculated trion binding energies agree with current literature 24,60,61 . For the trions one drawback of the method was, that we had to guess the spin configuration, the position of the initial carrier and also to use constraints for some states.…”

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…Charge-carrier complexes play a particularly important role in the optoelec-tronic properties of layered and 2D materials. In the field of 2D materials, the DMC-calculated binding energies of trions [165][166][167] and the binding energies of larger complexes such as biexcitons and quintons (charged biexcitons) 154,168 have been reported, as have the DMC-calculated binding energies and VMC-calculated recombination rates of ion-bound charge carrier complexes in heterobilayers of transition-metal dichalcogenides. 169,170 2.…”

Dark trions and biexcitons in WS2 and WSe2 made bright by e-e scattering

“…24 using diffusion quantum Monte Carlo, shown as DFT [TB], and the radiative lifetimes of the bright exciton, semi-dark trion and biexciton.…”

“…This results in slightly higher binding energies for the dark ground state charge complexes compared to the excited states, resulting in a larger value for their energy difference E b  −  E d . The mixing parameter , (where stands for the wave function of the trion or biexciton and , is determined by the electron-electron contact pair densities24 in the trion, g T and biexciton, g B . The mixing of the dark and bright states results in a slight shift of their energies and, most importantly, in a finite radiative decay rate, of the semi-dark ( sd ) trions ( T ) and biexcitons ( B ),…”