Excitons and trions in monolayer transition metal dichalcogenides: A comparative study between the multiband model and the quadratic single-band model

Abstract

The electronic and structural properties of excitons and trions in monolayer transition metal dichalcogenides are investigated using both a multi-band and a single-band model. In the multiband model we construct the excitonic Hamiltonian in the product base of the single-particle states at the conduction and valence band edges. We decouple the corresponding energy eigenvalue equation and solve the resulting differential equation self-consistently, using the finite element method (FEM), to determine the energy eigenvalues and the wave functions. As a comparison, we also consider the simple single-band model which is often used in numerical studies. We solve the energy eigenvalue equation using the FEM as well as with the stochastic variational method (SVM) in which a variational wave function is expanded in a basis of a large number of correlated Gaussians. We find good agreement between the results of both methods as well as with other theoretical works for excitons and we also compare with available experimental data. For trions the agreement between both methods is not as good due to our neglect of angular correlations when using the FEM. Finally, when comparing the two models, we see that the presence of the valence bands in the muti-band model leads to differences with the single-band model when (interband) interactions are strong.

Marrying Excitons and Plasmons in Monolayer Transition-Metal Dichalcogenides

“…When comparing the results in this work with experimental findings, one should recall that the theory only evaluates the pair function and its renormalization due to coupling with plasmons. Accordingly, the theory does not capture optical transitions that are associated with threebody complexes [21,22,[63][64][65][66][67][68][69][70], Fermi polarons [27,28], and exciton optical transitions next to localization centers [71]. Nonetheless, the theory in this work covers two important regimes.…”

“…Trions cease to exist at very large densities since their effective radius is larger than the average distance between electrons of the Fermi sea. The latter is proportional to 1= ffiffiffi n p , while the trion extension is of the order of 3-5 nm in ML-TMDs [69,70]. The main focus of this work is on the high-doping regime, and we attribute the observed optical transition to a new type of quasiparticle where the exciton is coupled to a shortwave charge fluctuation.…”

Localized interlayer complexes in heterobilayer transition metal dichalcogenides

“…where q is the wave vector, d is the interlayer distance, and r * and r * are the corresponding monolayer screening lengths. Previous works on monolayer TMDs have focused on interactions of the Keldysh form 19 to study their excitonic spectra and optical properties 6,[20][21][22][23] . For bilayers, this potential form is obtained from Eqs.…”

Dynamical screening in monolayer transition-metal dichalcogenides and its manifestations in the exciton spectrum

“…where H 0 and Y 0 are the zero-order Struve and Neumann special functions, and = ( t + b )/2. In spite of the recent popularity of the Rytova-Keldysh dielectric function [32,43,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88], one should bear in mind that it is a correct description at macroscopic distances compared to the lattice constant (r a). This problem is sharpened in ML-TMDs wherein the lattice constant is comparable to the thickness of the ML, and both are not excessively smaller than the Bohr radius.…”