Trion clustering structure and binding energy in 2D semiconductor materials: Faddeev equations approach

Abstract

In this work, we develop the basic formalism to study trions in semiconductor layered materials using the Faddeev equations in momentum space for three different particles lying in two dimensions. We solve the trion Faddeev coupled integral equations for both short-range one-term separable Yamaguchi potential and Rytova-Keldysh (RK) interaction applied to the MoS${}_2$ layer. We devise two distinct regularization methods to overcome the challenge posed by the repulsive electron-electron RK potential in the numerical solution of the Faddeev equations in momentum space. The first method regulates the repulsive interaction in the infrared region, while the second regulates it in the ultraviolet region. By extrapolating the trion energy to the situation without screening, the two methods gave consistent results for the MoS${}_2$ layer with a trion binding energy of $-49.5(1)$~meV for the exciton energy of $-753.3$~meV. We analyzed the trion structure for the RK and Yamaguchi potentials in detail, showing their overall similarities and the dominant cluster structure, where the strongly bound exciton is weakly bound to an electron. We found that this property is manifested in the dominance of two of the Faddeev components over the one where the hole is a spectator of the interacting electron pair.

16 pages, 11 figues, 8 tables

References in corpus (11)

• Observation of giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor
• Strong light-matter coupling in two-dimensional atomic crystals
• k.p theory for two-dimensional transition metal dichalcogenide semiconductors
• Probing excitonic states in ultraclean suspended two-dimensional semiconductors by photocurrent spectroscopy
• Excitons and trions in monolayer transition metal dichalcogenides: A comparative study between the multiband model and the quadratic single-band model
• Stark shift of excitons and trions in two-dimensional materials
• Trion and Biexciton in Monolayer Transition Metal Dichalcogenides
• Three-Nucleon Bound State in a Spin-Isospin Dependent Three Dimensional Approach
• The Relativistic Three-Body Bound State in a 3D Formulation
• A three-dimensional momentum-space calculation of three-body bound state in a relativistic Faddeev scheme
• D-dimensional three-body bound-state problem with zero range interactions

Cited by in corpus (5)

• The charge and mass symmetry breaking in the $KK\bar{K}$ system
• Brueckner $G$-matrix approach to two-dimensional Fermi gases with the finite-range attractive interaction
• Efficient calculation of trion energies in monolayer transition metal dichalcogenides
• Four-body bound states in momentum space: the Yakubovsky approach without two-body $t-$matrices
• Relativistic Faddeev 3D Equations for Three-Body Bound States Without Two-Body $t-$Matrices