Bound Trions in Two-Dimensional Monolayers: A Review

Abstract

Trions -- Coulomb-bound three-particle excitations composed of two like-charge carriers and one oppositely charged carrier -- are central quasiparticles in two-dimensional semiconductors. Reduced dielectric screening and quantum confinement strongly enhance their binding energies, making them robust and experimentally accessible. This review surveys theoretical and experimental advances in trion physics, emphasizing rigorous few-body approaches and the role of dielectric environment, anisotropy, and external electric and magnetic fields. We analyze computational methods for describing trions in two-dimensional configuration spaces and discuss how reduced dimensionality modifies their structure and stability. Connections to many-body phenomena, including screening, Landau-level mixing, and exciton--polaron crossover, are also highlighted.

Figures (6)

• Figure 1: Schematic representation of dipole electric fields in different dimensionalities. ($a$) The electric field of a dipole in a bulk 3D material. ($b$) Top-view schematic of a 2D monolayer, illustrating the in-plane electric field lines generated by an in-plane dipole. Fig. \ref{['fig:2D_top']}$a$ adapted from Kezerashvili2020FBProc..
• Figure 2: Typical experimentally measured trion binding energies $E_b$ in monolayer TMDCs from low-temperature optical spectroscopy. Points indicate representative mean values; error bars show reported experimental ranges, reflecting variations in dielectric environment, substrate, and carrier density. Experimental trion binding energies in monolayer TMDCs are taken from Refs. Mak2013NatMatRoss2013NatCommZhu2015SciRepJadczak2017NanoLettChen2023PRBHuang2016SciRepBiswas2023arXivYang2015ACSNanoLin2014NanoLettPlechinger2016ZhangMS2.
• Figure 3: Schematic illustration of the mass-scaled Jacobi coordinates set for three nonidentical particles forming a trion.
• Figure 4: (Color online) Schematic illustration of WSe$_{2}$ low-energy band structure and the spin-valley configurations of the constituent charge carriers. The topmost spin-subband for the valence band and the lower and upper spin-orbit split conduction band are shown. Arrows denote bands with up (down) spin. The hole has the opposite spin of the valence electron Robert2017. Light and dark rectangles indicate the bright and dark trions, respectively. $(a)$, $(b)$, $(c)$, $(d)$, and $(e)$ correspond to $X^{-}$ trions. $(g)$ and $(h)$ correspond to $X^{+}$ trions. The bright trions emit circularly polarized light in the out-of-monolayer plane direction, while the dark trions emit vertically polarized light in the in-monolayer plane direction Liu2019. Lines indicate interaction between three charged particles. The remaining configurations are the time reversal of those shown in the figure. Adapted from Ref. Kezerashvili2024PRB_TMDCHH.
• Figure 5: ($a$) Numerically obtained field dependence of the trion binding energy in monolayer MoS$_2$ in the freestanding case, on a hBN substrate, and encapsulated by hBN. The values of polarizability and hyperpolarizability (fitting parameters for the curves) are presented in Ref Cavalcante2018. ($b$) Contour map of the square modulus of the trion wave function in freestanding MoS$_2$. The left (right) column represents the exciton’s (trion’s) center of mass wave function in the absence of the electric field in the first row, and for a $E$ = 60 kV/cm field applied in the $x$ direction in the second row. The color scale goes from 0 (blue, MIN) to 0.012 (red, MAX). Adapted from Cavalcante2018.