Transient Trion Population Dynamics

Updated 3 January 2026

Transient trion populations are time-dependent ensembles of charged excitons generated by ultrafast optical or electrical excitation in semiconductors.
Their formation and decay kinetics, modeled through coupled rate equations and probed by ultrafast spectroscopy, reveal distinct temporal and spectral signatures.
Understanding these dynamics advances optoelectronic applications such as valleytronics and energy transport in low-dimensional quantum materials.

A transient trion population comprises non-equilibrium, time-dependent populations of charged excitons (trions) generated following ultrafast optical, electrical, or charge-transfer excitation in semiconductors and correlated quantum materials. Transient trions arise from dynamic processes such as exciton–carrier scattering, phonon-assisted carrier capture, or ultrafast charge transfer and are tracked using spectroscopic probes including transient absorption, time-resolved photoluminescence, and time- and angle-resolved photoemission. Their formation and decay kinetics, ultrafast build-up, and spectral signatures define a measurable and tunable platform for exploring many-body interactions and non-equilibrium quasiparticle dynamics in low-dimensional materials.

1. Physical Mechanisms for Transient Trion Generation

Transient trions can be formed via various non-equilibrium protocols:

Exciton–Carrier Scattering: In n-doped monolayer TMDs like MoSe₂, neutral excitons ( $X$ ) generated by resonant optical pumping interact with background free electrons ( $N_e$ ) to form negative trions ( $T^-$ ) via Coulomb-mediated scattering, $X + e^- \rightarrow T^-$ , on a timescale $\tau_f \sim 1/(k_f N_e)$ , where $k_f$ is the trion-formation rate coefficient (Singh et al., 2015).
Ultrafast Charge Transfer: In van der Waals heterostructures such as Gr/MoS₂, indirect optical doping excites only the graphene, enabling sub-picosecond electron transfer across a Schottky barrier into MoS₂, rapidly populating trionic states (Wang et al., 2024).
Above-Band-Gap Excitation: In MoS₂, above-gap photons generate hot carriers that relax into the K/K' valleys at different rates, creating a temporal imbalance of electrons and holes. Neutral excitons capture these excess carriers, inducing a delayed build-up of trion population over 10–30 ps (Mujeeb et al., 25 Aug 2025).
Direct Photoinduced Formation in Correlated Semiconductors: In quasi-1D Ta₂NiS₅, pump-induced population of conduction and valence bands can yield a bright, localized in-gap state identified as a transient trion, dynamically formed even in undoped crystals (Sidilkover et al., 27 Dec 2025).

These non-equilibrium pathways yield characteristic temporal signatures: fast <1 ps formation for geminate trions, 10–30 ps delayed build-up for exciton–carrier conversion, and sub-100 fs trion emergence seen in tr-ARPES for one-step processes in correlated systems.

2. Quantitative Models and Rate Equations

The dynamics of transient trion populations are captured by coupled rate equations describing exciton and trion number densities and their interconversion:

For exciton (N_X) and trion (N_T) populations (Singh et al., 2015, Sayer et al., 2023): $\begin{aligned} \frac{dN_X}{dt} &= -k_f\,n_e\,N_X - \frac{N_X}{\tau_X} + k_d N_T \ \frac{dN_T}{dt} &= +k_f\,n_e\,N_X - k_d N_T - \frac{N_T}{\tau_T} \end{aligned}$

$k_f$ : trion-formation rate constant (Coulomb-assisted capture)
$k_d$ : trion-dissociation rate
$\tau_X$ , $\tau_T$ : exciton and trion lifetimes (radiative plus non-radiative)
$n_e$ : free carrier density

For multichannel generation (direct and indirect) (Mujeeb et al., 25 Aug 2025): $\begin{aligned} \frac{dN_x}{dt} &= \alpha_x G - \gamma_x N_x + \beta_{tx} N_t - \beta_{xt}' n N_x \ \frac{dN_t}{dt} &= \alpha_t n G - \gamma_t N_t - \beta_{tx} N_t + \beta_{xt}' n N_x \ \frac{dn}{dt} &= \alpha_n G + \beta_{tx} N_t - \beta_{xt}' n N_x - \alpha_t n G \end{aligned}$ where $N_x =$ exciton population, $N_t =$ trion, $n =$ excess carriers, $G =$ photogeneration rate, and $\gamma_{x,t} =$ decay rates.

Trion–trion annihilation (TTA)—a non-radiative Auger recombination channel—introduces a bimolecular loss term: $\frac{dn_t}{dt} = -\frac{n_t}{\tau} - k_{TTA} n_t^2$ where $k_{TTA}$ is the Auger annihilation coefficient (Chatterjee et al., 2022).

In time-resolved ARPES of quasi-1D systems, extended models include one- and two-particle channels for exciton and trion formation and include fluence scaling (Sidilkover et al., 27 Dec 2025).

3. Experimental Probes and Observables

Ultrafast trion populations are resolved using a variety of experimental protocols:

Pump–Probe Differential Reflectivity/Absorption: The trion formation manifests as a finite rise time (ps-scale) in trion-resonant cross-peaks (XT), modeled by convolution of exponential rise and decay (Singh et al., 2015).
Time-Resolved Photoluminescence (TRPL): PL intensity from the trion feature exhibits non-instantaneous rise and non-exponential decay in the presence of strong trion–trion annihilation or multiple relaxation pathways (Chatterjee et al., 2022, Kim et al., 2023).
Transient Absorption Spectroscopy (TAS): The trion-induced bleach at the trion resonance exhibits a delayed rise (10–30 ps) under above-band-gap excitation, directly mapping exciton-to-trion conversion (Mujeeb et al., 25 Aug 2025).
Time- and Angle-Resolved Photoemission (tr-ARPES): Transient trion populations give rise to localized, in-gap features with distinct binding energies, asymmetries, and time evolution. The trion feature is red-shifted by the binding energy and can be uniquely separated from the exciton signal (Sidilkover et al., 27 Dec 2025, Wu et al., 24 Nov 2025).

Quantitative extraction of formation and decay times is performed via phenomenological fits: $n_T(t) = n_{T}^{\rm max}\left[1 - e^{-t/\tau_{\rm rise}}\right]e^{-t/\tau_{\rm decay}}$ and spectral features are interpreted in the context of many-body Hamiltonians or variational wavefunction projections (Wu et al., 24 Nov 2025).

4. Temporal and Spectral Signatures

Transient trion populations are characterized by several hallmark features:

Rise Time (Formation Time): Ranges from $\lesssim 1$ ps for resonant/geminate formation (Singh et al., 2015), to $15$–$25$ ps for above-gap, carrier relaxation-mediated build-up (Mujeeb et al., 25 Aug 2025), and up to 350 fs in 1D correlated systems (Sidilkover et al., 27 Dec 2025).
Decay Time (Lifetime): Typically, trion lifetimes are shorter than those of neutral excitons (e.g., 3–6 ps vs 8–12 ps in MoS₂ (Sayer et al., 2023)), but can be prolonged in the presence of charged defects (as in Gr/MoS₂ (Wang et al., 2024)).
Energy Shifts and Linewidths: Trion features are red-shifted relative to neutral excitons by the trion binding energy ( $\sim$ 25–135 meV depending on material) and often display broad, asymmetric lineshapes resulting from their composite nature (Wu et al., 24 Nov 2025). The lineshape, binding energy, and oscillator strength vary systematically with carrier density, doping, and time delay after excitation (Sayer et al., 2023).
Population Ratios and Tunability: The trion/exciton ratio is tunable via gate voltage, chemical potential (in charge-transfer devices), or pump fluence, and reflects the efficiency of transient doping or nonlinear formation processes (Wang et al., 2024, Chatterjee et al., 2022).

Table: Characteristic Experimental Timescales (Representative Values)

Material / System	$\tau_{f}$ (Rise)	$\tau_{T}$ (Decay)	Reference
MoSe₂ (n-doped, TMD)	1.6–2.3 ps	10–20 ps	(Singh et al., 2015)
MoS₂ (TMD, above-gap)	15–25 ps	200–300 ps	(Mujeeb et al., 25 Aug 2025)
Gr/MoS₂ heterostructure	<0.3 ps (CT)	1.0–1.05 ps	(Wang et al., 2024)
Ta₂NiS₅ (1D, bulk)	0.35 ps	1.5–2 ps	(Sidilkover et al., 27 Dec 2025)
WSe₂/MoSe₂ moiré trions	<1 ps (bright)	30–50 ns	(Kim et al., 2023)

5. Influence of Disorder, Many-Body Effects, and Annihilation Channels

Disorder and many-body interaction effects crucially dictate the nature of transient trion populations:

Exciton Mobility Edge: In disordered monolayer TMDs, the spread in formation time ( $\tau_f$ ) across the inhomogeneous exciton line reflects the presence of both localized and delocalized excitons, leading to a pronounced $\sim$ 50% increase in $\tau_f$ across a few meV energy range—a direct signature of a disorder-induced mobility edge (Singh et al., 2015).
Trion–Trion Annihilation (TTA): Auger-type TTA is observed in monolayer WS₂ under high excitation density, with the annihilation rate $k_{TTA}$ tunable over an order of magnitude by gate voltage and spectral overlap (Chatterjee et al., 2022). This nonlinear process leads to accelerated decay and an intensity-dependent suppression of trion emission.
Bright–Dark State Mixing: In moiré systems (e.g., WSe₂/MoSe₂), splitting and phonon-mediated coupling between bright and dark trion states produce bi-exponential PL transients, with temperature-activated mixing and population redistribution (Kim et al., 2023).
Carrier–Defect Interactions: In indirect optical doping (e.g., Gr/MoS₂), repulsive Coulomb interaction between negatively charged trions and defect states reduces non-radiative capture rates, slightly increasing trion lifetimes relative to excitons (Wang et al., 2024).

6. Implications for Optical and Transport Properties

Transient trion dynamics impact both optical emission and charge/energy transport:

Photoluminescence Dynamics: The kinetics of trion formation and decay govern the distribution of emission intensity between excitonic and trionic photoluminescence lines on picosecond to nanosecond timescales. Failure to correctly account for ETF (exciton-to-trion formation) can lead to misestimation of radiative lifetimes or quantum yields (Singh et al., 2015, Kim et al., 2023).
Photoconductivity and Energy Transport: Since trions carry net charge, their dynamical population modulates the transient conductivity following excitation, with the trion build-up and decay setting the timescale for photoconductive response and energy transfer (Singh et al., 2015).
Ultrafast Valleytronics and Polarization Effects: In moiré-trion systems, the slow (hundreds of ns) valley relaxation of trions enables transient preservation of valley polarization, with potential application in quantum optics and valleytronic devices (Kim et al., 2023).

7. Spectral Signatures in Time-Resolved Photoemission

Transient trion populations have direct, analytically predictable signatures in tr-ARPES (Wu et al., 24 Nov 2025, Sidilkover et al., 27 Dec 2025):

Asymmetric In-Gap Features: Trion peaks are red-shifted from the conduction band by the sum of the trion binding energy and residual correlation contributions. In positive trions, the spectral function exhibits an asymmetric tail, with a well-defined high-energy cutoff but no strict lower bound.
Inverted Exciton Replicas (Negative Trions): The photoemission of negative trions results in the appearance of inverted images of the exciton band for multiple Rydberg states, providing momentum-resolved identification of trion states.
Ultrafast Rise and Decay: The time evolution of momentum- and energy-integrated photocurrent at the trion feature directly yields formation and decay constants, enabling quantitative dynamic tracking on sub-ps to ps timescales.

These spectral fingerprints serve as unambiguous evidence of transient trion populations, and their systematic mapping provides direct access to underlying many-body physics and non-equilibrium processes.

In summary, the transient trion population is a dynamic, non-equilibrium ensemble of charged excitons arising from ultrafast excitation in semiconductors and low-dimensional quantum materials, governed by formation and recombination kinetics, many-body interactions, and material disorder. Its evolution and spectral consequences are now quantitatively accessible across a range of materials and device platforms by ultrafast spectroscopic techniques and are directly linked to the manipulation of optoelectronic functionality and collective quantum phenomena (Singh et al., 2015, Chatterjee et al., 2022, Mujeeb et al., 25 Aug 2025, Wang et al., 2024, Sayer et al., 2023, Sidilkover et al., 27 Dec 2025, Kim et al., 2023, Wu et al., 24 Nov 2025).