Optically Inactive Dark Trions in 2D Semiconductors

• Optically inactive dark trions are charged exciton complexes in 2D TMDs that remain non-emissive due to strict spin and momentum selection rules.
• Advanced spectroscopy reveals that defect-induced symmetry breaking, phonon-assistance, and Coulomb-mediated processes can partially brighten these trions.
• Their tunable binding energies, extended lifetimes, and distinct magnetic responses make them promising for valleytronics, quantum photonics, and many-body physics studies.

Optically inactive dark trions are three-particle (charged exciton) states in two-dimensional semiconductors, especially transition metal dichalcogenide (TMD) monolayers, whose radiative recombination is forbidden by spin or momentum selection rules and thus possess negligible direct optical activity. Their identification, physical origin, selection rules for radiative transitions, and mechanisms for "brightening" via higher-order or symmetry-breaking processes have become central topics in the spectroscopy of atomically thin semiconductors.

1. Definition, Classification, and Electronic Structure

Dark trions in monolayer TMDs are bound complexes formed by two like charges (electrons/electrons or holes/holes) and one oppositely charged carrier, where the recombination channel inherits strict selection rules from the underlying band structure and excitonic manifold. The two principal classes are:

• Spin-forbidden (intravalley) dark trions: Both minority carriers (e.g. electrons in a negative trion) and the recombining hole occupy the same valley (K or K′), but the electron–hole pair involved in recombination has parallel spins due to strong spin–orbit splitting. The interband dipole matrix element vanishes for in-plane polarized photons, making these states optically inactive in far-field emission (Borghardt et al., 2020, Liu et al., 2019, Zinkiewicz et al., 2020).
• Momentum-forbidden (intervalley) dark trions: The extra carrier occupies an opposite valley relative to the recombining pair (e.g. the trion is composed of two holes in K, the electron in K′). Momentum conservation forbids one-photon emission into the vacuum since the photon's in-plane momentum is negligible compared to the valley separation (Liu et al., 2020, Zinkiewicz et al., 2020).

A canonical notation is:

• $|X^{-}_{K,K}\rangle_\text{spin-dark}$ (intravalley),
• $|X^{-}_{K,K'}\rangle_\text{momentum-dark}$ (intervalley) (Liu et al., 2020).

In monolayer WSe$_2$ and WS$_2$, prevailing conduction-band spin–orbit orderings ensure that the lowest-energy negative trion state is a spin-forbidden dark trion, with binding energies typically ~14–16 meV (Liu et al., 2019, Li et al., 2019, Arora et al., 2019).

2. Optical Selection Rules and Mechanisms of Inactivity

The absence of direct radiative decay from dark trions is dictated by the symmetry of the electronic Bloch states and the electric-dipole selection rules. For direct emission, the relevant interaction Hamiltonian is

$\hat{H}_\text{int} = -\mathbf{d}\cdot\mathbf{E}$

where $\mathbf{d}$ is the dipole operator. For a spin-forbidden trion, $⟨0|\hat{d}|X^{-}_{K,K}⟩ = 0$ unless spin–orbit or symmetry-breaking perturbation admixes bright character. For a momentum-dark trion, the matrix element

$⟨0|\hat{H}_\text{int}|X^{-}_{K,K'}⟩ = 0$

due to the momentum orthogonality between the initial state (finite valley difference) and the photon (essentially zero in-plane momentum), as shown explicitly in both group-theoretical and $k\cdot p$ models (Liu et al., 2020, Zinkiewicz et al., 2020, Arora et al., 2019).

Consequently, dark trions possess out-of-plane dipole moments only, with photonic emission either strongly suppressed or radiated at angles far from the monolayer normal, often escaping conventional detection schemes (Borghardt et al., 2020).

3. Experimental Spectroscopy and Identification

Experimental access to dark trions relies on advanced photoluminescence (PL), gate-dependent, time-resolved, and magneto-spectroscopy:

• Gate-tuning: Electrostatic doping enables continuous tuning of dark trion species between negative (extra electron) and positive (extra hole) charge, with sharp control over trion PL intensity, binding energy (~14–16 meV), and radiative lifetime ($\tau\sim$0.4–1.3 ns, ∼100× longer than bright trions) (Liu et al., 2019, Li et al., 2019).
• Polarization-resolved imaging: Collection geometries with high numerical aperture objectives can access the in-plane polarized emission component from out-of-plane dipoles, revealing unique spatial patterns (e.g., ring-like, radially polarized beams) (Borghardt et al., 2020).
• Magneto-optical response: Out-of-plane magnetic fields ($B_z$) lift the valley degeneracy, splitting dark trion lines according to their $g$-factors:

$\Delta E_{Z}=g\mu_B B$

with characteristic $g$-factors: $g\sim-9$ to $-10$ for spin-dark, $g\sim-13$ for intervalley dark trions, distinct from $g\sim-4$ for bright counterparts (Liu et al., 2020, Liu et al., 2019, Zinkiewicz et al., 2020, Zinkiewicz et al., 2020).

A table of typical energy splittings is provided for key materials:

Material	$\Delta$ (Bright–Dark Trion) [meV]	Predominant Dark Trion Type
WSe$_2$	+19 ($\pm$3)	Spin-forbidden (K,K)
WS$_2$	+19 ($\pm$3)	Spin-forbidden (K,K)
MoSe$_2$	–6 ($\pm$3)	Bright lowest, dark higher
MoS$_2$	–2 ($\pm$3)	Nearly degenerate

Binding energies and splittings are corroborated by GW–BSE ab-initio calculations (Arora et al., 2019).

4. Brightening Mechanisms: Multipath and Symmetry-Breaking Processes

Despite their nominally "dark" nature, dark trions can be "brightened" via several extrinsic and intrinsic mechanisms:

(a) Defect- and symmetry-breaking:

Point defects (e.g., sulfur vacancies), rough substrate-induced symmetry breaking, or coupling to localized surface plasmons may admix bright and dark trion wavefunctions, producing finite oscillator strength (Cao et al., 21 Jun 2025, Raha et al., 11 Dec 2025). For example, sulfur vacancies in WS$_2$ enhance local spin–orbit coupling, enabling mixing terms:

$$H_{\mathrm{SOC}}^{\mathrm{defect}} \sim \lambda_d L\cdot S$$

which yield a finite dipole $$M_{cv}^\text{dark} \sim \frac{\lambda_d}{\Delta E}M_{cv}^\text{bright}$$ and observable PL (Cao et al., 21 Jun 2025). Plasmonic enhancement (Purcell effect $\propto Q/V$) increases radiative rates for out-of-plane dipoles (Raha et al., 11 Dec 2025).

(b) Intervalley electron–electron (e-e) or hole–hole (h-h) scattering:

Coulomb-mediated intervalley processes admix bright and dark trion sectors, producing so-called "semi-dark" eigenstates. The mixing amplitude (matrix element $\mu_T$) leads to new eigenstates:

$$E_{\pm} = \frac{E_b + E_d}{2} \pm \frac{1}{2}\sqrt{(E_b - E_d)^2 + 4|\mu_T|^2}$$

The lower branch, the "semi-dark" trion, acquires partial bright character with radiative lifetime

$$\tau_{\text{sd}} \sim \frac{2\Delta_{SO}^2}{|\mu_T|^2}\tau_X$$

yielding lifetimes on the order of 5–10 ps for typical TMDs (Danovich et al., 2017, Raha et al., 11 Dec 2025, Jindal et al., 4 Jun 2024). [Editor's term: "semi-dark trion" for mixed states by $e$-$e$ scattering.]

(c) Phonon-assisted emission:

Interaction with zone-center (Γ) or zone-corner (K) chiral phonons can supply the requisite momentum and/or spin, producing "phonon replica" peaks redshifted by the phonon energy (e.g., 21.4 meV for Γ-point $E''$-mode in WSe$_2$; 26.6 meV for K-point) (Liu et al., 2020, Liu et al., 2019, Zinkiewicz et al., 2020). Selection rules analyzed by group theory require strict matching of valley and phonon chirality: e.g., left-handed photon emitted with right-handed chiral phonon in the K valley, producing characteristic valley-locked phonon-sidebands (Liu et al., 2019, Liu et al., 2020).

(d) Second-order Coulomb-assisted recombination:

In monolayer WSe$_2$, dark trion recombination may proceed via a two-step process, whereby $e$–$e$ or $h$–$h$ interactions mediate a transition into a bright excitonic intermediate state before radiative decay, with the rate scaling as $|V_{ee}d/(\Delta_{c}+i\gamma)|^2$, providing brightened emission features below the pure dark trion peaks (Jindal et al., 4 Jun 2024). This mechanism is distinct from phonon-assistance by leveraging higher-lying spin-split bands.

5. Theoretical Models, Binding Energies, and Internal Structure

Variational approaches, GW–BSE calculations, and three-body Schrödinger equation solutions have been deployed to quantify dark trion energies. The measured splitting between exciton and trion is a composite of the bright–dark exciton difference ($\Delta_X$) and the true trion binding ($\Delta E_{\rm bind}$):

$$\Delta E_{\rm exp} = \Delta_X + \Delta E_{\rm bind}$$

Dark excitons and corresponding trions are more strongly bound than their bright analogues due to mass enhancement in the lower conduction band and the absence of short-range repulsive exchange (Christianen et al., 22 Jul 2025). The trion wavefunction becomes asymmetric, with a shorter bond length for the dark exciton pair and longer for the additional electron (Christianen et al., 22 Jul 2025).

For momentum-dark trions in "Mexican-hat" systems (e.g., InSe), the ground-state is realized at finite center-of-mass momentum ($Q \neq 0$), resulting in optically inactive modes unless phonon-assistance returns the system to $Q=0$ (Burke et al., 10 Feb 2025). Plasmonic or substrate engineering may similarly be exploited to redistribute oscillator strength.

6. Distinct Optical and Magnetic Fingerprints

Key experimental signatures of optically inactive dark trions include:

• Suppressed or absent in linear absorption/reflectivity, but visible in low-temperature PL via phonon-assisted or symmetry-broken channels (Arora et al., 2019, Zinkiewicz et al., 2020, Liu et al., 2019).
• Long radiative lifetimes: nanosecond-scale for "pure" dark states, picosecond-scale if intermediated by bright mixing (Liu et al., 2019, Zinkiewicz et al., 2020, Danovich et al., 2017).
• Distinct Zeeman response: $g$-factors ($|g|\sim9$ for spin-dark, $|g|\sim13$ for intervalley dark), providing separation from bright trion signals (Liu et al., 2020, Zinkiewicz et al., 2020).
• Magnetic and electric field control: Valley splitting, charge state, binding energies, and polarization response are tunable via gating and fields (Li et al., 2019, Liu et al., 2020).
• Phonon replica lines: Energy redshifts matching specific phonon energies, appearing with valley-locked polarization signatures (Liu et al., 2019, Zinkiewicz et al., 2020, Liu et al., 2020).
• Ring-shaped or radially polarized emission patterns in angle-resolved PL, revealing the out-of-plane dipole structure (Borghardt et al., 2020).

7. Applications and Outlook

The ability to manipulate dark trion states—via substrate design, defect engineering, plasmonic enhancement, and charge or field control—has central implications for:

• Valleytronics and quantum photonics: Dark trions enable valley-specific optoelectronic switching, information storage, and long-lived neutral or charged excitonic states (Li et al., 2019, Jindal et al., 4 Jun 2024).
• Room-temperature quantum light sources: Plasmonic or defect-induced brightening can extend dark trion emission well above cryogenic temperatures, offering pathways to robust, wavelength-tunable emitters with distinctive polarization (Raha et al., 11 Dec 2025, Cao et al., 21 Jun 2025).
• Probing many-body physics: Their distinct spectral, temporal, and magnetic signatures provide direct access to many-body interactions, spin–valley physics, and Coulomb correlations in TMD monolayers, with ARPES techniques uniquely sensitive to dark-trion signatures, otherwise "invisible" to optical methods (Meneghini et al., 14 Nov 2025).
• Control via material alloying and heterostructure engineering: Mixed-chalcogen systems (e.g., WSSe), hBN encapsulation, and gating platforms further expand the landscape for trion engineering and quantum optical phenomena (Olkowska-Pucko et al., 2022).

Through a combination of advanced spectroscopy, theory, and materials engineering, optically inactive dark trions have evolved from an enigmatic many-body state to a lever for exploring and controlling the quantum optical properties of 2D semiconductors (Liu et al., 2020, Jindal et al., 4 Jun 2024, Danovich et al., 2017, Liu et al., 2019).