Doping-Induced Brightening of Dark Excitons and Trions in a WSe$_2$ Monolayer

This study demonstrates that electrostatic doping in a gated WSe$_2$ monolayer induces a strong, nontrivial, and asymmetric dependence in the magnetic-field brightening rates of dark excitons and trions, revealing distinct carrier interaction mechanisms that govern the optical response of doped transition metal dichalcogenides.

The Gist

Imagine a single layer of a special material called WSe2 (Tungsten Diselenide) as a tiny, ultra-thin stage. On this stage, particles called excitons (pairs of an electron and a "hole," which is like a missing electron) dance around. These dancers are the source of light when the material is excited.

However, not all dancers are visible to the audience (us, the scientists). Some dancers are "bright" and shine easily. Others are "dark" or "grey"—they are there, but they are shy and refuse to emit light under normal conditions. In the world of physics, these are called dark excitons and dark trions (a trion is just a dancer with an extra partner, making it charged).

The Problem: The Invisible Dancers

For a long time, scientists could see the bright dancers but couldn't easily study the dark ones, even though the dark ones are crucial for how this material works. It's like trying to study a secret society that refuses to show up at the party.

The Solution: The Magnetic "Spotlight" and the "Gate"

The researchers in this paper used two main tools to make these shy dancers visible:

1. The Magnetic Spotlight: They applied a strong magnetic field lying flat against the stage (in-plane). Think of this as a special spotlight that forces the "dark" dancers to mix with the "bright" ones. Once mixed, the dark dancers are forced to shine, revealing their presence.
2. The Electronic Gate: They used a voltage (like a dimmer switch) to control how many extra dancers (electrons or holes) were on the stage. They could turn the stage into an n-type (extra electrons), p-type (extra holes), or neutral (balanced) environment.

What They Found: The "Brightening" Dance

The team watched what happened when they turned on the magnetic spotlight at different settings of the gate. They discovered that the "dark" dancers didn't all react the same way; their willingness to shine depended heavily on who else was on the stage.

Here is the breakdown of their findings using simple analogies:

• The Neutral Dancer (Dark Exciton, $X_D$):

  • Behavior: This dancer is very shy. They only show up and shine when the stage is perfectly balanced (neutral).
  • The Reaction: If you add too many extra electrons or holes (doping), this dancer gets overwhelmed and disappears from the light. It's like a quiet person at a party who leaves as soon as the crowd gets too rowdy.
  • Result: They shine brightest at the "neutrality point" and fade away quickly if you add more charge.

• The Charged Dancers (Dark Trions, $T_D^-$ and $T_D^+$):

  • Behavior: These are the dancers who need extra partners to exist. One needs extra electrons ($T_D^-$), and the other needs extra holes ($T_D^+$).
  • The Reaction: Unlike the neutral dancer, these guys love the crowd. The more extra electrons or holes you add to the stage, the more they shine when the magnetic spotlight hits them.
  • The Asymmetry: Interestingly, the "electron-hungry" dancer ($T_D^-$) shines much more intensely than the "hole-hungry" dancer ($T_D^+$) when the stage is crowded. It's as if the electron crowd is more energetic and makes the trion dance harder.

The "Why": A Simple Story of Formation

The researchers built a mathematical model (a set of rules) to explain why this happens. Imagine the stage as a factory:

1. In the Electron Crowd (n-type): The factory is flooded with electrons. The bright dancers quickly grab an extra electron to become a "dark trion." Because there are so many electrons, the dark trions form easily and become the main act. The neutral dark exciton gets crowded out.
2. In the Hole Crowd (p-type): The factory is flooded with holes. The bright dancers grab a hole to become a "positive dark trion." However, the process is slightly slower here. The bright dancers don't convert to dark trions as aggressively as they do in the electron crowd.
3. The Result: This explains why the "electron-hungry" trion shines so much brighter than the "hole-hungry" one. The crowd of electrons is more efficient at forcing the transformation.

The Big Picture

The paper concludes that by simply turning a voltage knob (the gate), you can control which "dark" dancers are on stage and how brightly they shine when you use a magnetic field.

• Key Takeaway: The "dark" states aren't just background noise; they are the main players that dictate how the material responds to light and electricity, but only if you know how to "dope" (add charge to) the material correctly.
• The Analogy: Think of the material as a radio. The "bright" excitons are the stations you can hear clearly. The "dark" excitons are the stations that are usually static. The researchers found that by adding specific amounts of "static" (doping) and using a "tuner" (magnetic field), they could suddenly make those hidden stations broadcast loud and clear.

This discovery helps scientists understand how to control the light and electricity in these tiny materials, which is essential for building future high-speed electronics and light-based computers.

Technical Summary

1. Problem Statement

Monolayer semiconducting transition metal dichalcogenides (S-TMDs), specifically Tungsten Diselenide (WSe2), possess a unique electronic structure where the ground state exciton is "dark" (optically inactive) due to spin-forbidden transitions. While electrostatic gating allows for continuous tuning of carrier density (from n-type to p-type), the behavior of these dark excitonic complexes under external perturbations remains poorly understood.

Specifically, there is a lack of systematic knowledge regarding:

• How electrostatic doping influences the activation (brightening) of dark excitons ($X_D$) and dark trions ($T_D^-$ and $T_D^+$) in an in-plane magnetic field.
• The distinct carrier interaction mechanisms governing the formation and recombination of neutral versus charged dark complexes across different doping regimes.
• The quantitative relationship between carrier density and the brightening efficiency of these states.

2. Methodology

The researchers employed a combination of device fabrication, low-temperature magneto-optical spectroscopy, and theoretical modeling.

• Sample Fabrication: A heterostructure was constructed consisting of a WSe2 monolayer sandwiched between hexagonal boron nitride (hBN) layers, with a graphite back-gate and Platinum (Pt) contacts. This architecture enables precise electrostatic control of the carrier density in the WSe2 layer.
• Experimental Setup:
  • Temperature: Measurements were conducted at cryogenic temperatures ($T \approx 10$ K).
  • Magnetic Field: Experiments utilized the Voigt geometry (magnetic field $B$ parallel to the monolayer plane) with fields up to 16 Tesla.
  • Spectroscopy: Micro-photoluminescence (PL) spectroscopy with high spatial resolution ($\sim 1$ $\mu$m) was used to track emission spectra.
• Experimental Protocol:
  • Gate voltage ($V_g$) was continuously tuned to access three distinct regimes: n-type ($V_g > -0.35$ V), charge-neutral ($V_g \approx -0.45$ V), and p-type ($V_g < -0.55$ V).
  • PL spectra were recorded at various magnetic fields to observe the evolution of emission intensities for bright ($X_B$, $T^\pm$) and dark ($X_D$, $T_D^\pm$) complexes.
• Data Analysis:
  • Spectral deconvolution using Lorentzian functions to isolate specific emission lines.
  • Fitting of integrated intensities ($I_D$) against magnetic field strength using the relation $I_D = I_0 + \alpha B^2$, where $\alpha$ represents the brightening factor.
  • Development of a rate-equation model to describe the steady-state populations of excitons and trions under electron and hole doping.

3. Key Contributions

• Systematic Doping Study: The first comprehensive mapping of dark exciton and trion brightening dynamics across the full spectrum of electrostatic doping (n-type, neutral, p-type) in WSe2.
• Quantification of Brightening Asymmetry: Discovery of a pronounced asymmetry in brightening efficiency between neutral dark excitons ($X_D$) and charged dark trions ($T_D^-$ and $T_D^+$), as well as between the trions themselves.
• Theoretical Framework: Introduction of a rate-equation model that successfully explains the non-trivial dependence of brightening on carrier density, attributing it to distinct formation pathways for electrons vs. holes.

4. Key Results

A. Spectral Evolution and Regimes

• Charge-Neutral Regime: The spectrum is dominated by the neutral dark exciton ($X_D$). The brightening factor $\alpha_{X_D}$ peaks at the neutrality point ($\approx 1.2$ T$^{-2}$) and is rapidly quenched as doping increases.
• n-type Regime: As electron density increases, $X_D$ emission is suppressed, and the dark negative trion ($T_D^-$) becomes dominant. The brightening factor $\alpha_{T_D^-}$ increases significantly with electron density, reaching 3.5 T$^{-2}$ at high doping.
• p-type Regime: Hole doping leads to the emergence of the dark positive trion ($T_D^+$). Its brightening factor $\alpha_{T_D^+}$ also increases with hole density, reaching 2.2 T$^{-2}$.
• Asymmetry: A critical finding is the asymmetry between n-type and p-type doping. The brightening of $T_D^-$ (n-type) is significantly stronger than that of $T_D^+$ (p-type). Furthermore, the neutral $X_D$ is highly sensitive to doping, vanishing quickly in both regimes, whereas the bright exciton ($X_B$) persists in p-type but is suppressed in n-type.

B. Brightening Dynamics

• The intensity of dark complexes scales quadratically with the in-plane magnetic field ($B^2$), confirming the mechanism of bright-dark mixing induced by the field.
• At 16 T, the $T_D^-$ emission in the n-type regime exhibits the highest intensity among all dark complexes, followed by $T_D^+$ in the p-type regime, with $X_D$ being the weakest.

C. Theoretical Insights (Rate-Equation Model)

The authors propose a model based on three observations:

1. Energy Levels: Dark trions ($T_D^\pm$) have lower energy than $X_D$, favoring thermal occupation.
2. Formation Efficiency:
   • n-type: Bright excitons ($X_B$) efficiently relax into $T_D^-$ via electron capture. This leads to a high generation rate ($g$) for dark trions and a depletion of $X_D$.
   • p-type: The conversion of bright excitons to dark complexes is less efficient. Consequently, the generation rate ($e_g$) for $X_D$ is lower, resulting in a smaller population of $T_D^+$ compared to $T_D^-$ under similar conditions.
3. Population Dynamics: The model predicts that once the capture rate exceeds the radiative decay rate ($\gamma n \tau \gtrsim 1$), trions dominate the population. The lower generation rate in p-type doping explains the observed asymmetry in brightening factors ($\alpha_{T_D^-} > \alpha_{T_D^+}$).

5. Significance

• Control of Dark States: The study establishes electrostatic doping as a powerful tool for controlling the population and optical visibility of dark excitonic complexes in S-TMDs.
• Valleytronics and Spintronics: Understanding the activation of dark states is crucial for valleytronic applications, as these states often carry valley information that is otherwise inaccessible.
• Many-Body Physics: The results provide deep insights into many-body interactions, specifically the competition between exciton formation, trion binding, and carrier scattering in 2D materials.
• Device Optimization: The findings suggest that the optical response of WSe2-based devices can be tuned by doping levels, which is vital for designing efficient light-emitting devices or quantum emitters based on dark states.

In conclusion, this work resolves the long-standing ambiguity regarding the doping-dependent behavior of dark excitons in WSe2, revealing a complex interplay between carrier density, energy landscapes, and formation kinetics that dictates the optical properties of these 2D semiconductors.