Sub-nm range momentum-dependent exciton transfer from a 2D semiconductor to graphene

Using time-resolved photoluminescence spectroscopy on MoSe$_2$/graphene heterostructures, this study demonstrates that sub-nanometer-range exciton transfer is governed by charge tunneling rather than dipolar interactions, as evidenced by a consistent $\approx 2.5$ ps transfer time that vanishes when a 1 nm hexagonal boron nitride spacer is introduced.

The Gist

The Big Picture: A High-Speed Energy Relay Race

Imagine you have two very special, ultra-thin sheets of material stacked on top of each other like a microscopic sandwich.

• The Top Sheet (MoSe₂): Think of this as a "solar panel" made of atoms. When you shine a light on it, it gets excited and creates tiny energy packets called excitons (like little balls of energy bouncing around).
• The Bottom Sheet (Graphene): Think of this as a super-fast "energy highway" or a sponge that loves to soak up energy.

The scientists wanted to answer a simple question: How fast does the energy jump from the top sheet to the bottom sheet, and how does the distance between them change the game?

The Experiment: The "Staircase" and the "Spacer"

To test this, the researchers built a very clever setup:

1. The Staircase: Instead of a flat sheet of graphene, they made a "staircase" where the graphene gets thicker step-by-step (from 1 layer up to 6 layers). They placed their energy-generating sheet (MoSe₂) right on top of this staircase.
2. The Spacer: They also built a version where they put a tiny, invisible wall (a thin layer of Boron Nitride) between the energy sheet and the graphene highway. They tested walls of different thicknesses, from almost non-existent to about 1 nanometer thick (that's roughly 1/100,000th the width of a human hair).

The Discovery 1: The "Tunnel" Effect (Direct Contact)

When the two sheets were touching (or separated by just a single atom), the energy transfer was incredibly fast.

• The Result: The energy jumped from the top sheet to the graphene in about 2.5 picoseconds.
  • Analogy: A picosecond is to a second what a second is to about 31.7 million years. It is practically instantaneous.
• The Surprise: It didn't matter if the graphene was 1 layer thick or 6 layers thick. The speed was almost exactly the same.
• The Lesson: The energy doesn't care how big the "sponge" is; it only cares about the very first layer it touches. It's like a person jumping off a diving board into a pool; whether the pool is 1 foot deep or 10 feet deep, the splash happens the moment they hit the water.

How does it happen? The scientists concluded this is Charge Tunneling.

• Analogy: Imagine the energy particles are ghosts. When the sheets are touching, the ghosts can simply "phase" through the barrier and appear on the other side instantly. They don't need to climb over; they just walk through the wall.

The Discovery 2: The "One Nanometer" Cutoff

When the researchers added a spacer (the Boron Nitride wall) that was just 1 nanometer thick, the magic stopped.

• The Result: The energy transfer vanished. The top sheet kept its energy, glowing brightly just like it did when there was no graphene underneath.
• The Lesson: The "ghost tunneling" only works if the gap is smaller than 1 nanometer. Once you put a tiny wall in the way, the ghosts can't pass through.

The Mystery: Why did the light dim so much?

Here is the tricky part. The scientists noticed that when the sheets were touching, the light coming from the top sheet didn't just get dimmer because the energy moved fast; it got much dimmer than the speed of the transfer alone could explain.

They realized there were two types of energy particles (excitons):

1. The "Cool" Ones (Bright Excitons): These are the calm, slow-moving particles that create the light we see. They jump to the graphene via the "tunneling" method described above.
2. The "Hot" Ones (Hot Excitons): These are the energetic, fast-moving particles that are too fast to be seen directly (they are "dark").

The "Förster" Analogy:
The scientists found that while the "Cool" particles use the tunneling method, the "Hot" particles use a different trick called Förster Resonance Energy Transfer (FRET).

• Analogy: Imagine the "Cool" particles are walking through a door (tunneling). But the "Hot" particles are like people shouting across a canyon. Even if they are a bit further apart, their "shout" (electromagnetic waves) can be heard by the graphene, which grabs the energy.
• This "shouting" method depends on how many layers of graphene are there. The more layers (the bigger the canyon wall), the better it catches the shout. This explains why the light got dimmer as they added more graphene layers, even though the transfer speed stayed the same.

Why Does This Matter?

This research is a big deal for the future of technology:

• Solar Cells: If we can control how fast energy moves between layers, we can make solar panels that capture sunlight and turn it into electricity much more efficiently.
• Super-Fast Computers: Understanding how to move energy at the speed of light (or faster) between atom-thin materials helps us build computers that are tiny, fast, and use very little power.
• The "Rulebook": Before this, scientists were guessing how these materials talked to each other. Now, they have a clear rulebook: If the gap is tiny (<1nm), use the "Tunnel" (fast transfer). If the gap is bigger, the transfer stops.

Summary

The scientists discovered that in a microscopic sandwich of special materials, energy jumps from the top to the bottom in the blink of an eye (2.5 picoseconds) as long as they are almost touching. This happens because the energy "tunnels" through the tiny gap. However, if you put even a tiny wall (1 nanometer) between them, the connection breaks. This helps us understand how to build the next generation of super-efficient energy devices.

Technical Summary

1. Problem Statement

Van der Waals heterostructures combining transition metal dichalcogenides (TMDs) and graphene are promising platforms for optoelectronics and fundamental 2D physics. While efficient photoluminescence (PL) quenching and picosecond-scale energy/charge transfer in TMD/graphene systems are well-documented, the microscopic mechanisms governing these processes remain debated. Key open questions include:

• What is the dominant transfer mechanism: charge tunneling or dipole-dipole (Förster-type) energy transfer?
• How does the transfer rate depend on the interlayer distance (specifically in the sub-nanometer regime) and the number of graphene layers?
• How do these mechanisms differ between "bright" excitons (near-zero center-of-mass momentum, $X_0$) and "hot" excitons (finite momentum, $X_h$)?

Theoretical models often struggle to quantitatively predict rates in the sub-nm limit where orbital overlap becomes significant, necessitating precise experimental validation.

2. Methodology

The authors employed time-resolved photoluminescence (TRPL) spectroscopy with high temporal resolution ($\sim$1 ps) to investigate exciton dynamics in cryogenic conditions ($T \approx 6-16$ K).

Sample Design:

• Sample S1 (Direct Coupling): A monolayer of $MoSe_2$ was placed directly on a "staircase-like" graphene flake, allowing comparison across domains with $N=1$ to $N=6$ graphene layers. The $MoSe_2$ was capped with thin hBN ($<10$ nm). The substrate ($SiO_2$) thickness was tuned (500 nm) to place the $MoSe_2$ at an optical field node, suppressing radiative recombination to enhance the visibility of non-radiative transfer.
• Samples B1 & B2 (Decoupled Systems): $MoSe_2$ was separated from a single-layer graphene flake by hexagonal boron nitride (hBN) spacers of varying thicknesses (1 nm, 2 nm, and 5 nm) to test the distance dependence of the transfer.

Techniques:

• PL Mapping: To characterize spectral shifts, intensity ratios (neutral excitons $X_0$ vs. trions $X^*$), and spatial homogeneity.
• TRPL: To measure exciton lifetimes ($\tau$) and rise times, distinguishing between radiative recombination and non-radiative transfer channels.
• Theoretical Modeling: Comparison of experimental data against electrodynamic models for Förster Resonance Energy Transfer (FRET) and analytical calculations of charge tunneling.

3. Key Results

A. Direct Coupling ($MoSe_2$/Graphene)

• PL Quenching: Direct contact with graphene causes a massive reduction in PL intensity (quenching factor $>10\times$). The quenching factor increases slightly with the number of graphene layers ($N$), saturating for $N \geq 3$.
• Exciton Lifetime: The lifetime of bright excitons ($X_0$) drops from $\sim 8.9$ ps (reference $MoSe_2$) to $\sim 2.2 - 2.5$ ps in the heterostructure.
• Layer Independence: Crucially, the transfer time ($\sim 2.5$ ps) is marginally dependent on the number of graphene layers ($N$). The transfer is essentially determined by the first graphene layer.

B. Distance Dependence (hBN Spacer)

• Critical Cutoff: When an hBN spacer of 1 nm (3 atomic layers) is inserted between $MoSe_2$ and graphene, the exciton dynamics revert to those of bare $MoSe_2$ (lifetimes $\sim 10-15$ ps).
• Implication: The transfer mechanism is extremely short-range. A 1 nm barrier is sufficient to completely suppress the transfer, ruling out long-range dipolar interactions as the primary driver for $X_0$ quenching.

C. Mechanism Differentiation ($X_0$ vs. $X_h$)

• Bright Excitons ($X_0$): The observed sub-nm range and independence from $N$ strongly suggest direct charge tunneling (sequential tunneling of electrons and holes) is the dominant mechanism for $X_0$ quenching. FRET is theoretically inefficient for $X_0$ because momentum conservation forbids transfer for excitons with near-zero momentum ($q_X \approx 0$).
• Hot Excitons ($X_h$): The total PL quenching factor ($Q_{tot}$) is significantly larger than what can be explained by the reduction in $X_0$ lifetime alone. This discrepancy implies that hot excitons (finite momentum) are transferred much faster (sub-ps) and more efficiently.
• Role of FRET: While FRET is negligible for $X_0$, the authors argue it contributes significantly to the quenching of hot excitons. Theoretical models show FRET rates scale with momentum ($q_X^2$) and distance, aligning with the observed $N$-dependence of the total quenching factor.

4. Key Contributions

1. Quantification of Transfer Time: Established a consistent exciton transfer time of $\sim 2.5$ ps for bright excitons in tightly coupled TMD/graphene systems at cryogenic temperatures.
2. Mechanism Identification: Provided definitive experimental evidence that charge tunneling (not FRET) governs the dynamics of bright excitons in the sub-nm regime, as evidenced by the sharp cutoff at 1 nm separation.
3. Momentum-Dependent Dynamics: Demonstrated that while bright excitons transfer via tunneling, hot excitons likely utilize a FRET-mediated channel, explaining why total PL quenching increases with graphene thickness while the bright exciton lifetime does not.
4. Experimental Benchmark: Offered a robust dataset distinguishing between tunneling and dipolar regimes, challenging existing theoretical models that often overestimate FRET efficiency in 2D-2D systems at sub-nm distances.

5. Significance

• Fundamental Physics: The work clarifies the interplay between orbital overlap (tunneling) and dipolar interactions in 2D materials, resolving ambiguities regarding momentum conservation in energy transfer.
• Device Engineering: Understanding that charge tunneling dominates at sub-nm distances is critical for designing efficient optoelectronic devices, such as ultrafast photodetectors and energy harvesting systems. It suggests that for efficient energy funneling, minimizing the dielectric spacer is essential, but for specific applications requiring long-range coupling, dipolar mechanisms may still play a role for specific excitonic species.
• Theoretical Impact: The results provide a necessary constraint for theoretical frameworks, urging a shift from pure FRET models to hybrid models incorporating charge tunneling for sub-nm TMD/graphene interfaces.