Nonequilibrium dynamics of high energy transitions in monolayer WSe$_{2}$

This study combines broadband ultrafast transient absorption spectroscopy with first-principles calculations to reveal that high-energy optical transitions in monolayer WSe$_{2}$ exhibit significantly slower formation and relaxation dynamics than band-edge excitons due to the phonon-mediated formation of momentum-dark excitons.

The Gist

Imagine a single layer of a special material called WSe2 (Tungsten Diselenide) as a tiny, bustling city where electrons are the citizens. In this city, there are specific neighborhoods called "valleys" where these citizens like to hang out.

The Usual Suspects (The A and B Excitons)
Most of the time, scientists study the "bright" citizens who live in the main downtown area (the K valleys). When you shine a light on them, they react instantly. It's like ringing a doorbell and having someone answer immediately. These are the famous "A" and "B" excitons, and they are well understood.

The Mystery at the High-Rise (The D Transition)
However, this paper looks at the "high-energy" parts of the city—places far above the downtown area. Specifically, they focused on a high-energy event called the "D transition."

When the researchers shone a specific light to wake up the downtown citizens (the A excitons), they expected the high-energy citizens (the D transition) to react immediately, just like the downtown ones. But something strange happened.

The "Delayed Arrival" Analogy
Think of the downtown citizens as people who get a text message and instantly reply.
Now, imagine the high-energy D citizens are like people who receive a message but have to take a long, winding bus ride to get to the party before they can reply.

The paper found that when the downtown citizens were excited, the D transition didn't show up right away. Instead, it took a tiny, but measurable, amount of time to "build up." It was as if the signal was delayed, waiting for something to happen before it could appear.

The Solution: The "Dark" Bus Ride
Why the delay? The researchers used powerful computer simulations to map out the city's layout. They discovered that the high-energy D citizens live in a different neighborhood (the Q valleys) that is hard to reach directly.

Here is the mechanism they found:

1. The Start: You excite the downtown citizens (A excitons).
2. The Transfer: These excited citizens don't stay put. They hop onto a "phonon bus" (a vibration in the material's structure) and travel to the Q valley neighborhood.
3. The Dark Stop: In this new neighborhood, they become "dark excitons." These are like citizens who are invisible to the naked eye (they don't absorb or emit light easily) but are very important.
4. The Blockage: Once these "dark" citizens arrive in the Q valley, they crowd the area. This crowding prevents other electrons from doing what they usually do, which creates a "blockage" (Pauli blocking).
5. The Signal: This blockage is what we see as the D transition signal. Because the citizens had to take the bus ride to get there first, the signal appears with a delay.

What They Didn't Find
The researchers also checked if the temperature of the room changed how fast this bus ride happened. They found that it didn't matter if the room was hot or cold; the delay remained the same. This told them that the "bus ride" is driven by the material's own internal vibrations (spontaneous phonon emission), not by heat from the outside.

In Summary
This paper is like a detective story about a delayed reaction in a microscopic city. The scientists found that a high-energy signal (the D transition) is slow to appear because it relies on excited electrons traveling from one part of the material to another via vibrations, becoming "dark" along the way, and only then creating the signal we can measure. This helps us understand how energy moves and settles in these tiny materials, specifically revealing a hidden pathway involving "dark" states that we couldn't see before.

Technical Summary

Technical Summary: Nonequilibrium dynamics of high energy transitions in monolayer WSe2

Problem Statement
Monolayer transition-metal dichalcogenides (TMDs) exhibit strong light-matter interactions and form tightly bound excitons, making them promising for optoelectronics. While the dynamics of the low-energy band-edge excitons (A and B) are well-characterized, the non-equilibrium behavior of high-energy optical transitions (C, D, and E) remains less understood. Previous studies on other TMDs (e.g., MoS2) suggested that high-energy resonances possess distinct relaxation pathways, often involving intervalley scattering. However, a clear connection between the specific electronic states involved in these high-energy transitions and their ultrafast formation dynamics has been lacking. Specifically, the mechanisms governing the delayed response observed in certain high-energy transitions compared to the instantaneous response of band-edge excitons require further elucidation.

Methodology
The authors employed a combined experimental and theoretical approach to investigate the ultrafast dynamics of monolayer WSe2 (1L-WSe2):

• Experimental: Broadband ultrafast transient absorption spectroscopy was performed on large-area 1L-WSe2 samples on SiO2 substrates at 77 K. The setup utilized a femtosecond Ti:sapphire laser system with a tunable optical parametric amplifier or second harmonic generation for pump pulses (~150 fs resolution). An ultrabroadband supercontinuum probe (1.6–3.7 eV) tracked the differential transmission ($\Delta T/T$) across the visible to ultraviolet spectral range. Experiments involved resonant pumping of the A exciton (1.70 eV) as well as high-energy pumping of the C (2.53 eV) and D (3.10 eV) transitions. Temperature dependence was also explored.
• Theoretical: First-principles calculations were conducted using many-body perturbation theory (MBPT). Electronic properties were derived using the GW approximation, while optical properties and excitonic effects were evaluated by solving the Bethe–Salpeter Equation (BSE). The authors mapped the excitonic wavefunctions across the Brillouin zone (BZ) to identify the momentum distribution of states contributing to specific absorption peaks (A, B, C, and D). They also calculated exciton dispersion relations to analyze momentum-dependent (dark) exciton states.

Key Results

1. Distinct Dynamics of the D Transition: Upon resonant excitation of the A exciton, the transient signals for the A and B excitons, as well as the C transition, exhibit an instantaneous rise limited by the pump pulse width, followed by multicomponent decay. In contrast, the D transition (centered around 3.0 eV) displays a unique delayed build-up component. This signal rises instantaneously (within resolution limits) but is followed by a distinct, slower rise and a plateau, occurring on a sub-picosecond timescale.
2. Pump Energy and Temperature Dependence:
   • When the sample is excited directly at the C or D transition energies, the delayed rise component of the D signal disappears, although its relaxation remains slower than other transitions. This indicates the delay is specific to the scattering pathway from the photoexcited A exciton population.
   • The delayed dynamics of the D transition are independent of temperature (up to the range tested), suggesting the process is not mediated by the absorption of thermally activated phonons but rather by spontaneous phonon emission.
3. Theoretical Origin:
   • Simulations reveal that the A and B excitons are localized at the K/K' valleys. The C peak involves transitions primarily around K/K' with minor contributions from Q/Q' valleys.
   • The D peak, however, shows a significant contribution from transitions involving the Q/Q' valleys in the conduction band.
   • Crucially, the zero-momentum (optically bright) D transition shares the same conduction-band electronic states as finite-momentum, optically dark excitons located at the Q and M points (specifically $q=Q$ and $q=M$).
   • The authors propose that after resonant photoexcitation of the bright A exciton, the population undergoes phonon-mediated intervalley scattering into these energetically favorable, momentum-dark exciton states. The Pauli blocking induced by the population of these dark states (which share the conduction band states with the D transition) leads to the observed delayed bleaching signal.

Key Contributions

• The study identifies and characterizes a distinct, delayed formation timescale for the D excitonic transition in 1L-WSe2, contrasting it with the instantaneous dynamics of lower-energy excitons.
• It establishes a direct link between the electronic structure of high-energy transitions and their non-equilibrium dynamics, attributing the delay to the scattering of bright A excitons into momentum-dark excitons.
• The work provides a comprehensive theoretical mapping of the excitonic landscape in 1L-WSe2, highlighting the role of Q/Q' valleys and finite-momentum dark excitons in shaping the broadband optical response.

Significance and Claims
The paper claims that understanding the formation and coupling of high-energy excitons is essential for a complete picture of the excitonic landscape in TMDs. By revealing that high-energy transitions provide direct access to momentum-indirect and dark excitons, the work elucidates the mechanisms governing ultrafast carrier relaxation and intervalley scattering. The authors state that these insights are critical for understanding the broadband optical response and many-body interactions that emerge on sub-picosecond timescales, which are fundamental to the material's behavior under high fields and photon energies. The study does not propose specific new applications but emphasizes that clarifying these dynamics is a prerequisite for advancing technological applications relying on efficient energy redistribution.