🔬 mesoscale physics

Effect of spin-dependent tunneling and intervalley scattering in magnetic-semiconductor van der Waals heterostructures on exciton and trion polarization

This paper presents a theoretical analysis demonstrating how spin-dependent interlayer charge transfer and intervalley scattering in magnetic-semiconductor van der Waals heterostructures govern the photoluminescence polarization dynamics of excitons and trions, enabling long-distance manipulation and sign switching of valley pseudospin.

Original authors: V. N. Mantsevich

Published 2026-05-12

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CC BY 4.0

Original authors: V. N. Mantsevich

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A High-Tech Dance Floor

Imagine a very thin, two-dimensional dance floor made of a special material called a TMD (Transition Metal Dichalcogenide). On top of this floor, we place a "magnetic blanket" (a 2D magnetic layer).

In this world, tiny particles called electrons and excitons (which are pairs of an electron and a "hole," like a dance partner) are constantly moving around. The goal of this research is to understand how to control the "spin" (which way they are spinning) and the "valley" (which side of the dance floor they are on) of these particles to create a specific type of light signal called Photoluminescence (PL).

The authors built a mathematical model to predict how this light behaves when we shine a laser on it.

The Main Characters and Rules

1. The Tunneling (The Secret Tunnel)
Imagine the TMD dance floor and the magnetic blanket are separated by a small gap. Electrons can jump across this gap, but it's not easy.

The Analogy: Think of the gap as a tunnel with two lanes. One lane is a smooth, wide highway (Resonant tunneling), and the other is a bumpy, narrow dirt path (Non-resonant tunneling).
The Rule: Because the magnetic blanket is magnetized, it treats "spin-up" electrons (let's say, red shirts) differently than "spin-down" electrons (blue shirts). One color of shirt finds the smooth highway much easier to cross than the other. This is called spin-dependent tunneling.

2. The Scattering (The Crowd Jostle)
While the electrons are dancing, they bump into each other or the walls.

The Analogy: Imagine the dancers are trying to stay on one side of the room (a specific "valley"). But the crowd is jostling them, pushing them to the other side of the room. This is intervalley scattering.
The Conflict: The tunneling wants to separate the red and blue shirts (creating polarization), but the jostling (scattering) tries to mix them back up, ruining the separation.

3. The Lifetimes (How Long They Stay)

Free Excitons: These are the energetic dancers who leave the party quickly (short life).
Trions: These are groups of three dancers who stick together longer (medium life).
Localized Excitons: These are dancers who get stuck in a corner (trapped by defects) and stay for a very long time.

What the Model Found

The authors ran simulations to see what happens when we shine a laser on this system. They found that the final light signal depends entirely on a race between time.

Scenario A: The Race (Linear Polarized Light)
If we shine a standard laser (no specific spin direction):

If the tunnel is too slow: The electrons don't have time to cross the gap before they disappear. The light signal shows no special spin properties.
If the tunnel is too fast: The electrons cross the gap so quickly that the "red shirt" group disappears almost instantly, leaving only a tiny bit of "blue shirt" electrons. The signal is weak and hard to see.
The Sweet Spot: The best results happen when the tunnel is fast enough to separate the spins, but slow enough that the "red" and "blue" groups both have time to form stable dance pairs (excitons/trions) before vanishing. In this "Goldilocks" zone, you get a strong, clear signal of polarized light.

Scenario B: The Switch (Circular Polarized Light)
If we shine a laser that already has a specific spin (like a spinning top):

The Surprise: The authors discovered a "sign switch."
The Analogy: Imagine you start with a crowd that is 55% Red and 45% Blue. You expect the light to look Red. However, because the "Red" electrons can cross the tunnel much faster than the "Blue" ones, the Red group leaves the dance floor so quickly that, after a few moments, the Blue group actually becomes the majority remaining on the floor.
The Result: The light signal starts as Red (matching the laser) but then flips to Blue (matching the tunneling speed). The paper calls this "switching the PL polarization sign."

The "Dark" Side (Advanced Details)

The paper also looked at what happens if we consider "Dark Excitons."

The Analogy: These are like dancers wearing sunglasses. They are there, but they don't shine light (they are "dark").
The Finding: Sometimes, the bright dancers (who shine light) accidentally bump into a wall and turn into these "dark" dancers. The authors added this to their model. They found that while it changes the numbers slightly (quantitative change), it doesn't change the main story or the rules of the race. The main effects (tunneling vs. scattering) still hold true.

The Conclusion

The paper concludes that by carefully tuning the speed of the "tunnel" (how fast electrons move between layers) and understanding how fast the "jostling" (scattering) happens, scientists can control the spin and valley of these particles.

This allows for long-distance manipulation of these particles. Essentially, you can use the magnetic layer to "steer" the light emitted by the semiconductor layer, even though the light is generated far away from the magnet. This opens the door to better control over information stored in the "spin" and "valley" of these particles, which is crucial for future ultra-fast, low-power electronic devices.

In short: The paper explains that the color and spin of the light coming from these special sandwich structures depend on a tug-of-war between how fast electrons can escape to the magnetic layer and how fast they get bumped around inside the layer. By balancing these speeds, we can flip the light's properties on and off.

Technical Summary: Effect of Spin-Dependent Tunneling and Intervalley Scattering in Magnetic-Semiconductor van der Waals Heterostructures

Problem Statement
Transition metal dichalcogenide (TMD) monolayers offer a unique platform for valleytronics due to strong spin-valley coupling, allowing optical selection of specific valleys via circularly polarized light. However, the practical application of TMDs in valleytronic devices is hindered by the extremely short lifetime of exciton valley polarization (on the order of picoseconds). While external magnetic fields can lift valley degeneracy, they are often too strong for device integration. An alternative approach involves magnetic proximity effects in van der Waals heterostructures, where a 2D magnetic layer induces magnetization in the TMD. Although experimental studies on systems like WS $_2$ /CrI $_3$ and MoS $_2$ /CrBr $_3$ have demonstrated enhanced photoluminescence (PL) circular polarization, a consistent theoretical framework is lacking. Specifically, no existing model simultaneously accounts for the interplay between spin-dependent interlayer charge transfer (tunneling) and intervalley scattering of excitons and trions, which are the two dominant mechanisms governing PL dynamics in these heterostructures.

Methodology
The authors propose a general theoretical model based on a system of rate equations describing the time evolution of spin-up and spin-down electron occupancies ( $n_{k\sigma}$ ), free excitons ( $N^X_{k\sigma}$ ), localized excitons ( $N^{X_{loc}}_{k\sigma}$ ), and positive trions ( $N^T_{k\sigma}$ ). The model is designed to be applicable to a wide class of TMD/magnetic material heterostructures without relying on fitting parameters; all parameters are derived directly from experimental measurements.

Key components of the theoretical framework include:

Spin-Dependent Tunneling: The model incorporates two distinct tunneling channels (resonant and non-resonant) for electrons moving from the TMD conduction band to the 2D magnetic layer. The tunneling rates ( $\Gamma_\uparrow, \Gamma_\downarrow$ ) differ due to the spin-split sub-bands of the magnetic material and the Type-II band alignment. Hole tunneling is neglected due to large effective mass and valence band offsets.
Quasi-Particle Dynamics: The equations account for the formation of bright excitons and trions, the capture of excitons into localized states (via deep traps), and their subsequent radiative recombination.
Scattering Mechanisms: The model explicitly includes intervalley scattering times ( $T^X_{sc}, T^T_{sc}$ ) for free excitons and trions.
Generalization: The model is extended to include intravalley scattering processes involving spin-forbidden and momentum-forbidden dark excitons, mediated by spin-orbit interaction and electron-phonon coupling.

The analysis focuses on the PL circular polarization degree ( $P_{X(T)}$ ), defined by the difference in population between spin-up and spin-down quasi-particles, under both linearly and circularly polarized laser excitation.

Key Results
The study reveals that the PL polarization dynamics are governed by the competition between the timescales of electron tunneling, intervalley scattering, and radiative lifetimes.

Linear Polarization Excitation:
- Tunneling vs. Lifetime: The degree of PL polarization is highly sensitive to the ratio between electron tunneling rates and quasi-particle lifetimes.
  - If tunneling is slower than the lifetimes, spin imbalance does not manifest, resulting in negligible polarization.
  - If tunneling is faster than all lifetimes, polarization is pronounced but the PL signal amplitude is weak due to rapid carrier depletion.
  - The most experimentally favorable regime occurs when tunneling is faster than trion and localized exciton lifetimes but slower than free exciton lifetimes. In this regime, free exciton polarization dominates initially, followed by sustained, well-resolved polarization for trions and localized excitons.
- Scattering Impact: Fast intervalley scattering suppresses valley polarization. The damping effect is significantly stronger for free excitons than for trions, as trions possess a much longer valley-polarization lifetime.
Circular Polarization Excitation:
- Sign Switching: A novel mechanism for switching the sign of PL circular polarization is identified. This occurs when the initial valley polarization (induced by the laser) is low (e.g., 5%), and the concentration of electrons capable of fast tunneling exceeds that of the opposite spin. As the system evolves, the faster-tunneling majority spin depletes, allowing the slower-tunneling minority spin to dominate the remaining population, thereby reversing the PL polarization sign.
- Initial Polarization Dependence: For higher initial polarizations (e.g., 10%), the tunneling process does not have sufficient time to invert the population ratio before recombination, resulting in a sign change relative to the initial state but not a full temporal switch.
Role of Dark Excitons:
- The inclusion of intravalley scattering between bright and dark excitons (spin-forbidden and momentum-forbidden) results in only quantitative changes to the PL polarization dynamics, not qualitative ones. The primary mechanism remains the interplay between interlayer charge transfer and intervalley scattering.

Significance and Claims
The paper claims to provide the first self-consistent theoretical analysis that unifies spin-dependent interlayer charge transfer and intervalley scattering to explain PL polarization peculiarities in TMD/magnetic van der Waals heterostructures. The authors assert that their model:

Successfully describes experimental observations across various TMD/magnetic combinations (e.g., MoS $_2$ /CrI $_3$ ) using only experimentally determined parameters.
Offers a mechanism for the long-distance manipulation of exciton and trion behaviors in multilayer structures through spin-selective charge transfer.
Reveals a controllable method to switch the sign of PL polarization via quasi-particle dynamics under circularly polarized excitation, dependent on the initial valley polarization and tunneling rates.
Provides a generalizable framework applicable to a wide class of magnetic-semiconductor heterostructures, facilitating the effective control of spin and valley pseudospin for potential spintronic and valleytronic applications.

The work does not propose new experimental setups or specific future applications beyond the control of spin/valley degrees of freedom, maintaining a focus on the theoretical elucidation of the underlying physical mechanisms.