🔬 mesoscale physics

Steady-state cooperative emission of interlayer excitons in atomically thin light-emitting diodes

This study demonstrates steady-state cooperative emission of electrically injected interlayer excitons in an atomically thin 2D TMD light-emitting diode, evidenced by distinctive photon correlation signatures that align with a many-body quantum master equation model of superradiance.

Original authors: Andrés M. Mier Valdivia, Pavel E. Dolgirev, Grace H. Chen, Nadine Leisgang, Andrew Y. Joe, Stefan Ostermann, Deepankur Thureja, Yongxin Zeng, Dapeng Ding, Daniel Rhodes, Bumho Kim, Song Liu, Takashi T

Published 2026-10-21

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CC BY 4.0

Original authors: Andrés M. Mier Valdivia, Pavel E. Dolgirev, Grace H. Chen, Nadine Leisgang, Andrew Y. Joe, Stefan Ostermann, Deepankur Thureja, Yongxin Zeng, Dapeng Ding, Daniel Rhodes, Bumho Kim, Song Liu, Takashi Taniguchi, Kenji Watanabe, James C. Hone, Susanne F. Yelin, Hongkun Park, Mikhail D. Lukin, Philip Kim

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

Light is usually thought of as a stream of independent particles, each photon traveling its own path without regard for its neighbors. However, when a large group of light-emitting atoms or molecules is packed tightly enough into a space smaller than the wavelength of the light they produce, they can begin to act as a single, coordinated unit. In this state, the emission of one photon encourages the others to emit in step, creating a burst of light that is far more intense and correlated than the sum of its parts. This phenomenon, known as cooperative emission, has been observed in gases and crystals, but achieving it in solid materials at cryogenic temperatures has remained a significant challenge. The difficulty lies in the fact that solid-state materials are often messy and disordered, causing the delicate quantum connections between emitters to break apart almost instantly. Understanding how to maintain these connections in a stable, electrically driven system could unlock new ways to create ultra-efficient light sources and study the strange behaviors of quantum matter.

A team of researchers has now demonstrated this cooperative behavior in a new type of atomically thin light-emitting diode. They constructed a device using two different layers of a semiconductor material, each only a single molecule thick, stacked on top of one another. When an electric voltage is applied, electrons from one layer and holes (the absence of electrons) from the other layer are drawn together to form a special particle called an interlayer exciton. These excitons are unique because the electron and the hole are separated by a tiny gap, giving them a long life and making them easier to control with electric fields. The researchers engineered their device so that these excitons would not spread out randomly across the material. Instead, they used the geometry of the device's edges to create a strong electric field that funneled the excitons into a very small, confined area near the corners of the stack. This confinement was crucial, as it forced the excitons to stay close enough together to interact with one another through the light they emit.

To see if these excitons were truly working together, the scientists measured the timing of the photons coming out of the device. They looked for a specific pattern in the arrival times of the light particles. If the light were coming from independent sources, the photons would arrive at random intervals. Instead, they observed a distinct signature of cooperation: the photons arrived in tight clusters, or bunches, followed by a brief pause where no photons arrived at all, and then another cluster. This pattern, which repeated over time, is a clear fingerprint of a system where the emitters are linked. The researchers found that this behavior only appeared when the excitons were in a specific, neutral state or when they were weakly trapped by localized defects in the material. When they added too many free electrons or holes to the system, creating a dense "sea" of charge carriers, the cooperative effect vanished immediately. This suggests that the excitons need to be somewhat isolated and stationary to maintain their connection, rather than moving freely through the material.

The team also discovered that the strength of this effect depended heavily on how quickly the device could refill the excitons after they emitted light. By adjusting the electrical current, they could control the rate at which new excitons were created. When the refilling was slow, the excitons had time to organize themselves into a highly correlated state before the next batch arrived, leading to very strong bunching of the light. When the refilling was fast, the system became chaotic, and the light returned to a random, uncorrelated state. The researchers used a mathematical model to describe this process, treating the excitons as a group of emitters that are constantly being knocked out of their excited state by light emission and then slowly recharged by the electric current. This model successfully predicted the complex timing patterns they observed, including the long delays between photon clusters.

Importantly, the researchers ruled out several other explanations for their findings. They showed that the effect was not caused by a phase transition where the excitons condensed into a single quantum state, as the emission remained confined to the edges rather than spreading throughout the device. They also determined that the effect was not due to simple thermal fluctuations or the interaction of the excitons with free-moving electrons, as the behavior changed drastically when the nature of the charge carriers shifted from localized to delocalized. The results point to a new form of light-matter interaction where the steady flow of electricity drives a collective quantum state without the need for an optical cavity or laser mirrors. This work establishes a platform for studying how light can mediate interactions between particles in a solid, opening the door to new types of electronic devices that operate on the principles of quantum optics.

Technical Summary: Steady-State Cooperative Emission of Interlayer Excitons in Atomically Thin Light-Emitting Diodes

Problem and Motivation
Cooperative emission, or superradiance, arises when an ensemble of emitters confined within an optical wavelength volume radiates in a correlated manner, leading to enhanced photon bunching. While theoretically established by Dicke in 1954 and observed in various systems ranging from molecular gases to quantum dots, realizing this phenomenon in solid-state materials is challenging. Solid-state emitters typically suffer from rapid decoherence due to environmental coupling, disorder, and phonon scattering. Furthermore, standard photoluminescence (PL) studies of interlayer excitons (IXs) in transition metal dichalcogenide (TMD) heterobilayers face inherent limitations: off-resonant excitation generates uncorrelated intralayer pairs that relax into IXs, coherent excitation can imprint phases that obscure spontaneous correlations, and diffraction limits the excitation area to $\sim 1 \mu m^2$ , often preventing the satisfaction of the Dicke criterion ( $V \lesssim \lambda^3$ ) for collective decay. The authors aim to overcome these constraints by engineering an electrically driven system where IXs are incoherently injected and spatially confined, allowing for the observation of steady-state cooperative emission without the complications of optical excitation.

Methodology
The researchers fabricated dual-gated atomically thin light-emitting diodes (LEDs) using MoSe $_2$ /WSe $_2$ heterobilayers separated by a monolayer hexagonal boron nitride (h-BN) spacer. The h-BN spacer was selectively inserted to restrict direct interlayer coupling to a narrow strip near the edge of the WSe $_2$ flake. By applying specific gate voltages ( $V_g$ ) and bias voltages ( $V_b$ ), they created a 2D p-n junction that facilitates the injection of electrons and holes from independent reservoirs.

Key experimental techniques included:

Electroluminescence (EL) Spectroscopy: To characterize the emission energy and intensity under various doping regimes (neutral, positively charged, negatively charged with in-gap states, and degenerate n-doping).
Hanbury-Brown-Twiss (HBT) Interferometry: To measure the second-order photon correlation function $g^{(2)}(\tau)$ , quantifying photon bunching ( $g^{(2)}(0) > 1$ ) and antibunching ( $g^{(2)}(0) < 1$ ).
Spectrally Resolved Correlations: Using tunable filters to isolate specific energy bands within the EL spectrum to identify the origin of correlations.
Temperature and Current Dependence: Varying temperature (6 K to 80 K) and current to probe energy scales and recharging dynamics.
Theoretical Modeling: Development of a quantum master equation describing an ensemble of $N$ emitters undergoing collective radiative decay with incoherent repopulation on a timescale $\tau_{ir}$ .

Key Results

Spatial Confinement and Emission: Electroluminescence was observed exclusively at three diffraction-limited spots along the heterobilayer edge. This confinement is attributed to an edge-enhanced fringing electric field that lenses charge carriers, creating a recombination region where the geometric discontinuity and field lensing satisfy the Dicke criterion for superradiance.
Charge-State Dependent Statistics:
- Uncorrelated Emission: In regimes with degenerate Fermi seas (heavily n-doped or p-doped), the emission was uncorrelated ( $g^{(2)}(\tau) \approx 1$ ).
- Cooperative Emission: In the charge-neutral ( $IX^0$ ) and weakly localized negatively charged ( $IX^-_{IGS}$ ) regimes, pronounced photon bunching was observed ( $g^{(2)}(0) > 1$ ).
- Oscillatory Dynamics: In the $IX^-_{IGS}$ regime (specifically at $V_g = -0.85$ V), the correlation function exhibited a complex temporal structure: a giant zero-delay bunching peak ( $g^{(2)}(0) \sim 5$ ), followed by finite-delay antibunching, and subsequent bunching revivals. The oscillation period ( $\tau_{osc}$ ) ranged from 1 to 5 $\mu$ s, significantly longer than the decay time ( $\tau_d \sim 100-300$ ns).
Temperature and Doping Sensitivity: The cooperative signatures disappeared above 70–80 K, corresponding to an energy scale of $\sim 6-7$ meV. The correlations were suppressed by the introduction of delocalized free carriers (Fermi sea) but enhanced by localized electrons (in-gap states), suggesting that localized trion-like states are crucial for the effect.
Recharging Rate Control: By varying the bias voltage at a fixed gate voltage, the authors tuned the incoherent recharging rate. They observed that $g^{(2)}(0)$ decreased steeply as the current (and thus the recharging rate) increased. The maximum observed bunching ( $g^{(2)}(0) \sim 13$ ) occurred at low currents.

Theoretical Interpretation
The authors propose a quantum master equation model where an ensemble of emitters undergoes collective decay while being replenished incoherently. The model identifies two regimes based on the ratio of the recharging time to the radiative lifetime ( $\tau_{ir}/\tau_{IX}$ ):

Fast Recharging: Resembles standard Dicke superradiance where bunching increases with emitter density.
Slow Recharging (Experimental Regime): The uncorrelated recharging channel populates both bright (superradiant) and dark (subradiant) states. The dark states act as long-lived reservoirs that intermittently feed the superradiant manifold. This mechanism explains the observed finite-delay antibunching and revival dynamics, which are absent in standard Dicke theory. The model successfully reproduces the experimental $g^{(2)}(\tau)$ traces, including the giant bunching and oscillatory behavior.

Significance and Claims
The paper claims to establish the first observation of steady-state cooperative emission in an electrically driven 2D TMD LED. By utilizing electrical injection and edge confinement, the work overcomes the limitations of optical excitation and decoherence that have hindered the observation of collective effects in solid-state systems. The authors assert that their results demonstrate a unique form of collective light-matter interaction governed by incoherent recharging, distinct from the conventional Dicke paradigm. This platform provides a new avenue for studying strong light-matter interactions in non-equilibrium phases of Bose-Fermi mixtures. Furthermore, the demonstration of large photon bunching and dynamical correlations without an optical cavity suggests potential for developing mirrorless lasers and sources of nonclassical light based on 2D materials. The work bridges quantum optics and many-body physics in a tunable, electrically controllable optoelectronic device.

Technical Summary: Steady-State Cooperative Emission of Interlayer Excitons in Atomically Thin Light-Emitting Diodes

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