🔬 mesoscale physics

Graphene double quantum dot as a solid-state two-level system in the THz range

This paper demonstrates that an hBN-encapsulated graphene double quantum dot functions as a solid-state two-level system with a tunable THz transition frequency, offering a scalable platform for future THz quantum technologies and the exploration of ultra-strong light-matter interactions.

Original authors: Alexis Wietzke, Solen Coeymans, Benjamin Hue, Simon Messelot, Aurelien Schmitt, Michael Rosticher, Kenji Watanabe, Takashi Taniguchi, Jerome Tignon, Sukhdeep Dhillon, Rebeca Ribeiro, Audrey Cottet, Ma

Published 2026-10-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alexis Wietzke, Solen Coeymans, Benjamin Hue, Simon Messelot, Aurelien Schmitt, Michael Rosticher, Kenji Watanabe, Takashi Taniguchi, Jerome Tignon, Sukhdeep Dhillon, Rebeca Ribeiro, Audrey Cottet, Matthieu Delbecq, Takis Kontos, Juliette Mangeney

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

In the world of modern technology, the ability to control individual particles of matter is the foundation of the next generation of computers and sensors. Scientists have long mastered this control using systems that operate at very low frequencies, like the radio waves used in Wi-Fi, or at very high frequencies, like the light that allows us to see. However, there is a vast, difficult-to-reach region in between known as the terahertz range. This part of the spectrum holds great promise for secure wireless communication and advanced medical imaging because it can pass through materials that block visible light, yet it has remained stubbornly difficult to harness for quantum technologies. The challenge lies in creating a simple, controllable system that can act as a switch or a memory bit at these specific frequencies, bridging the gap between the familiar world of electronics and the exotic world of quantum physics.

To solve this, researchers have turned to a material that is both incredibly thin and remarkably strong: graphene. Imagine a single layer of carbon atoms arranged in a honeycomb pattern, so thin that it is essentially two-dimensional. By shaping this material into tiny islands and connecting them, scientists can create artificial atoms, known as quantum dots, where electrons are trapped. In this new study, a team of physicists has successfully built a device using two of these graphene islands placed side by side, separated by a narrow barrier. They have demonstrated that this setup functions as a two-level system, a fundamental building block for quantum technology, that operates precisely within the elusive terahertz range.

The researchers constructed their device by stacking sheets of graphene between layers of hexagonal boron nitride, a material that acts like a protective shell, keeping the graphene clean and free from defects. They then used advanced lithography to carve out two circular dots, each about 130 nanometers in diameter, and connected them with a very narrow bridge only 40 nanometers wide. This bridge allows electrons to tunnel, or jump, from one dot to the other. By applying precise voltages to nearby metal gates, the team could tune the energy levels of the electrons inside the dots, effectively controlling how easily they could move between the two islands. The entire structure was cooled to a temperature just above absolute zero to eliminate thermal noise, allowing the delicate quantum behavior of the electrons to be observed clearly.

When the team measured the flow of electricity through this double-dot system, they found that the electrons were not just hopping randomly. Instead, the two dots were so strongly coupled that the electrons behaved as if they belonged to a single, larger molecule. In this state, the electrons could exist in two distinct configurations simultaneously, creating what are known as bonding and antibonding states. The energy difference between these two states corresponds to a frequency of approximately 0.145 terahertz. This is a significant achievement because it places the system's operation squarely in the terahertz spectrum, a range where most solid-state quantum devices have struggled to function. The researchers confirmed this frequency by analyzing the electrical current flowing through the device and comparing their measurements with sophisticated computer models that accounted for the complex interactions between the electrons and their environment.

A key part of this discovery was the method used to measure these properties. Typically, scientists probe such systems by shining microwave or light radiation on them to see how they respond. However, at terahertz frequencies, sending such signals into a tiny chip is extremely difficult due to signal loss and technical limitations. The team bypassed this hurdle by using a technique called dark transport spectroscopy. Instead of shining light on the device, they simply measured how the electrical current changed as they adjusted the voltages on the gates. By carefully mapping these changes, they could deduce the energy levels and the strength of the connection between the dots without needing any external radiation. This approach proved to be a powerful and practical way to characterize open quantum systems, offering a new tool for researchers who want to study these materials without the complexity of high-frequency radiation sources.

The findings suggest that this graphene-based device is not just a laboratory curiosity but a viable candidate for future quantum technologies. Because the system is built from standard materials and can be integrated directly onto a computer chip, it offers a path toward scalable quantum devices that operate at terahertz frequencies. Furthermore, because the transition involves a single electron moving between two states, it opens the door to exploring the most extreme forms of interaction between light and matter. If this device were coupled with a resonator designed to trap terahertz waves, it could allow scientists to study the fundamental limits of how a single quantum system interacts with a single photon, a scenario that has so far been out of reach for existing technologies. This work provides a concrete step forward in filling the terahertz quantum gap, turning a theoretical possibility into a physical reality that could one day power new kinds of sensors and communication networks.

Technical Summary: Graphene Double Quantum Dot as a Solid-State Two-Level System in the THz Range

Problem Statement
Quantum technologies have advanced significantly at microwave and optical frequencies, but their extension into the terahertz (THz) range remains underdeveloped, a gap referred to as the "THz quantum gap." While various systems (Rydberg atoms, trapped ions, molecules) can operate at THz frequencies, they often suffer from scalability issues or operational complexity due to the need for isolated environments. Solid-state alternatives, such as single quantum dots (QDs), face a different challenge: in the low-energy THz regime, broadening effects often blur the energy differences between multiple electronic states, making it difficult to isolate a distinct two-level system (TLS). While double quantum dots (DQDs) offer a solution by allowing the isolation of transition energies via interdot tunnel coupling, their realization in the THz spectral range has remained largely unexplored. Furthermore, conventional characterization techniques like photon-assisted tunneling are difficult to implement at THz frequencies due to transmission-line losses.

Methodology
The authors fabricated a DQD device using an hBN-encapsulated graphene heterostructure in a single-electron transistor geometry. The device consists of two 130 nm-diameter graphene QDs connected by 40 nm-wide constrictions acting as tunnel barriers, all encapsulated in hexagonal boron nitride (hBN) to minimize disorder. The device was cooled to a base temperature of 280 mK in a $^3$ He cryostat.

The study employed low-temperature DC transport spectroscopy in the dark to probe the system. By tuning plunger gate voltages ( $V_{g1}, V_{g2}$ ) and interdot tunnel coupling gates ( $V_t$ ), the authors mapped charge stability diagrams to identify coupling regimes. To quantitatively extract the system's parameters, they utilized two theoretical approaches:

Stoof and Nazarov formalism: A sequential tunneling model (valid when $\Gamma < k_B T$ ) used for initial estimation.
Nonequilibrium Green's function (NEGF) formalism: An equation-of-motion method combined with the Meir–Wingreen current formula. This approach was chosen because it remains valid for tunneling rates ( $\Gamma$ ) larger than the thermal energy ( $k_B T$ ), allowing for the analysis of open DQD systems where the sequential tunneling limit is not met.

Key Results

Device Characterization: The charge stability diagrams revealed distinct coupling regimes. In the intermediate coupling regime, the system exhibited a honeycomb pattern characteristic of a DQD. In the strong coupling regime, the pattern transitioned toward that of a single large QD.
Hybridization and Two-Level System Formation: In the intermediate coupling regime, the authors observed energy-level hybridization, evidenced by the parabolic curvature of co-tunneling lines and the splitting of stability triangles. This hybridization creates delocalized bonding and antibonding molecular states, forming a TLS.
Parameter Extraction:
- Using the NEGF model, the authors fitted the experimental tunneling current ( $I_{SD}$ ) as a function of energy detuning ( $\varepsilon_\delta$ ).
- The model yielded an interdot tunnel coupling energy of $t = 0.30 \pm 0.025$ meV.
- This coupling energy corresponds to a resonance frequency of $f_{res} = 2t/h \approx 0.145 \pm 0.012$ THz.
- The dot-lead tunnel coupling energies were extracted as $\Gamma_L = 0.04$ meV and $\Gamma_R = 0.28$ meV.
Model Validation: The NEGF model successfully reproduced the experimental data, including the sharp suppression of current at large detunings, which deviates from a simple Lorentzian lineshape predicted by sequential tunneling models. The agreement confirmed that the system operates in a regime where thermal energy is smaller than the resonance width, necessitating the more advanced theoretical treatment.

Significance and Claims
The paper claims to demonstrate the first realization of a solid-state two-level system based on a 2D material (graphene) operating in the THz spectral range. The significance of this work is framed as follows:

Bridging the THz Quantum Gap: The system provides a platform with a resonance frequency ( $\sim 0.145$ THz) significantly higher than previous condensed-matter-based TLSs (typically up to 50 GHz).
Methodological Advancement: The study establishes that low-temperature transport spectroscopy in the dark, combined with NEGF modeling, is a viable and practical alternative to photon-assisted tunneling for probing open DQD systems in the THz regime. This method allows for the direct extraction of tunneling rates and coupling energies without the technical challenges of THz radiation coupling.
Technological Potential: Due to the large electric dipole moment of graphene QDs ( $d \approx 230$ nm) and the compatibility of the device with on-chip integration, the authors suggest this system could serve as a building block for future THz quantum technologies, including the generation and detection of non-classical light states.
Fundamental Physics: By involving a single-electron transition rather than a collective ensemble, coupling this system to a THz resonator with small mode volumes could enable the exploration of ultra-strong light-matter interactions at the fundamental limit of a single quantum transition coupled to a single cavity.

The authors maintain a modest tone regarding future applications, noting that while the system could serve as a building block, the primary contribution is the demonstration of the system's existence and the extraction of its parameters. They also note that further theoretical development is required to fully interpret experimental traces involving interdot interactions and many-body phenomena like the Kondo effect.

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