Research Report on the Paper on Fractional Quantum Hall Phases in High Mobility n-Type Molybdenum Disulfide Transistors

Background and Motivation

At low temperatures, field-effect transistors (FETs) based on semiconducting transition metal dichalcogenides (TMDs) theoretically provide high carrier mobility, strong spin-orbit coupling, and intrinsic strong electron interactions. This makes them an ideal platform for exploring many-body electronic interactions and quantum states. However, achieving robust Ohmic contacts with TMD materials at cryogenic temperatures has long been a challenge, preventing comprehensive studies of electronic correlations near the band edge, especially in the fractional quantum Hall (FQH) regime in partially filled Landau levels (LLs).

This paper introduces a “windowed contact technique” to achieve Ohmic contact for n-type molybdenum disulfide (MoS₂) over a temperature range—from millikelvin to room temperature. The researchers report direct evidence of FQH states at filling factors ⁴⁄₅ and ²⁄₅ in the lowest Landau levels of bilayer MoS₂, opening new avenues for applying TMDs in quantum computing and low-temperature electronics.

Source of the Paper

This paper was co-authored by Siwen Zhao, Jinqiang Huang, Valentin Crépel, and others, from well-known research institutions in China, the United States, France, and Japan. It was published in the December 2024 issue of Nature Electronics (Volume 7, pp. 1117–1125). Corresponding authors include Jing Zhang (Shanxi University), Nicolas Regnault (École Normale Supérieure, Paris), among others.

Research Design and Methods

Study Process and Experimental Approach

1. Sample Preparation and Structural Design
   The researchers developed a “windowed” electrode contact method to create Ohmic contacts for n-type monolayer and bilayer MoS₂. Using a dry transfer method in a nitrogen-filled glove box, MoS₂ was encapsulated with hexagonal boron nitride (hBN) to form a “hBN/MoS₂/hBN” sandwich structure. Pre-etched windows in the top hBN layer exposed regions of the MoS₂ for contact, and Bi/Au electrodes were deposited via thermal evaporation, creating low-temperature Ohmic contacts.

2. Mobility Measurement and Comparison
   Across the temperature range of 300 mK to 300 K, sample mobility was measured using two-terminal and four-terminal methods. Field-effect mobilities exceeding 100,000 cm²·V⁻¹·s⁻¹ and quantum mobilities over 3,000 cm²·V⁻¹·s⁻¹ were observed. These results outperformed other TMD contact methods, such as edge-engineered contacts.

3. Landau Levels and Quantum State Characterization
   Within high magnetic fields up to 34 T and ultralow temperatures around 300 mK, the researchers systematically examined the Landau level distribution via dual-gate tuning. At extremely low carrier densities and under the quantum limit (filling fraction ν ≤ 1), FQH states with filling factors ⁴⁄₅ and ²⁄₅ were revealed. These FQH states were confirmed through quantized longitudinal and transverse conductance features.

4. Theoretical Modeling and Computation
   Based on microscopic models, the researchers explored inter-layer effects and electronic interactions in bilayer MoS₂. Haldane pseudopotential calculations were used to model the effective potential interactions between electrons. The experimental observations of specific FQH states and the potential absence of others (e.g., filling factor ¹⁄₃) were rationalized through numerical analysis.

Innovations in the Research Process

• Innovative Ohmic Contact Methodology
  Unlike edge or bottom contact methods, the “windowed contact technique” significantly lowered contact resistance under low temperatures (~450 Ω·μm). This robust method provided a stable platform for quantum Hall transport studies.

• Exploration of Bilayer TMD Properties
  The study revealed inter-layer coupling effects in bilayer MoS₂. Under a finite vertical electric field (Ez), bilayer MoS₂ exhibited single-layer-like electronic behavior with layer-valley locking, offering a novel direction for exploring electronic interactions in layered TMD heterostructures.

Results and Conclusions

1. Primary Experimental Findings

   • For the first time, FQH states at filling factors ⁴⁄₅ and ²⁄₅ in the lowest Landau levels of bilayer MoS₂ were observed. These states showed layer-polarized symmetry, consistent with theoretical predictions.
   • The energy gaps of these fractional states were estimated to be on the order of ~1 K, with limited tunability by an applied vertical electric field.

2. Theoretical Validation
   Theoretical models verified the significant impact of finite sample thickness and dielectric screening on Haldane pseudopotentials, explaining the absence of specific fractional states such as ν = ¹⁄₃. The calculations demonstrated that screening effects particularly suppress FQH states with narrower energy gaps.

3. Potential Applications

   • The developed high-mobility dual-gated TMD devices offer promising applications in low-temperature quantum computing platforms.
   • The research also provided fundamental insights for designing high-performance quantum devices like TMD-based twistronics, Coulomb drag devices, and low-temperature high-electron-mobility transistors.

Academic and Practical Significance

The significance of this study lies in the following aspects: 1. Scientific Contribution
The work extends foundational studies of FQH states from conventional two-dimensional electron gas systems (e.g., GaAs and graphene) to two-dimensional semiconductors like TMDs, unveiling the role of dielectric screening and inter-layer coupling in stabilizing fractional states. 2. Technological Advances
The developed low-contact-resistance method provides unprecedented experimental capabilities for studying quantum transport phenomena, which can be applied to other TMDs and 2D materials. 3. Application Potential
By tuning inter-layer coupling and band features in TMDs, this research paves the way for high-performance devices in quantum computing and ultralow-temperature electronics.

Research Highlights

• State-of-the-Art Experimental Advancements: The study leveraged magnetic fields up to 34 T and temperatures near 300 mK, representing cutting-edge quantum experimentation.
• Novel Methodology: The unique 2D windowed contact technique introduced a distinctive approach for exploring bilayer TMD properties.
• Robust Findings: Experimental data, thoroughly supported by theoretical modeling, elucidated the presence and stability of FQH states within bilayer MoS₂.

This study not only advances the feasibility of TMDs in low-temperature electronic systems but also provides a foundational basis for developing novel quantum computing and electronic devices, demonstrating immense research potential and future prospects.