Extended Quantum Anomalous Hall States in Graphene/Hexagonal Boron Nitride Moiré Superlattices

Academic Background

In recent years, the behavior of electrons in topological flat bands has attracted widespread attention in the field of condensed matter physics. Electrons in topological flat bands can form new topological states driven by strong correlation effects, which exhibit the Quantum Anomalous Hall Effect (QAHE) at zero magnetic field. In particular, moiré superlattice systems formed by multilayer graphene and hexagonal boron nitride (hBN) provide an ideal platform for studying these topological states. Previous studies have shown that the moiré superlattice of five-layer rhombohedral graphene (RG) with hBN exhibits the Fractional Quantum Anomalous Hall Effect (FQAHE) at temperatures around 400 millikelvin, sparking extensive discussions on its mechanism and the role of moiré effects.

However, many questions remain unanswered regarding the formation mechanisms of these topological states and their behavior at even lower temperatures. In particular, the influence of the moiré potential on electron behavior and the absence of isolated moiré minibands in the single-particle picture make the study of this system more challenging. Therefore, the research team aimed to explore new topological states in RG/hBN moiré superlattices through electrical transport measurements at extremely low temperatures and to reveal the underlying physical mechanisms.

Source of the Paper

This paper was jointly completed by a research team from the Massachusetts Institute of Technology (MIT), Florida State University, and the National Institute for Materials Science (NIMS) in Japan. The main authors include Zhengguang Lu, Tonghang Han, Yuxuan Yao, and others. The paper was published in the journal Nature in 2024, titled “Extended quantum anomalous hall states in graphene/hBN moiré superlattices.”

Research Process and Results

1. Experimental Design and Device Fabrication

The research team designed and fabricated multilayer graphene/hBN moiré superlattice devices, including five-layer and four-layer graphene devices. The fabrication process included the following key steps:

• Graphene Stacking and Imaging: Using infrared imaging technology (based on an InGaAs camera) and Raman spectroscopy, the research team was able to quickly screen graphene flakes with rhombohedral stacking order. This stacking order is crucial for the formation of topological flat bands.
• Device Assembly: The selected graphene flakes were stacked with hBN layers to form moiré superlattice structures. The devices were patterned into Hall bar structures using electron beam lithography and reactive ion etching, and Cr/Au electrodes were deposited for electrical measurements.
• Low-Temperature Measurements: The devices were measured in a Bluefors LD250 dilution refrigerator, with electronic temperatures as low as below 40 millikelvin. Longitudinal resistance (Rxx) and Hall resistance (Rxy) were measured using lock-in amplifiers, and the transport properties of the devices were studied by applying DC and AC currents.

2. Electrical Transport Measurements and Results

The research team conducted systematic electrical transport measurements on five-layer and four-layer graphene/hBN moiré superlattice devices at extremely low temperatures, with the following main results:

• Fractional Quantum Anomalous Hall Effect (FQAHE): In the five-layer device, the research team observed FQAHE states at multiple fractional filling factors (e.g., v=²⁄₅, ³⁄₇, ⁴⁄₉, etc.). These states remained stable at temperatures as low as 10 millikelvin, with Rxx values lower than previously reported. In the four-layer device, the team observed FQAHE states at v=³⁄₅ and ²⁄₃ filling factors for the first time.
• Extended Quantum Anomalous Hall State (EQAH): At extremely low temperatures and small currents, the research team discovered a new topological state, termed the Extended Quantum Anomalous Hall State (EQAH). This state exhibited quantized Hall resistance (Rxy=h/e2) and vanishing longitudinal resistance (Rxx) over a wide range of filling factors (v=0.5 to 1.3). As the temperature or current increased, the EQAH state gradually disappeared and partially transitioned into FQAHE liquid states.
• Displacement Field-Induced Quantum Phase Transitions: By tuning the displacement field (D), the research team observed quantum phase transitions from the EQAH state to Fermi Liquid (FL), FQAHE liquid, and possibly Composite Fermi Liquid (CFL). These phase transitions revealed rich quantum phenomena in the RG/hBN moiré superlattice.

3. Data Analysis and Theoretical Interpretation

The research team extracted Rxx and Rxy values at zero magnetic field by symmetrizing and anti-symmetrizing the data. They also analyzed the band structure of the devices using Landau fan diagrams and verified the topological nature of the FQAHE and EQAH states. Theoretical calculations suggested that the EQAH state might resemble a Quantum Anomalous Hall Crystal (QAHC) or a Re-entrant Quantum Hall Insulator state.

Conclusions and Significance

This study is the first to observe the Extended Quantum Anomalous Hall State (EQAH) at zero magnetic field and reveal its universality in multilayer graphene/hBN moiré superlattices. The discovery of the EQAH state not only enriches the quantum phenomena in topological flat band materials but also provides a new platform for studying topological states in strongly correlated electron systems. Furthermore, by tuning the displacement field and temperature, the research team demonstrated phase transitions from the EQAH state to other quantum phases, laying the foundation for further exploration of the formation mechanisms and potential applications of topological quantum states.

Research Highlights

1. Discovery of a New Topological State: The Extended Quantum Anomalous Hall State (EQAH) was observed for the first time at zero magnetic field, revealing its universality over a wide range of filling factors.
2. Precision Measurements at Extremely Low Temperatures: By improving filters and dilution refrigeration techniques, the research team achieved electronic temperatures below 40 millikelvin, providing the necessary conditions for observing new topological states.
3. Displacement Field-Tuned Quantum Phase Transitions: By adjusting the displacement field, the research team demonstrated phase transitions from the EQAH state to Fermi Liquid, FQAHE liquid, and Composite Fermi Liquid, revealing rich quantum phenomena in the RG/hBN moiré superlattice.
4. Integration of Theory and Experiment: By comparing theoretical calculations with experimental data, the research team proposed that the EQAH state might resemble a Quantum Anomalous Hall Crystal or a Re-entrant Quantum Hall Insulator state, providing new directions for future theoretical research.

Additional Valuable Information

The research team also developed an infrared imaging technique based on an InGaAs camera for rapidly screening graphene flakes with specific stacking orders. This technology not only improved the efficiency of device fabrication but also provided a new tool for studying stacking orders in other two-dimensional materials.

This study provides important experimental evidence for understanding strongly correlated electron behavior in topological flat bands and opens new avenues for exploring the potential applications of topological quantum states in the future.