Evidence for Electron–Hole Crystals in a Mott Insulator

Physical Chemistry Materials Science Quantum Physics Chemistry Physics Condensed Matter Physics
electron-hole crystals Mott insulator graphene scanning tunneling microscopy long-range quantum entanglement

Background

In recent years, researchers have shown significant interest in electron-hole crystals within Mott insulators. These types of crystals can achieve quantum excited states, have the potential to support counterflow superfluidity and topological order, and possess long-range quantum entanglement characteristics. However, experimental evidence for the coexistence of electron and hole crystals in Mott insulators has not been sufficiently demonstrated. Under typical conditions, strong electron-electron interactions can drive the formation of new crystal orders, leading to phenomena such as Wigner crystals or charge ordering in doped Mott insulators. These types of electron crystals represent a strongly quantum-fluctuating many-body system with multiple degrees of freedom, which has been utilized in quantum simulations.

Source Information

This research paper was co-authored by researchers from multiple institutions, including the Institute of Functional Intelligent Materials at the National University of Singapore, the Department of Chemistry, the Centre for Advanced 2D Materials, Peking University’s Shenzhen Graduate School of Advanced Materials, and the Photonics and 2D Materials Center of the Moscow Institute of Physics and Technology in Russia. Specific authors include Zhizhan Qiu, Yixuan Han, Keian Noori, Zhaolong Chen, among others. The paper was published in Nature Materials and was accepted on April 30, 2024.

Research Process

Research Procedure

  1. Sample Preparation and Device Assembly: Researchers prepared heterostructures of graphene and few-layer α-RuCl3 using a dry transfer technique, placing them on graphite or hexagonal boron nitride (h-BN) flakes. The primary technique for sample characterization in the experiment was scanning tunneling microscopy (STM).

  2. Electronic Structure and Scanning Tunneling Microscopy Imaging: Using STM imaging technology, researchers discovered atomically clean surfaces over large areas of the graphene and α-RuCl3 heterostructures, and exhibited two distinct charge-ordered structures through STM imaging.

  3. Bilayer Heterostructure Characterization: Researchers used Fourier transform filtering to remove moiré modulation, obtaining pure lattice images of α-RuCl3.

  4. Three-Dimensional Imaging of Electron-Hole Crystals: Under different sample bias voltages, long-wavelength modulated imaging of multi-layer α-RuCl3 in the upper Hubbard band (UHB) and the lower Hubbard band (LHB) energy ranges was acquired, revealing the specific form of electron-hole crystals.

Experimental Results

  1. Confirmation of Electronic Structure: Through dI/dV spectra, researchers found that, unlike the spectra of graphene/graphite or h-BN, α-RuCl3 exhibited two significant peaks corresponding to the LHB and UHB, indicating the crystalline form of electrons and holes. Here, the LHB band showed a hexagonal symmetric arrangement, while the UHB band displayed features of broken rotational symmetry, corresponding to different lattice arrangements.

  2. Charge Modulation Imaging and Analysis: Using STM imaging technology, researchers observed that under negative bias voltages, the charge ordering of the LHB formed a (2√3 a0 × 2√3 a0)r30° triangular (honeycomb) lattice structure, while under positive bias voltages, the charge ordering of the UHB formed a (√7a0 ×√7a0) superlattice structure, corresponding to different electron-hole crystal structures.

  3. Charge Transfer and Control Experiments: By adjusting the gate voltage, researchers observed significant changes in the charge ordering of the UHB under gate voltage modulation, further proving the existence of electron-hole crystals and their nature of being dependent on charge transfer.

Conclusion and Value

Research Conclusions

The study shows that by non-invasively van der Waals doping graphene on doped Mott insulator α-RuCl3, real-space imaging of imbalanced electron-hole crystals was successfully achieved. These charge ordering phenomena validate the existence of electron-hole crystals and their correlation-driven charge crystal nature within strongly correlated materials. Specifically, hole crystals in the LHB formed a lattice at 4d^4 Ru sites, while electron crystals in the UHB formed a pairing electron crystal with broken Ru-Ru bond symmetry.

Research Significance

This study opens a new avenue for exploring correlated bosonic states in strongly correlated materials. This discovery not only provides a detailed understanding of electron-hole crystals but also offers new research directions for quantum information technology. On a mesoscopic scale, previous transport and optical studies revealed characteristics of coexistent correlated electrons and holes in multi-layer structures, while this study directly confirmed the existence of electron-hole crystals through STM imaging technology.

Research Highlights

  1. Method Innovation: For the first time, non-invasive van der Waals doping and STM imaging technology were used to visualize correlation-driven electron-hole crystals at atomic resolution.
  2. Dual Charge Ordering: For the first time, two distinct charge-ordered structures were observed, corresponding to a hexagonally symmetric hole crystal and a symmetry-broken electron crystal.
  3. Gate Voltage Control: Achieved controllable transformation of electron-hole crystals through gate voltage adjustment, further demonstrating the correlation-driven properties of these crystals.