Bilayer Graphene Cavities Demonstrate Chaos Via Rotation, Revealing Wigner-Dyson Statistics and Ergodic Space
Summarize this article with:
Confining electrons within tiny spaces creates opportunities to explore fundamental physics, and recent work demonstrates this principle using bilayer graphene cavities. Jucheng Lin, Yicheng Zhuang, and Anton M. Graf, all from Harvard University, alongside Joonas Keski-Rahkonen and Eric J. Heller, investigate how manipulating the shape of these cavities influences electron behaviour.
The team discovered that rotating the cavity boundary relative to the graphene lattice introduces chaos, shifting the system from predictable electron patterns to a more random, uncorrelated state. This achievement establishes bilayer graphene cavities as a promising platform for studying chaotic phenomena and potentially designing novel electronic devices, offering a new route to understanding and harnessing complex quantum behaviour.
Shaping Electron Waves in Graphene Cavities This research investigates the control of electron trajectories within bilayer graphene cavities.
The team demonstrates that electron waves can be shaped and manipulated using specifically designed cavity geometries, exploiting the unique electronic properties of bilayer graphene. Through numerical simulations, scientists demonstrate the ability to sculpt the probability density of electron waves within these cavities by designing cavities with complex boundary shapes. Simulations reveal that certain cavity shapes effectively suppress or enhance electron transmission, leading to localized wave patterns. Researchers demonstrate that by tuning the cavity geometry, they can achieve near-perfect transmission through a single channel, even with disorder. This level of control is achieved by manipulating the chaotic dynamics of the electron waves, allowing for the creation of highly directional electron beams with potential applications in nanoscale electronic devices. The research provides insights into the relationship between cavity geometry, chaotic dynamics, and electron transport, offering a new perspective on quantum device design. Graphene Chaos, Localization and Magnetic Fields This research investigates the quantum chaos and wave localization properties of electrons in bilayer graphene subjected to a perpendicular magnetic field and a specific potential. It explores how these factors influence the electronic band structure, wavefunction localization, and the emergence of chaotic behaviour, connecting the geometry of electron motion in phase space to the statistical properties of its energy levels. The research aims to understand how classical chaos manifests in the quantum realm within a realistic 2D material. The study explores how disorder can lead to the localization of electron wavefunctions, impacting the material’s conductivity. Bilayer graphene, with its tunable band gap and high carrier mobility, is an ideal platform for studying quantum chaos and localization. Applying a perpendicular magnetic field quantizes electron energy and alters its behaviour. The research employs theoretical and computational techniques, including a tight-binding model and numerical simulations, to calculate electronic properties and analyse energy level statistics. The research demonstrates evidence of quantum chaos, manifested through energy level statistics and electron wavefunction dynamics. Disorder leads to wavefunction localization, reducing conductivity. The magnetic field shapes the electronic band structure and influences localization and chaos. The research establishes a connection between classical phase space dynamics and quantum mechanical behaviour, providing insights into the emergence of chaos in the quantum realm.
Graphene Cavities Exhibit Quantum Chaos Transition This research demonstrates that rotating bilayer graphene cavities induces a transition from predictable to quantum chaotic electron behaviour. By employing a tight-binding model and analysing eigenenergy level statistics, the team established that misalignment between the graphene lattice and the cavity geometry leads to level repulsion consistent with Wigner-Dyson statistics, a hallmark of chaotic systems. Corresponding analysis of the electron wavefunctions revealed a shift from spatially correlated patterns to spatially uncorrelated random waves, confirming the onset of chaos within the cavity. Further investigation using semiclassical ray dynamics revealed that the trigonal warping of the graphene’s electronic band structure plays a crucial role in shaping the cavity’s dynamics. Aligning the cavity boundary with the graphene lattice’s crystalline axes results in predictable electron trajectories, whereas rotation disrupts this order, leading to quasi-ergodic behaviour. This work establishes a pathway to engineer chaotic phenomena in bilayer graphene cavities, potentially opening new avenues for device engineering and exploring fundamental aspects of quantum chaos in condensed matter systems. 👉 More information 🗞 Shaping chaos in bilayer graphene cavities 🧠 ArXiv: https://arxiv.org/abs/2512.10914 Tags: