Direct visualization of relativistic quantum scars in graphene quantum dots

• 成果类型: Article
• 署名作者: Ge, Zhehao; Graf, Anton M.; Keski-Rahkonen, Joonas; Slizovskiy, Sergey; Polizogopoulos, Peter; Taniguchi, Takashi; Watanabe, Kenji; Van Haren, Ryan; Lederman, David; Fal'ko, Vladimir I.; Heller, Eric J.; Velasco Jr, Jairo
• 署名单位: University of California System; University of California Santa Cruz; Harvard University; Harvard University; Harvard University; University of Manchester; University of Manchester; National Institute for Materials Science; National Institute for Materials Science; University of California System; University of California Berkeley
• 刊物名称: Nature
• ISSN/ISSBN: 0028-5104
• DOI: 10.1038/s41586-024-08190-6
• 发表日期: 2024-11-28
• 关键词: dirac fermions; eigenfunctions; symmetry; systems

摘要

Quantum scars refer to eigenstates with enhanced probability density along unstable classical periodic orbits. First predicted 40 years ago1, scars are special eigenstates that counterintuitively defy ergodicity in quantum systems whose classical counterpart is chaotic2,3. Despite the importance and long history of scars, their direct visualization in quantum systems remains an open field4-10. Here we demonstrate that, by using an in situ graphene quantum dot (GQD) creation and a wavefunction mapping technique11,12, quantum scars are imaged for Dirac electrons with nanometre spatial resolution and millielectronvolt energy resolution with a scanning tunnelling microscope. Specifically, we find enhanced probability densities in the form of lemniscate infinity-shaped and streak-like patterns within our stadium-shaped GQDs. Both features show equal energy interval recurrence, consistent with predictions for relativistic quantum scars13,14. By combining classical and quantum simulations, we demonstrate that the observed patterns correspond to two unstable periodic orbits that exist in our stadium-shaped GQD, thus proving that they are both quantum scars. In addition to providing unequivocal visual evidence of quantum scarring, our work offers insight into the quantum-classical correspondence in relativistic chaotic quantum systems and paves the way to experimental investigation of other recently proposed scarring species such as perturbation-induced scars15-17, chiral scars18,19 and antiscarring20. Using a graphene quantum dot creation and a wavefunction mapping technique, quantum scars are directly visualized for Dirac electrons with a scanning tunnelling microscope.