Direct visualization of relativistic quantum scars in graphene quantum dots

Zhehao Ge (), Anton M. Graf, Joonas Keski-Rahkonen, Sergey Slizovskiy, Peter Polizogopoulos, Takashi Taniguchi, Kenji Watanabe, Ryan Haren, David Lederman, Vladimir I. Fal’ko, Eric J. Heller and Jairo Velasco ()
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Zhehao Ge: University of California, Santa Cruz
Anton M. Graf: Harvard University
Joonas Keski-Rahkonen: Harvard University
Sergey Slizovskiy: University of Manchester
Peter Polizogopoulos: University of California, Santa Cruz
Takashi Taniguchi: National Institute for Materials Science
Kenji Watanabe: National Institute for Materials Science
Ryan Haren: University of California, Santa Cruz
David Lederman: University of California, Santa Cruz
Vladimir I. Fal’ko: University of Manchester
Eric J. Heller: Harvard University
Jairo Velasco: University of California, Santa Cruz

Nature, 2024, vol. 635, issue 8040, 841-846

Abstract: Abstract 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 ∞-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.

Date: 2024
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DOI: 10.1038/s41586-024-08190-6

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