Direct visualization of relativistic quantum scars in graphene quantum dots

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 chaotic^2,3. Despite the importance and long history of scars, their direct visualization in quantum systems remains an open field^4-10. Here we demonstrate that, by using an in situ graphene quantum dot (GQD) creation and a wavefunction mapping technique^11,12, 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 scars^13,14. 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 scars^15-17, chiral scars^18,19 and antiscarring²⁰.