Direct Visualization of Relativistic Quantum Scars

Abstract

Quantum scars refer to eigenstates with enhanced probability density along unstable classical periodic orbits (POs). First predicted 40 years ago, scars are special eigenstates that counterintuitively defy ergodicity in quantum systems whose classical counterpart is chaotic. Despite the importance and long history of scars, their direct visualization in quantum systems remains an open field. Here we demonstrate that, by using an in-situ graphene quantum dot (GQD) creation and wavefunction mapping technique, quantum scars are imaged for Dirac electrons with nanometer spatial resolution and meV energy resolution with a scanning tunneling 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. By combining classical and quantum simulations, we demonstrate that the observed patterns correspond to two unstable POs that exist in our stadium-shaped GQD, thus proving they are both quantum scars. In addition to providing the first 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, chiral scars, and antiscarring.