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^{4,5,6,7,8,9,10}. 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^15,16,17, chiral scars^18,19 and antiscarring²⁰.

The existence of strong trigonal warping around the K point for the low-energy electronic states in multilayer ($N\ge 2$) graphene films and graphite is well established. It is responsible for phenomena such as Lifshitz transitions and anisotropic ballistic transport. The absolute orientation of the trigonal warping with respect to the center of the Brillouin zone is, however, not agreed upon. Here, we use quasiparticle scattering experiments on a gated bilayer graphene/hexagonal boron nitride heterostructure to settle this disagreement. We compare Fourier transforms of scattering interference maps acquired at various energies away from the charge neutrality point with tight-binding-based joint density of states simulations. This comparison enables unambiguous determination of the trigonal warping orientation for bilayer graphene low-energy states. Our experimental technique is promising for quasidirectly studying fine features of the band structure of gated two-dimensional materials such as topological transitions, interlayer hybridization, and moiré minibands.

Electrostatically defined quantum dots (QDs) in Bernal stacked bilayer graphene (BLG) are a promising quantum information platform because of their long spin decoherence times, high sample quality, and tunability. Importantly, the shape of QD states determines the electron energy spectrum, the interactions between electrons, and the coupling of electrons to their environment, all of which are relevant for quantum information processing. Despite its importance, the shape of BLG QD states remains experimentally unexamined. Here we report direct visualization of BLG QD states by using a scanning tunneling microscope. Strikingly, we find these states exhibit a robust broken rotational symmetry. By using a numerical tight-binding model, we determine that the observed broken rotational symmetry can be attributed to low energy anisotropic bands. We then compare confined holes and electrons and demonstrate the influence of BLG’s nontrivial band topology. Our study distinguishes BLG QDs from prior QD platforms with trivial band topology.