Chiral Quantum Scars In 2-D Massless Dirac Billiards

In this work, we shall directly solve the Dirac equation in a finite region confined by an infinite-mass potential, to investigate quantum chaos of Dirac fermion bil-liards. In particular, we develop a new semi-analytic, conformal-mapping based method to calculate an unprecedentedly large number of eigenenergies and eigen-states with high accuracy and identify a peculiar characteristics of quantum scars for relativistic fermion:due to a combined effect of chirality intrinsic and the ge-ometry of the underlying classical orbit, the massless Dirac fermions associated with odd times bounces return to the original values or acquire a 2π change only after circulating twice about a classical unstable periodic orbit. This result, on the one hand, will enrich the understanding of quantum confinement behavior of massless Dirac fermions, one of the fundamental issues in basic physics. On the other hand, it will have potetial applications in graphene or topological insulator-based nano-devices.