Chiral scars in chaotic Dirac fermion systems

Do relativistic quantum scars in classically chaotic systems possess unique features that are not shared by nonrelativistic quantum scars? We report a class of relativistic quantum scars in massless Dirac fermion systems whose phases return to the original values or acquire a 2π change only after circulating twice about some classical unstable periodic orbits. We name such scars chiral scars, the successful identification of which has been facilitated tremendously by our development of an analytic, conformal-mapping-based method to calculate an unprecedentedly large number of eigenstates with high accuracy. Our semiclassical theory indicates that the physical origin of chiral scars can be attributed to a combined effect of chirality intrinsic to massless Dirac fermions and the geometry of the underlying classical orbit.