Chiral Scars in Chaotic Dirac Fermion Systems

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Chiral Scars in Chaotic Dirac Fermion Systems

Hongya Xu, Liang Huang, Ying-Cheng Lai, and Celso Grebogi

Phys. Rev. Lett. 110, 064102 – Published 5 February 2013

Abstract

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 $2 π$ 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.

Received 28 November 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.064102

Authors & Affiliations

Hongya Xu¹, Liang Huang^1,2,*, Ying-Cheng Lai^2,3,4,†, and Celso Grebogi^4,5,‡

¹Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
²School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
³Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
⁴Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
⁵Freiburg Institute for Advanced Studies, University of Freiburg, 79104 Freiburg, Germany