title: Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards.
abstract: A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.
authors.affiliation: School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China.
authors.forename: Pei
authors.initials: P
authors.lastname: Yu
authors.affiliation: School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China.
authors.forename: Zi-Yuan
authors.initials: ZY
authors.lastname: Li
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Hong-Ya
authors.initials: HY
authors.lastname: Xu
authors.affiliation: School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China.
authors.forename: Liang
authors.initials: L
authors.lastname: Huang
authors.affiliation: School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China.
authors.forename: Barbara
authors.initials: B
authors.lastname: Dietz
authors.affiliation: Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
authors.forename: Celso
authors.initials: C
authors.lastname: Grebogi
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.|Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.|Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai