Properties of the eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry

Abstract

We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational C3 symmetry. Its band structure exhibits two Dirac points (DPs) that are separated by a nearly flat band. We present a procedure which we employed to identify eigenfrequencies and to separate the eigenstates according to their transformation properties under rotation by 2π3 into the three C3 subspaces. This allows us to verify previous numerical results of Ref.[W. Zhang and B. Dietz, Phys. Rev. B 104, 064310 (2021)], thus confirming that the properties of the eigenmodes coincide with those of artificial graphene around the lower DP, and are well described by a tight-binding model (TBM) for a honeycomb-kagome lattice of corresponding shape. Above all, we investigate properties of the wave-function components in terms of the fluctuation properties of the measured scattering matrix, which are numerically not accessible. They are compared to random-matrix theory predictions for quantum-chaotic scattering systems exhibiting extended or localized states in the interaction region, that is, the DB. Even in regions, where the wave functions are localized, the spectral properties coincide with those of typical quantum systems with chaotic classical counterpart.

Semi-Poisson Statistics in Relativistic Quantum Billiards with Shapes of Rectangles

“…Boundary conditions on the spinor components in a graphene billiard were formulated in [55][56][57]. We modeled rectangular, Africa-shaped and threefold-symmetric graphene billiards experimentally with flat superconducting microwave photonic crystals [58][59][60][61][62] and found agreement with the spectral properties of massive neutrino billiards only beyond a certain mass. In addition, theoretical studies of rectangular graphene quantum dots yielded deviations from those of massless neutrino billiards [63].…”