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

TL;DR

This study experimentally investigates the eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry, confirming theoretical predictions and analyzing wave-function properties in relation to random-matrix theory.

Contribution

The paper provides experimental verification of eigenmode properties and wave-function analysis in a microwave Dirac billiard, aligning with numerical models and extending understanding of quantum chaos in such systems.

Findings

Eigenmodes match tight-binding model predictions.

Wave-function components show properties consistent with quantum chaos.

Spectral properties are similar to those of chaotic quantum systems.

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 60 degree 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.