Quantum Scars in Microwave Dielectric Photonic Graphene Billiards

In the band structure of graphene, the dispersion relation is linear around a Dirac point at the corners of the Brillouin zone. The closed graphene system has proven to be the ideal model to investigate relativistic quantum chaos phenomena. The electromagnetic material photonic graphene (PG) and electronic graphene not only have the same structural symmetry, but also have the similar band structure. Thus, we consider a stadium shaped resonant cavity filled with PG to demonstrate the relativistic quantum chaos phenomenon by numerical simulation. It is interesting that the relativistic quantum scars not only are identified in the PG cavities, but also appear and disappear repeatedly. The wave vector difference between repetitive scars on the same orbit is analyzed and confirmed to follow the quantization rule. The exploration will not only demonstrate a visual simulation of relativistic quantum scars but also propose a physical system for observing valley-dependent relativistic quantum scars, which is helpful for further understanding of quantum chaos.