Lifshitz and excited-state quantum phase transitions in microwave Dirac billiards

We present experimental results for the density of states (DOS) of a superconducting microwave Dirac billiard which serves as an idealized model for the electronic properties of graphene. The DOS exhibits two sharp peaks which evolve into Van Hove singularities with increasing system size. They divide the band structure into regions governed by the relativistic Dirac equation and by the non