Status and perspectives of experiments with superconducting microwave billiards on graphene
à 11h en salle C. Brot
We present experimental results on relativistic phenomena occuring in graphene obtained with Dirac billiards consisting of a photonic crystal enclosed in a microwave billiard. Here we use the analogy between the associated scalar Helmholtz equation and the Dirac equation, and the fact that the peculiar properties of graphene are solely due to the symmetry properties of its hexagonal lattice structure. We will present results on the spectral properties and length spectra of periodic orbits that were obtained in high precision experiments with superconducting Dirac billiards. Furthermore we determined the density of states with an unprecedented accuracy and investigated the effect of edge states on its features. It exhibits two sharp peaks at the frequencies of the van Hove singularities. There, a topological transition between the relativistic to the non-relativistc Schrödinger regime takes place which can be identified with a neck-disrupting Lifshitz and with an excited state quantum phase transition. The theoretical considerations are corroborated by experimental results on the features of the density of states. The talk will be terminated with an outlook on current and planned experimental and theoretical projects concerning relativistic phenomena and other peculiar properties of graphene.
*Supported by the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center SFB634.
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