B. Dietz, M. Miski-Oglu, N. Pietralla, A. Richter, L. von Smekal, J. Wambach, F. Iachello
We present experimental results for the density of states (DOS) of a superconducting microwave Dirac billiard. Such systems serve as models for the electronic properties of finite graphene sheets. The DOS exhibits two sharp peaks which evolve into van Hove singularities with increasing system size. These divide the Fermi surface into regions governed by the relativistic Dirac equation and by the non-relativistic Schr\"odinger equation, respectively. We demonstrate that there a topological transition appears as a neck-disrupting Lifshitz transition in the number susceptibility and as an excited state transition in the electronic excitations. Furthermore, we recover the finite-size scaling typical for excited state quantum phase transitions involving logarithmic divergences.
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http://arxiv.org/abs/1304.4764
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