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 divi...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2013-09, Vol.88 (10), Article 104101
Main Authors: Dietz, B., Iachello, F., Miski-Oglu, M., Pietralla, N., Richter, A., von Smekal, L., Wambach, J.
Format: Article
Language:English
Subjects:
Band structure of solids
Condensed matter
Density of states
Excitation
Graphene
Microwaves
Phase transformations
Schroedinger equation
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Summary: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 nonrelativistic Schrodinger equation, respectively. We demonstrate that in the thermodynamic limit, 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 and identify a quasiorder parameter.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.88.104101