Lifshitz and Excited State Quantum Phase Transitions in Microwave Dirac Billiards

TL;DR

This study experimentally investigates the density of states in a microwave Dirac billiard, revealing Lifshitz and excited state quantum phase transitions that mirror electronic properties of graphene and topological changes in the system.

Contribution

It provides the first experimental observation of Lifshitz and excited state quantum phase transitions in a microwave analog of graphene, highlighting finite-size scaling and topological transitions.

Findings

Observation of van Hove singularities evolving with system size

Identification of a topological Lifshitz transition in the thermodynamic limit

Detection of finite-size scaling and a quasi-order parameter for excited state transitions

Abstract

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 \emph{relativistic} Dirac equation and by the \emph{non-relativistic} Schr\"odinger 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 quasi-order parameter.