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Quantum nucleation of effective Minkowski spacetime in hyperbolic metamaterials based on high Tc superconductors

We demonstrate that high Tc superconductors exhibit hyperbolic metamaterial behavior in the far infrared and THz frequency ranges. In the THz range the hyperbolic behavior occurs only in the normal state, while no propagating modes exist in the superconducting state. Wave equation, which describes propagation of extraordinary light inside a hyperbolic metamaterial exhibits 2+1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate aligned perpendicular to the copper oxide layers. Such superconductor-based hyperbolic metamaterials exhibit a quantum phase transition at T=0, in which the effective Minkowski spacetime arise in the mixed state of the superconductor at some critical value of external magnetic field. Nucleation of Minkowski spacetime occurs via formation of quantized Abrikosov vortices, so that these vortices play the role of effective Minkowski spacetime quanta.