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We demonstrate that high Tc superconductors exhibit hyperbolic metamaterialbehavior in the far infrared and THz frequency ranges. In the THz range thehyperbolic behavior occurs only in the normal state, while no propagating modesexist in the superconducting state. Wave equation, which describes propagationof extraordinary light inside a hyperbolic metamaterial exhibits 2+1dimensional Lorentz symmetry. The role of time in the corresponding effective3D Minkowski spacetime is played by the spatial coordinate alignedperpendicular to the copper oxide layers. Such superconductor-based hyperbolicmetamaterials exhibit a quantum phase transition at T=0, in which the effectiveMinkowski spacetime arise in the mixed state of the superconductor at somecritical value of external magnetic field. Nucleation of Minkowski spacetimeoccurs via formation of quantized Abrikosov vortices, so that these vorticesplay the role of effective Minkowski spacetime quanta.

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