Quantum topological transition in hyperbolic metamaterials based on high Tc superconductors

Hyperbolic metamaterials are known to exhibit a transition in the topology of the photon iso-frequency surface from a closed ellipsoid to an open hyperboloid, resulting in a considerable increase of the photonic density of states. This topological transition may also be described as a change of metric signature of the effective optical space. Here 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 photon modes exist in the superconducting state. Thus, a quantum topological transition may be observed for THz photons at zero temperature as a function of the external magnetic field, in which the effective Minkowski spacetime arises in the mixed state of the superconductor at some critical value of the external magnetic field. Nucleation of effective Minkowski spacetime occurs via the formation of quantized Abrikosov vortices.