Giant spatial Goos-Hänchen shift achieved in superconducting hyperbolic metamaterials with graphene

We have theoretically analyzed the enhancement and regulation of the Goos-Hänchen (GH) shift within hyperbolic metamaterials in the near-infrared band under low-temperature conditions. Given a fixed incident wavelength, photonic crystals constructed from graphene and superconductor present hyperbolic dispersion characteristics in the dispersion space by modulating the Fermi energy of graphene. Near the critical phase transition point from elliptic dispersion to hyperbolic dispersion, the phase of the reflection coefficient undergoes an abrupt alteration. Consequently, a remarkably large GH shift occurs precisely at the resonant state. A substantial GH shift can be effectively realized by regulating the layers of graphene, the thickness of the superconductor, and the temperature. The largest positive GH shift reaches up to 4000<i>λ</i> at <i>T</i> = 200 K. This research is anticipated to provide theoretical guidance for devising high-sensitivity temperature sensors based on the GH shift effect in hyperbolic materials within a low-temperature environment.