The Elusive High-Tc Superinductor

Ginzburg-Landau (GL) parameters formed the basis for Abrikosov discovery of the quantum vortex of a supercurrent in type-II superconductor with a normal core of size $\xi$, the superconductor coherence length and circulating supercurrent induced magnetic field diverging as $log(1/r)$ from the core with a decay length of the London penetration depth, $\lambda_L.$ In 1964, J. Pearl predicted the slowly decaying $(1/r^2)$ field around a vortex spreading out to Pearl length, $P_L=2\lambda_L^2/t$, in a superconductor film of thickness $t < \lambda_L$. However, his quintessential theory failed to predict the existence of giant kinetic inductance (GKI) that arises from the enlarged screening currents of the vortex. Here, we discover giant kinetic inductance in a $high-T_c$ metasurface due to the 1400% expansion of the vortex screening supercurrent from $\lambda_L$ to 14$\lambda_L$ in ultrathin film meta-atom of $\lambda_L/7$ thickness, which leads to the emergence of terahertz superinductance possessing quantum impedance exceeding the resistance quantum limit of $R_Q=h/(2e)^2 =6.47 k\Omega$ by 33%. Our discovery presents a new class of $high-T_c$ superconductor electronic, photonic, and quantum devices enabled through metasurface designed at the Pearl length scales, providing novel applications in quantum circuitry, metrology, and single photon kinetic inductance detectors.