Dielectric properties on the insulating side of the superconductor-insulator transition

Abstract

Amorphous indium oxide is the prime example of strongly disordered superconductors showing a quantum phase transition at strong levels of disorder, where a disorder-driven superconductor-insulator transition (SIT) is found. While there are studies focusing on the superconducting side, the insulating side is much less explored because experimental means are lacking. In this work an experimental approach is presented, employing coplanar microwave resonators in GHz frequency range and down to mK-temperatures, giving access to dielectric properties and the finite-frequency conductivity of amorphous indium oxide as a function of temperature, frequency and disorder. It is found that depending on disorder, indium oxide has a large dielectric constant with a critical value of ~100, separating samples with and without localized Cooper-pairs. From scaling, the fractal nature of electronic eigenstates is inferred. Strong effects of a gap are found, giving direct evidence for a finite pairing pseudogap even in the insulating phase, perfectly matching fractal Anderson localization theory.