Quasiparticle Screening near a Bosonic Superconductor-Insulator Transition Revealed by Magnetic Impurity Doping

Experiments show that the Cooper pair transport in the insulator phase that forms at thin film superconductor to insulator transitions (SIT) is simply activated. The activation energy $T_0$ depends on the microscopic factors that drive Cooper pair localization. To test proposed models, we investigated how a perturbation that weakens Cooper pair binding, magnetic impurity doping, and phase frustration affects $T_0$. The data show that $T_0$ decreases monotonically with doping in films tuned farther from the SIT and increases and peaks in films that are closer to the SIT critical point. The observations provide strong evidence that the bosonic SIT in thin films is a Mott transition driven by Coulomb interactions that are screened by virtual quasiparticle excitations. This dependence on underlying fermionic degrees of freedom distinguishes these SITs from those in microfabricated Josephson Junction arrays, cold atom systems, and likely in high temperature superconductors with nodes in their quasiparticle density of states.

Figure 1

(a) Sketch of experimental setup displaying side by side flat glass (REF) and AAO substrates positioned over the Sb, Bi, and Gd evaporation sources in a magnetic field $\mathbf{B}$ directed as shown. (b) Atomic force microscopy (AFM) image of AAO falsely colored to indicate the evaporation layers, substrate height variations and 100 nm period nanopore array. (c) Schematic phase diagram of temperature vs coupling constant, $\delta \sim R_N$ for a superconductor to Cooper pair insulator quantum phase transition. I and II refer to the films investigated. There is a critical point for each of the frustrations, $f=0$ and $1/2$. (d) Sheet resistance on a logarithmic scale versus inverse temperature for undoped films, I and II, at $f=0$ (solid lines) and $f=1/2$ (dashed lines).

Figure 2

Magnetic impurity doping response of resistance and activation energy. Left panels: Arrehenius plots of $R(T)$ at 3 Gd doping levels for both $f=0$ and $f=1/2$ for films I (a) and II (b). The numerical labels increase with Gd doping, where 0 represents no doping. The dashed lines give examples of linear fits that yield $T_0$ values. Right panels: Activation energy vs pairbreaking strength for films I (c) and II (d). The arrows indicate the pair breaking strengths corresponding to $R(T)$ in the left panels. The filled squares correspond to $f=0$ and open squares are $f=1/2$. The lines are guides to the eye. Inset: $\delta T_0=T_0^{f=1/2}-T_0^{f=0}$ as a function of doping induced pair breaking.

Figure 3

Comparison with Mott insulator transport model with virtual quasiparticle screening. Activation energy as a function of magnetic impurity doping calculated using Eq. (6) as described in the text. The red and blue lines correspond to films I and II, respectively, and the solid and dashed lines correspond to $f=0$ and $f=1/2$, respectively. The black dots give the measured $T_0$ at zero doping. Inset: Representation of the experimental results in Fig. 2 for films I and II with lines to guide the eye.