Microwave Spectroscopy Evidence of Superconducting Pairing in the Magnetic-Field-Induced Metallic State of InO$_x$ Films at Zero Temperature

TL;DR

This study uses microwave spectroscopy to reveal a superconducting metallic phase in InO$_x$ films under magnetic fields, showing a quantum phase transition from superconductor to metal, not insulator, with unique properties.

Contribution

It provides evidence that the superconductor-metal transition in 2D InO$_x$ films occurs at a field below the conventional critical field, redefining the quantum critical point.

Findings

Identification of a metallic phase with finite resistance and superconducting response.

The quantum critical point is at a field $B_{sm}$ below $B_{cross}$.

Superfluid stiffness vanishes at $B_{sm}$, indicating a true quantum critical point.

Abstract

We investigate the field tuned quantum phase transition in a 2D low-disorder amorphous InO$_x$ film in the frequency range of 0.05 to 16 GHz employing microwave spectroscopy. In the zero temperature limit, the AC data are consistent with a scenario where this transition is from a superconductor to a metal instead of a direct transition to an insulator. The intervening metallic phase is unusual with a small but finite resistance that is much smaller than the normal state sheet resistance at the lowest measured temperatures. Moreover, it exhibits a superconducting response on short length and time scales while global superconductivity is destroyed. We present evidence that the true quantum critical point of this 2D superconductor metal transition is located at a field $B_{sm}$ far below the conventionally defined critical field $B_{cross}$ where different isotherms of magnetoresistance cross each other. The superfluid stiffness in the low frequency limit and the superconducting fluctuation frequency from opposite sides of the transition both vanish at B $\approx B_{sm}$. The lack of evidence for finite-frequency superfluid stiffness surviving $B_{cross}$ signifies that $B_{cross}$ is a crossover above which superconducting fluctuations make a vanishing contribution to DC and AC measurements.