# Local spectroscopies across the superconductor-insulator transition

## TL;DR

This study uses local spectroscopic measurements and Monte Carlo simulations to analyze quantum fluctuations across the superconductor-insulator transition, revealing spatially varying spectral and magnetic properties.

## Contribution

It introduces a detailed local analysis of quantum fluctuations across the SIT using simulations and connects findings to experimental techniques.

## Key findings

- Zero-energy spectral weight diminishes in insulating regions.
- Correlations between spectral weight and compressibility are observed.
- Quantum fluctuations influence local magnetic susceptibility across the transition.

## Abstract

We explore the manifestation of quantum fluctuations across the superconductor-insulator transition (SIT) in three different local measurements: the two-particle density of states $P(\mathbf{r},\omega)$, compressibility $\kappa(\mathbf{r})$, and diamagnetic susceptibility $\chi(\mathbf{r})$. We perform Monte Carlo simulations on the 2D quantum Josephson junction array model and present local maps of these quantities as the system is tuned across the SIT. $P(\mathbf{r},\omega)$, obtained using Maximum Entropy analytic continuation techniques, shows strongly diminished zero-energy spectral weight in nearly-insulating islands, that also correlate with regions of suppressed $\kappa(\mathbf{r})$. We investigate the signatures of quantum fluctuations in the evolution of $\kappa(\mathbf{r})$ and $\chi(\mathbf{r})$ across the SIT, distinct from thermal fluctuations. We discuss the experimental implications of our results for scanning Josephson spectroscopy, compressibility, and scanning SQUID measurements.